Product Cost Estimation: Theoretical Development And Industrial Validation

Product and Manufacturing Cost Estimation: Theoretical Development and Industrial Validation

By

Adnan Niazi

This thesis is submitted to the Department of Mechanical Engineering, School of Physical Sciences and Engineering, King’s College London, University of London, for the Degree of Doctor of Philosophy.

1

To

My Mum and Dad My Wife and

My Children

2

Abstract

Product Cost Estimation (PCE) deals with predicting the cost of a product before it is manufactured. Due to market competitiveness, there is a need to predict product costs early and accurately. However, the available methods of cost estimation compromise accuracy in an attempt to deliver early results. Conversely, the accuracy can only be fully achieved once the design and process planning details are available by which time cost estimation will be too late. The main aim of the work is to develop a methodology for early and accurate estimation of a product’s cost without relying on design and process planning details.

The main contributions of the thesis are as follows. First, following a comprehensive literature review of the available techniques, an extensive hierarchical classification system is developed. The classification is based on categorizing the techniques into qualitative and quantitative with further subdivisions down to four levels. The developed system identifies that qualitative techniques deliver early results and quantitative techniques are known for accuracy. The review also identifies that overall accuracy greatly depends on accurate estimation of overheads. Secondly, based on the feedback from the review and the proposed classification system, a new method of overhead estimation based on separating time- and material-dependent overheads is developed with improved accuracy. Thirdly, a comprehensive mathematical model based on combining the attributes of early and accurate estimation from the qualitative and quantitative techniques is developed and called a Hybrid Model. The developed model is optimized through the introduction of the cost deviation indices. Fourthly, the deviation indices are modelled considering past product cost details, inflation and other deviations in order to predict future costs early and accurately without requiring product design and process planning details.

3

Abstract

The developed models are validated by industrial trials on two distinct global locations adding further towards understanding the implications of geographical locations on aspects of cost control.

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Table of Contents Abstract ........................................................................................................................ 3 Table of Contents.......................................................................................................... 5 List of Figures............................................................................................................. 11 List of Tables.............................................................................................................. 14 List of Notations ......................................................................................................... 16 List of Acronyms ........................................................................................................ 22 Acknowledgements..................................................................................................... 24 C hapt e r 1

Introduction ......................................................................................... 27

1.1

Overview..................................................................................................... 27

1.2

Problems identification................................................................................ 29

1.3

Aims and objectives .................................................................................... 33

1.4

Thesis structure ........................................................................................... 35

1.5

Conclusions................................................................................................. 38

C hapt e r 2

Background and Related Work ............................................................ 39

2.1

Introduction................................................................................................. 39

2.2

Manufacturing and cost control ................................................................... 41

2.3

Cost estimation............................................................................................ 45

2.4

Cost estimation in the early design stages .................................................... 47

2.5

Cost estimation for specific applications...................................................... 48

2.5.1

Cost estimation for a specific segment in a production cycle................ 49

2.5.2

Cost estimation for specific machining and manufacturing processes... 50

5

Table of Contents

2.5.3

Cost forecasting for specific parts and products ................................... 50

2.5.4

Cost estimation for generic systems ..................................................... 51

2.6

Conclusions................................................................................................. 53

C hapt e r 3

PCE Technique Classification System ................................................. 55

3.1

Introduction................................................................................................. 55

3.2

Development of hierarchical classification system (HCS)............................ 57

3.3

Intuitive cost estimation techniques ............................................................. 60

3.3.1

Case-based methodology ..................................................................... 60

3.3.2

Decision support systems (DSS) .......................................................... 63

Rule-based systems ......................................................................................... 65 Fuzzy logic approach....................................................................................... 68 Expert systems ................................................................................................ 69 3.4

Analogical cost estimation techniques ......................................................... 70

3.4.1

Regression analysis models.................................................................. 70

3.4.2

Back-propagation neural network (BPNN) models............................... 70

3.5

Parametric cost estimation techniques.......................................................... 71

3.6

Analytical cost estimation techniques .......................................................... 73

3.6.1

Operation based approach .................................................................... 73

3.6.2

Breakdown approach ........................................................................... 75

3.6.3

Tolerance-based cost models ............................................................... 76

3.6.4

Feature-based cost estimation .............................................................. 78

3.6.5

Activity-based costing (ABC) system .................................................. 79

3.7

Conclusions................................................................................................. 81

C hapt e r 4

MRO and TRO Estimation Methods .................................................... 87

4.1

Introduction................................................................................................. 87

4.2

Cost estimation methodology at the selected company................................. 91 6

Table of Contents

4.2.1

Material cost estimation ....................................................................... 92

4.2.2

Direct labour costs ............................................................................... 93

4.2.3

Overheads estimation........................................................................... 93

4.3

Proposed methodology for overheads estimation ......................................... 95

4.3.1

MRO estimation model........................................................................ 95

4.3.2

TRO estimation model......................................................................... 98

4.4

Model implementation and validation........................................................ 101

4.5

Conclusions............................................................................................... 112

C hapt e r 5

PCE Hybrid Model ............................................................................ 114

5.1

Introduction............................................................................................... 114

5.2

Product cost and modelling approach......................................................... 116

5.3

Direct cost elements .................................................................................. 122

5.3.1

Direct material costs .......................................................................... 123

5.3.2

Direct labour...................................................................................... 126

Labour units .................................................................................................. 128 Labour rate.................................................................................................... 130 5.4

Indirect cost elements ................................................................................ 132

5.4.1

Processing cost .................................................................................. 132

Processing units............................................................................................. 133 Processing rate .............................................................................................. 134 5.4.2

Material dependent cost ..................................................................... 135

5.4.3

Tooling cost....................................................................................... 136

Machine tool rate........................................................................................... 137 Labour tool rate............................................................................................. 138 5.4.4

Building space cost ............................................................................ 139

Building space rate........................................................................................ 140 7

Table of Contents

Manufacturing space ..................................................................................... 141 5.5

Production overheads ................................................................................ 142

5.6

Conclusions............................................................................................... 143

C hapt e r 6

Industrial Implementation and Analysis of the PCE Hybrid Model .... 145

6.1

Introduction............................................................................................... 145

6.2

HMI algorithm and the implementation methodology................................ 148

6.3

PCE at the company .................................................................................. 157

6.3.1

Information and details ...................................................................... 157

6.3.2

Material cost estimation ..................................................................... 160

6.3.3

Labour cost estimation....................................................................... 163

6.3.4

Overhead estimation .......................................................................... 165

6.4

Implementation of the PCE Hybrid Model................................................. 168

6.4.1

Material cost estimation ..................................................................... 169

6.4.2

Labour cost estimation....................................................................... 171

6.4.3

Processing cost estimation ................................................................. 173

6.4.4

MDC estimation ................................................................................ 175

6.4.5

Production overheads estimation........................................................ 177

6.5

Conclusions............................................................................................... 179

C hapt e r 7

Comparisons and Validation Analysis................................................ 181

7.1

Introduction............................................................................................... 181

7.2

Preparations for comparisons..................................................................... 183

7.2.1

Labour and machine cost estimation .................................................. 185

7.2.2

Material cost and factory expenses..................................................... 187

7.3

Comparison analysis for product cost ........................................................ 189

7.4

Comparison analysis for cumulative costs ................................................. 202

7.5

Comparison analysis for product and production overheads....................... 206 8

Table of Contents

7.6

Cost breakdown analysis ........................................................................... 212

7.7

Conclusions............................................................................................... 223

C hapt e r 8

Conclusions ....................................................................................... 225

8.1

Summary................................................................................................... 225

8.2

Contributions............................................................................................. 231

8.2.1

Development of a technique classification system.............................. 231

8.2.2

Development of a decision support model (DSM).............................. 231

8.2.3

Development of time- and material-based overhead estimation methodology...................................................................................... 232

8.2.4

Development of a PCE methodology for batch production................. 233

8.2.5

Development of cost deviation indices............................................... 234

8.2.6

Development of HMI algorithm and industrial implementation.......... 234

8.2.7

Comparison and validation ................................................................ 235

8.2.8

By – products..................................................................................... 235

8.3

Current Trends and Future Work ............................................................... 236

8.4

Concluding remarks .................................................................................. 239

Publications Arising from the PhD Study.................................................................. 241 References ................................................................................................................ 243 Appendix A

Bill of Material (BOM)...................................................................... 261

A.1

Introduction............................................................................................... 261

A.2

BOM for Hammer Drill ............................................................................. 262

Appendix B

Deviation Indices............................................................................... 274

B.1

Material cost deviation index..................................................................... 274

B.2

Labour cost deviation index....................................................................... 276

B.3

Processing cost deviation index ................................................................. 277

B.4

MDC deviation index ................................................................................ 277 9

Table of Contents

B.5

Tool cost deviation index........................................................................... 278

B.6

Building cost deviation index .................................................................... 279

B.7

PO deviation index .................................................................................... 279

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List of Figures Figure 1-1: Main area of research................................................................................ 29 Figure 2-1: Relationship between productivity and flexibility ..................................... 41 Figure 2-2: Flexibility and productivity of different manufacturing systems................ 44 Figure 3-1: PCE Preliminary Technique Classification................................................ 59 Figure 3-2: Flow Diagram of the Case-Based Approach for Cost Estimation............... 61 Figure 3-3: Decision support system approach to cost estimation ................................ 64 Figure 3-4 Cost Estimation Process Model Based On User Constraints ....................... 66 Figure 3-5: Classification of the PCE Techniques ....................................................... 84 Figure 3-6: Decision Support Model for cost estimation methodology selection.......... 86 Figure 4-1: Break down of Selling Price and Manufacturing costs .............................. 89 Figure 4-2: Cost estimation results for 25, 100, 200, 500 and 1000kVA transformers............................................................................................ 104 Figure 4-3: Cost element values in DT and PT .......................................................... 106 Figure 4-4: TRO and MRO values breakdown for DT and PT................................... 107 Figure 4-5: Cost trends in (a) DT and (b) PT............................................................. 109 Figure 4-6: Cost trends comparison in DT and PT..................................................... 110 Figure 5-1: Pictorial representation of the mathematical model for product cost estimation ............................................................................................... 119 Figure 5-2: Development of the Hybrid Model within the framework of the technique classification system ............................................................... 125 Figure 5-3: Types of work centres............................................................................. 126 Figure 6-1: PCE Hybrid Model implementation phase .............................................. 150

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List of Figures

Figure 6-2: Material cost estimation implementation process .................................... 151 Figure 6-3: Labour cost estimation implementation process ...................................... 153 Figure 6-4: Processing cost estimation implementation process................................. 154 Figure 6-5: MDC estimation implementation process................................................ 155 Figure 6-6: Manufacturing cost estimation implementation process .......................... 155 Figure 6-7: PO estimation implementation process ................................................... 156 Figure 7-1: The comparison of the actual costs against the estimated costs................ 190 Figure 7-2: Estimation error trends for the three methods (2003 – 2005) ................... 192 Figure 7-3: Percentage cost estimation variations from actual product costs. ............. 194 Figure 7-4: Estimation error trend across the product range....................................... 196 Figure 7-5: Error linearization for the results given by the company’s method .......... 198 Figure 7-6: Error linearization for the results given by the Jung’s method ................. 199 Figure 7-7: Error linearization for the results given by the Hybrid Model.................. 200 Figure 7-8: (a) Cumulative actual costs against total estimated values, (b) estimation errors for cumulative costs..................................................... 203 Figure 7-9: Optimization for the estimation accuracy achieved by the Hybrid Model against (a) the company’s method (b) the Jung’s model ............... 205 Figure 7-10: Estimation error trends for overheads using the three methods (2003 – 2005) ......................................................................................... 208 Figure 7-11: Overheads estimation analysis for the cumulative values ...................... 209 Figure 7-12: Optimization achieved for overhead estimation based on (a) the Company’s method (b) the Jung’s model ................................................ 211 Figure 7-13: Production cost (actual) break down analysis (2002 – 2005) presented in values and percentage ......................................................... 213 Figure 7-14: Production cost elements trends ............................................................ 214 Figure 7-15: (a) Production and manufacturing costs (b) elemental costs effect on production and manufacturing costs ................................................... 216

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List of Figures

Figure 7-16: Overheads break down analysis (2002 – 2005) presented in values and percentage........................................................................................ 217 Figure 7-17 Overhead elements trends (2002 – 2005) ............................................... 218 Figure 7-18: Production overheads breakdown (2002 – 2005)................................... 219 Figure 7-19: Production overhead elements trends analysis....................................... 220 Figure 7-20: Processing cost elements trends ............................................................ 221 Figure 7-21: MDC elements trends ........................................................................... 222 Figure A-1 Hammer drill .......................................................................................... 262 Figure A-2 Product structure (Hammer Drill)............................................................ 264 Figure A-3 Dismantled drill with assemblies and sub-assemblies.............................. 265 Figure A-4 Parts and components in product structure .............................................. 266 Figure A-5 Winding (Stator and rotor) and drive assembly ....................................... 266 Figure A-6 Driven assembly (with gear and shock absorber) and Drill/Hammer switch ..................................................................................................... 267 Figure A-7 Trigger assembly .................................................................................... 267

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List of Tables Table 2-1: Summary of the published literature references for various applications of PCE .................................................................................. 53 Table 3-1: The PCE techniques; key advantages, limitations and list of discussed references.................................................................................. 85 Table 4-1: MRO for power and distribution transformers (2003-2004)........................ 97 Table 4-2: Budgeted time related overhead rate calculation (2003-2004)..................... 99 Table 4-3: Summary of TRO rates, MRO percentage fractions and overhead rates for 4 years ...................................................................................... 100 Table 4-4: Cost estimation for 25kVA transformer.................................................... 102 Table 6-1: Industrial output values for the CMD (2002 – 2005) ............................... 158 Table 6-2: Product range at the SPSD ....................................................................... 159 Table 6-3: Yearly production quantities for the product range in the SPSD (2001 – 2005) and Actual unit product cost for the given product range (2002 – 2005)................................................................................ 160 Table 6-4: Actual material cost (Cumulative and per unit costs)................................ 161 Table 6-5: Estimated unit material costs for the given product range (2003 – 2005) ...................................................................................................... 162 Table 6-6: Aggregate labour rate calculation............................................................. 164 Table 6-7: Total man-hours and estimated labour costs (2003 – 2005) for the given product range ................................................................................ 165 Table 6-8: Overhead costs for individual elements (2001 – 2005) ............................. 167 Table 6-9: Estimated product cost values (2003 – 2005)............................................ 168

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List of Tables

Table 6-10: Material cost deviation index and estimated unit material cost values (2003 – 2005) .............................................................................. 170 Table 6-11: Labour units calculation ......................................................................... 172 Table 6-12: Labour cost deviation index and estimated labour costs.......................... 173 Table 6-13: Estimation of processing units, deviation indices, rates and costs ........... 174 Table 6-14: MDC deviation index and estimated MDC per unit values ..................... 176 Table 6-15 PO fractions (actual & estimated) and deviation indices .......................... 177 Table 6-16: Estimated per unit values for manufacturing, PO and product costs........ 178 Table 7-1: Lead times, machine running costs, rates (operator and machine) and labour and machine costs.................................................................. 186 Table 7-2: The total factory expenses, the expenses rate, the estimated per unit values (factory expenses, product cost) (2003-2005)............................... 188 Table A-1 Hammer Drill (product level) 1.6 Kg........................................................ 268 Table A-2 Cumulative material quantities at the lowest level for the hammer drill......................................................................................................... 273

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List of Notations

The following is a list of the main symbols used for modelling in the thesis, together with their brief descriptions.

a

Total no. of broken or worn out labour tools in the ‘nth’ year

b

Total no. of broken or worn out machine tools in the ‘nth’ year

d

No. of time dependent cost elements

h

No. of building space cost elements

i

No. of machine centres

j

No. of work centres

mk

Amount of the kth material in product ‘p’

mn

amount of nth direct material

q

No. of overhead elements

r

No. of work centres routed by the ‘pth’ product

t ipn

Work time consumed by the ‘pth’ product at the ‘ith’ machine centre in the ‘nth’ year

t njp

Work time consumed by the ‘pth’ product at the ‘jth’ work centre in the ‘nth’ year.

tx

time spent by a skilled labour in the ‘jth’ work centre working on product ‘p’

ty

time spent by a semi-skilled labour in the ‘jth’ work centre working on product ‘p’

tz

time spent by a non-skilled labour in the ‘jth’ work centre working on product ‘p’

w

No. of material dependent cost elements

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List of Notations

x

No. of skilled labour working on product ‘p’ in the ‘jth’ work centre

y

No. of semi-skilled labour working on product ‘p’ in the ‘jth’ work centre

z

No. of non-skilled labour working on product ‘p’ in the ‘jth’ work centre

C dn

Total cost in the individual time dependent cost elements (such as utility cost, maintenance cost, repair cost, depreciation, insurance, tax etc.) for the ‘nth’ year

n −1 Cdmt

overall direct material costs in the (n-1)th year

Cdn

unit cost of the nth direct material

C nft−1

overall freight & transportation costs in the (n-1)th year

C hn

Total cost in the individual building space cost elements (such as plant depreciation, building insurance, maintenance, repair, tax, utilities etc.) for the ‘nth’ year

Cin −1

overall inspection costs in the (n-1)th year

Cimn −1

overall indirect material costs in the (n-1)th year

C kn

Unit cost of the kth material in product ‘p’ in the nth year

n C md

Total material dependent costs in the ‘nth’ year

n +1 C mdp

Estimated material dependent cost for the ‘pth’ product in the (n+1)th year

n C mp

Material cost for ‘pth’ product in the nth year

n +1 C mp

Material cost for ‘pth’ product in the (n+1)th year

n C mt

Cumulative material cost for ‘p’ products in the nth year.

n +1 C mt

Cumulative material cost for ‘p’ products in the (n+1)th year.

C pn +1

Estimated cost for the ‘pth’ product in the (n+1)th year

C Pn −1

overall purchase department costs in the (n-1)th year

C sin −1

overall stores & inventory costs

C tdn

Total time dependent costs in the ‘nth’ year

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List of Notations

n +1 Ctdp

Estimated processing cost for the ‘pth’ product in the (n+1)th year

n −1 Ctotal

total capacity in the (n-1)th year

C wn

Total cost in the individual material dependent cost elements (such a indirect material, purchasing cost, stores & inventory cost, freight & transportation cost, material inspection cost, packaging cost, quality cost, etc.) for the ‘nth’ year

n +1 C Bp

Estimated building cost for the ‘pth’ product in the (n+1)th year

C Btn

Total building space cost in the ‘nth’ year

n +1 C Ep

Estimated engineering cost for the ‘pth’ product in the (n+1)th year

n +1 CGp

Estimated manufacturing cost for the ‘pth’ product in the (n+1)th year

C Gtn

Total manufacturing cost in the ‘nth’ year

n C Lp

Direct labour cost for the ‘pth’ product in the nth year

n +1 C Lp

Estimated direct labour cost for the ‘pth’ product in the (n+1)th year

n C LT

Total labour tool cost for the ‘nth’ year

C Ltn

Total labour cost in the ‘nth’ year

C Ltn +1

Total estimated direct labour for the (n+1)th year

n C MT

Total machine tool cost for the ‘nth’ year

CTpn +1

Estimated tooling cost for the ‘pth’ product in the (n+1)th year

CTtn

Total tooling cost in the ‘nth’ year

Da

Total depreciation of the broken labour tool

Db

Total depreciation of the broken machine tool

D Ln

Total depreciation of the ‘Lth’ tool in the ‘nth’ year

DMn

Total depreciation of the ‘Mth’ tool in the ‘nth’ year

Gtjn

Total wages for ‘jth’ work centre in the ‘nth’ year,

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List of Notations

H qn

Total cost in the individual overhead elements (such as computer software cost, general administration cost, financing expenses, selling expenses etc.) for the ‘nth’ year

L

Total no. of useable labour tools in the ‘nth’ year

Lnjp

Labour units consumed by the ‘pth’ product at the ‘jth’ work centre in the ‘nth’ year.

M

Total no. of useable machine tools in the ‘nth’ year

M ipn

Processing units consumed by the ‘pth’ product at the ‘ith’ machine centre in the ‘nth’ year

MLT

manufacturing lead time

N pn

No. of units of ‘pth’ product produced in the nth year.

N pn +1

No. of units of ‘pth’ product produced in the (n+1)th year.

O nj

Occupied space by the ‘jth’ work centre in the ‘nth’ year

O pn +1

Estimated overheads for the ‘pth’ product in the (n+1)th year

Orpn +1

Space occupied by the ‘pth’ product at the ‘rth’ work centre in the (n+1)th year

Otn

Total overheads for the ‘nth’ year

OM

Material-related overhead for a new product in the nth year

OT

time-related overhead for a new product in the nth year

Pa

Initial purchase price of the broken labour tool

Pb

Initial purchase price of the broken machine tool

R Bn

Building space rate for the ‘nth’ year

RBn+1

Estimated building space rate for the (n+1)th year

n R LA

Actual labour rate for the ‘nth’ year;

n RLT

Labour tool rate for the ‘nth’ year

n +1 RLT

Estimated labour tool rate for the (n+1)th year

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List of Notations

n +1 RLE

Estimated labour rate for the (n+1)th year

n RMA

Actual processing rate for the ‘nth’ year

n +1 RME

Estimated processing rate for the (n+1)th year

n RMT

Machine tool rate for the ‘nth’ year

n +1 RMT

Estimated machine tool rate for the (n+1)th year

Sn

Total scrap value in the ‘nth’ year

S opn +1

Total space occupied by the ‘pth’ product in the (n+1)th year

S otn

Total space occupied by all work centres in the ‘nth’ year

S utn

Total unoccupied space on the manufacturing floor in the ‘nth’ year

n +1 S Gp

Total manufacturing space for the ‘pth’ product in the (n+1)th year

S Gtn

Total manufacturing space in the ‘nth’ year

n −1 TROtotal

total time-related overhead in the (n-1)th year

n U Lp

Labour units for ‘pth’ product in the ‘nth’ year

n +1 U Lp

Labour units for the ‘pth’ product in the (n+1)th year

U Ltn

Total labour units consumed in the ‘nth’ year.

U Ltn +1

Total labour units consumed in the (n+1)th year

n U Mp

Processing units consumed for ‘pth’ product in the nth year

n +1 U Mp

Processing units for the ‘pth’ product in the (n+1)th year

n U Mt

Total processing units consumed in the ‘nth’ year

α

skill index for semi-skilled labour (0.4
0.8)

β

skill index for non-skilled labour (0.25
0.4)

δ n+1

Building space cost deviation index in the (n+1)th year

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List of Notations

ε n +1

Labour cost deviation index in the (n+1)th year

φ n+1

Material cost deviation index in the (n+1)th year

ψ n +1

Machine tool cost deviation index in the (n+1)th year

ηi

Machine index (1.25
2.0)

µ n +1

Processing cost deviation index in the (n+1)th year

ρ n+1

MDC deviation index in the (n+1)th year

σ n +1

Labour tool cost deviation index in the (n+1)th year

τ n +1

PO deviation index in the (n+1)th year

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List of Acronyms

The following is a list of acronyms used in the thesis, together with their brief descriptions.

ABC

Activity based costing

ASSD

assembly & services sub-division

BCDI

building cost deviation index

BOM

bill of materials

BPNN

back-propagation neural network

CBR

case-based reasoning

CCS

cost control system

CIM

computer integrated manufacturing

CMD

crane manufacturing division

CMR

cumulative material requirements

CUI

cost uncertainty index

DFC

Design for cost

DSM

decision support model

DSS

decision support system

DT

distribution transformers

HCS

hierarchical classification system

HMI

Hybrid Model Implementation

ICSD

installation & commissioning sub-division

22

List of Acronyms

LCDI

labour cost deviation index

JIT

Just-in-time

LTCDI

labour tool cost deviation index

MCDI

material cost deviation index

MDC

material-dependent costs

MDCDI

material-dependent costs deviation index

MLT

manufacturing lead time

MRO

material related overheads

MRP

material requirement planning

MTCDI

machine tool cost deviation index

MTO

make-to-order

PCE

product cost estimation

PCDI

Processing cost deviation index

PO

production overheads

PODI

production overheads deviation index

PT

power transformers

QFD

Quality Function Deployment

SED

ship engineering division

SPSD

spares & parts sub-division

TRO

time related overheads

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Acknowledgements

Alhamdulillah, with the thesis finally in my hand, a long and hard struggle seems to have concluded with nothing less than a sweet reward. My efforts alone in treading this difficult journey from its very start would take me no where, had it not always been coupled with the explicit or implicit support of various people all along.

I would like to heartily acknowledge the never-ending support of Prof Jian Dai as not only my PhD Supervisor but as a kind and compassionate mentor. His valuable guidance in matters of both personal and professional grooming played a pivotal role. I would like to extend my special thankfulness to Dr Stavroula Balabani whose continued assistance in issues of academic and non-academic relevance has been instrumental to the overall success of the project. I would also like to acknowledge the support of Prof Lakmal Seneviratne as Head of the Division of Engineering, King’s College London. The active support and dedication of all these academics made the publication of two quality journal papers possible. The submission of another three papers in leading journals was also made easier with their continued support.

It is difficult to find words to pay gratitude to Dr Salim Habib’s generosity through Pakistan Scholarship without which my PhD simply would not have been achieved. His unceasing personal interest in my academic progress remained a revitalizing element

24

Acknowledgements

throughout my PhD studies. King’s College’s support through Principal’s Discretionary Fund during crucial stages of my PhD proved vital. Caroline Usher played an important part not only in liaising with Dr Habib but in guiding me towards the discretionary fund.

I would like to remember the support of Mr Muhammad Arif Hasan and Mr Saeed Iqbal in making the industrial visit to an Electrical Engineering Company in South Asia possible. I would also like to name Mr Peter Faccenda from Manufacturing Advisory Service UK for making the industrial visit in the UK possible by liaising with the Crane and Ship Engineering Company. I would have liked to name the companies involved that were central to the success of the project. I would acknowledge the support provided by both the companies that agreed to disclose very sensitive data crucial to their business competitiveness and equally vital to advance my research studies. Due to the confidentiality accord and understanding the need for their anonymity, I would like to thank all those namelessly who provided key information necessary for the research progress and its eventual completion. I would also like to acknowledge the positive feedback and interest from Professor Frank J Fabozzi of Yale School of Management (USA) for my first journal publication.

This uphill task simply would not have been possible without the support and care from a loving family like mine. My parents visited the UK twice from Pakistan during the course of my PhD to reassure their heartfelt love at times when I really needed it most. I would not be where I am now without the infinite love and guidance from my parents. My wife Uzma stood by all my judgements with an unwavering belief in my abilities at times when any uncertainty on her part would not be unreasonable. My daughters, Daanya and Iqra remained the inner strength for me. Last but not least, the support from 25

Acknowledgements

my brother, Kamran and my sister, Farhea peaked when they visited me from Pakistan during some of the very difficult times during my studies.

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Chapter 1

Introduction

This chapter outlines the scope of the thesis by giving an overview of the research area under study. Main problems are identified in the field and aims and objectives of the study are outlined. The chapter also outlines the structure of the thesis and ends with the conclusions.

1.1

Overview

Chapter 1 is an introductory chapter and is aimed at providing an overview of the research field; identifying main problems and setting the relevant aims and objectives for the research study.

The advent of information technology has brought with it an unprecedented era of globalization. The ever-increasing pressure on firms to stay competitive in such an environment is constantly forcing them to remain innovative in all aspects of their business. No wonder, not only products and services are increasingly customized to suit the end users’ needs but the required business tools are ever more novel. One of the key business tools is a pricing strategy that combined with market awareness not only allows an enterprise to remain competitive but thrive in the market.

27

Chapter 1: Introduction

A good pricing system rests on the application of cost engineering. The fundamentals of the former and the principles of the latter are not mutually exclusive. Cost estimating, cost control and profitability are the elements of cost engineering [1]. The American Association of Cost Engineers (AACE) defines cost engineering as “that area of engineering practice where engineering judgement and experience are utilized in the application of scientific principles and techniques to the problems of cost estimation, cost control, and profitability”.

Whereas market awareness can deal with the issues of profitability to some extent, maximizing profits comes down to better cost control. An effective cost control system (CCS) aims to reduce the gap between the budgeted and the actual costs. Setting the realistic budgets in turn is one of the functions of cost estimation. The ultimate responsibility of maximizing profits is, therefore, often closely linked with the provisions of accurate and timely cost estimates in order to facilitate key managerial decisions.

Cost estimating unlike cost accountancy requires sound engineering knowledge in order to deal with problems involving scientific principles and techniques. Cost estimation deals with predicting the cost of a product, project or a service. Product cost estimation (PCE) methodologies aim to predict product costs early and accurately before the actual production takes place and sometimes even before the design cycle. The scope of the thesis is PCE with specific focus on manufacturing costs. Figure 1-1 highlights the area of research followed in the thesis.

28

Chapter 1: Introduction

Area of research

Applied Cost Engineering Cost Estimation

Project Cost Estimation Service Cost Estimation

Cost Control Profitability

Product Cost Estimation

Figure 1-1: Main area of research

1.2

Problems identification

There are a number of issues in the area of PCE that need investigation. Following is the brief outline of some of the problems that form the basis of the research study:

•

A vast number of estimation techniques are available but no classification system available

•

Difficulty in selecting an estimation methodology for a given condition

•

Early estimation and accuracy are counter to each other

•

Available methodologies mostly estimate only part or component costs not the entire product cost

•

Most of the methodologies that can predict the entire product cost, fall short of predicting accurately the costs breakdown 29

Chapter 1: Introduction

•

One of the breakdown elements is overhead (sometime referred to as indirect costs) that is difficult to predict accurately for individual products

A vast number of methods and techniques have been developed over a period of time to facilitate estimators and designers to predict a product’s cost. However, they differ in applications in terms of compatibility to the needs of a system, delivering optimized results in given conditions and the level of resource consumption. A great number of methods, on the other hand, share common grounds. Estimators often find it difficult to select a methodology to suit the needs of a system under consideration. This is normally because an in depth analysis of a specific methodology to check its compatibility with an organizational framework is often time-consuming let alone analyzing more than one techniques. The selection of a particular methodology is normally based on the availability of data, level of accuracy and the stage of estimates required. A better exploitation of the differences and similarities of the techniques could result in helping estimators to select a specific methodology to suit the needs of a system. The nonavailability of a classification system is a barrier to the notion. Such a system could also help in developing a decision support tool in order to help estimators of product costs to make decisions to select an estimation methodology to satisfy a system’s needs and make the best use of available resources.

The aim of estimating a product’s cost is not just predicting it accurately but as early as possible in order to facilitate key business policy decisions. Often a methodology selected for PCE in the early stages of a design cycle, does not furnish accurate enough results due to the non-availability of the design details. Historical data can overcome the problems to some extent but the requirement of extensive past results limits the use of

30

Chapter 1: Introduction

relevant techniques. Such techniques also fall short of predicting accurate results for new designs. Study of a product’s features could be helpful in such circumstances but not only require skilled estimators but mostly fall short of delivering early results due to the detailed designs required. The reliance of the existing methods on product design and process planning details could result in accurate estimation but often leads to unnecessary delays. On the other hand, the uses of past experience, data or knowledge do have the potential to deliver early estimates but compromise accuracy. Such discussion is elaborated with necessary references in detail in chapter 3. Due to the significance of an early and accurate estimation process, it is important that a correct technique is employed within a specific set of conditions. However, most of the available techniques make a compromise between early estimation and accurate results.

Most of the available techniques predict part or component costs instead of an entire product’s cost using certain design parameters (such as design features, dimensions, tolerances etc.) and manufacturing operation times. The individual components’ costs add up to an entire product’s cost along with considering any process planning details for assembly operations based on standard techniques, historical data or time and motion studies etc. The process is time and resource consuming. A methodology aiming to predict an entire product’s cost by not relying on details like product designs or process planning details could be the answer. However, an alternative to such details would have to be found.

A more traditional approach can predict the entire product cost based on allocating the factory-wide resources to individual products. Such a method divides the entire product costs into direct and indirect costs. Direct costs refer to direct material and labour 31

Chapter 1: Introduction

consumed for the benefit of the product whereas, indirect costs, also referred to as overheads, are incurred for the shared benefit of all the products. The method obtains material and labour costs either from past data for the existing products or uses design and process planning details to calculate for the new products. However, using such details for a new product design could not allow the method to predict costs early. The method allows the allocation of the third cost element, overheads, to individual products by considering their lead times and an aggregate overhead rate. However, again not only the similar problem arises for any new products but the use of the aggregate rate results in less accurate estimates.

Another problem with using the traditional method is its breakdown of the entire product cost into only three elements (i.e. material, labour, overheads) resulting in overlooking possible areas of optimization for cost control. In a production environment where a product is the result of a mix of activities, the degree of consumption of these activities is reflected in a product’s cost. However, in such an environment, finding the costs incurred on individual breakdown elements and sub-elements is difficult, especially for overheads. The early and accurate estimation of this element and its subelements is crucial to the overall accuracy of a product’s cost. Predicting such costs beforehand requires much more than just accountancy laws. The early and accurate estimation of the individual elements and sub-elements costs could provide effective cost control opportunities.

32

Chapter 1: Introduction

1.3

Aims and objectives

The set of identified problems in the area of PCE is helpful in establishing an outlook within which the aims and objectives for the overall research work can be set. The individual problems identified would help to establish the objectives for the research work in order to find or attempt to find pragmatic solutions. The overall aim of the work, however, is to make a genuine and significant contribution to the area of cost engineering in general and to PCE in particular.

Following is the list of the objectives set for the research study: 1.

Development of a technique classification system

2.

Development of a decision support model (DSM) to allow estimators and designers to select an estimation methodology in given conditions

3.

Development of an overhead estimation methodology

4.

Development of a PCE methodology with cost deviation indices for early and accurate estimation of a product’s cost with its elements’ costs

5.

Industrial implementation of the developed cost estimation technique

6.

Comparison analysis for the validation of the developed model

A comprehensive review of the available cost estimation techniques could help to identify the similarities and the differences between them. A careful analysis of their advantages and limitations could be useful in grouping them. This in turn would allow the development of a technique classification system. Such a system would also lead the way to establish conditions under which designers and estimators make decisions to select a specific methodology. A DSM can, therefore, be developed too. 33

Chapter 1: Introduction

The development of a PCE methodology for early and accurate estimation of a product’s cost would require a thorough analysis of the existing methods. One of the problems of the existing methods is their reliance on product designs and process planning details. The developed method should aim at eliminating or reducing the need of such details. This can be achieved by making use of the past production details in order to predict the estimates for the future production. However, if a precedent is not available, the use of such technique can be limited. Such a limitation can be overcome by making use of past design cases resulting in a case-based framework. One of the objectives of the study would, therefore, be to develop a case-based framework in order to facilitate effective utilization of past details for early and accurate estimation of product costs.

The determination of an entire product’s cost instead of only part and component costs would require evaluating any existing methodologies that can predict such costs. The areas of improvement in those methods will be identified. One of the areas, for example, is overhead estimation that leads to inaccurate estimation of an entire product’s cost. Another objective of the study, therefore, would be to identify problems with the existing method of overhead estimation and develop an improved methodology. The effect of the proposed methodology on the overall estimation of a product’s cost will then be studied. An indication of improved overhead estimation results would pave a way for modelling an entire product’s cost with its breakdown elements.

Finding pragmatic solutions would require industrial implementation, comparisons and validation to back up any theoretical advancement in the field. One of the objectives of the research would, therefore, be to validate the proposed mathematical models from 34

Chapter 1: Introduction

industrial applications. The aim of the study is, therefore, to make theoretical advancement in the area of PCE and present industrial validation analysis.

1.4

Thesis structure

The overall research work is detailed in the thesis with the aim of disseminating not just the research findings but knowledge in the area of PCE. A logical sequence is maintained in presenting the work throughout the thesis starting from general concepts and literature review to methodology development, implementation, application and validation. The work comprises eight chapters in all.

Chapter two uncovers the background and related work in the area of cost estimation. The concepts of costs and costing are outlined. Price and pricing are briefly described. Cost estimation is defined and discussed with a special focus on manufacturing and cost control. Manufacturing systems are discussed with a view of selecting a suitable system to develop a methodology for. The functions of cost estimation are outlined and its significance in the early stages of a design cycle is highlighted. A comprehensive literature review in the area of cost estimation with special emphasis on its specific applications is also presented in this chapter. The chapter identifies a batch manufacturing environment as a potential area to develop a cost estimation methodology for.

Chapter three establishes comprehensive theories in the area of PCE. Existing technique classification systems are briefly discussed before developing a comprehensive

35

Chapter 1: Introduction

classification system for the available techniques in the area. The literature for each category is comprehensively reviewed along the course with the identification of strengths and weaknesses for the individual methods. The underlying principles for the categories are mentioned and the conditions for selecting a method from each one of them are set out. Establishing such conditions helped to develop a DSM for methodology selection. The chapter also presents a framework for the case-based methodology. A useful summary of the reviewed work and the key advantages and limitations for the proposed categories is then presented in the end. The chapter identifies that a hybrid approach combining the elements of qualitative and quantitative techniques could result in early and accurate estimation of a product’s cost.

Chapter four forms part of the methodology development for PCE. It considers a representative case of the existing method for overhead estimation. Problem identification leads to the development of a new overhead estimation methodology based on material– and time– dependent overheads. The effects of the proposed methodology on the estimation results for the overall product costs are analysed retrospectively for a four year period. The industrial validation analysis results reveal the superiority of the proposed methodology. However, the room for further improvement in the proposed methodology are also identified. The chapter also reveals cost elements breakdown statistics typical of the South Asian region and help to understand the implications of geographical locations on the effectiveness of a CCS.

Chapter five is a step forward in the development of a comprehensive methodology for PCE in a batch type manufacturing environment. The concept of overhead estimation proposed in the preceding chapter is carried forward to develop comprehensive 36

Chapter 1: Introduction

mathematical models for estimating an entire product’s cost in a batch type manufacturing environment. The developed model is hybrid in nature based on a cost breakdown structure and the concepts of modified activity-based costing (ABC) system. The proposed methodology is based on an effective utilization of past data to predict future costs facilitated by incorporation of cost deviation indices.

Chapter six is based on the industrial implementation and application of the proposed Hybrid Model in a batch type manufacturing environment in the UK. The chapter is a step towards the overall validation of the developed Hybrid Model. In order to facilitate the industrial implementation of the proposed model, an implementation algorithm is developed and the already proposed indices from the preceding chapter are modelled. The developed model is then implemented retrospectively in a crane and ship engineering company based in the UK. The implementation process generates the cost estimates for a given product range. The company’s own method of cost estimation is also described and is used to generate cost results for further comparison analysis.

Chapter seven presents the comparisons and validation analysis of the Hybrid Model. The developed model is compared against a published model and the company’s own method as the representative cases from the two domains. A carefully selected published model is used to furnish cost estimates. Comparison analysis includes comparing the estimated costs obtained from the three methods against the actual costs. The developed model is validated based on generating more accurate and more consistent results as opposed to both the company’s own method and the published model. The chapter also reveals cost elements breakdown statistics typical for the UK.

37

Chapter 1: Introduction

Chapter eight concludes the research work and the thesis. The overall contents in general and the research work in particular are summarized. The main achievements of the work are highlighted and the success of the research study is evaluated. This involves a comparison of the achievements against the planned aims and objectives. The work is also evaluated for the originality and its contribution. The areas for possible improvements in the research work are pointed out with a focus on the existing limitations. The chapter also discusses the current and future research trends in the field. Finally, the possible avenues for future research directions in the established research work are highlighted with a view of providing a platform for any further research in the area.

1.5

Conclusions

This chapter presented the scope of the research work. An overview of the research area focussed on the importance of cost estimation for cost control. Some of the problems were outlined and discussed briefly in order to establish the likely aims and objectives for the study. Aims and objectives were set with the view of furnishing solutions to the outlined problems and establishing a significant theoretical development in the area. Finally, the overall structure of the thesis was outlined with the aim of translating the objectives in logical order in different chapters.

38

Chapter 2

Background and Related Work

The aim of Chapter 2 is to develop background information in the area of cost estimation. The concepts of cost and costing are established. Manufacturing systems with a focus on CCS are discussed. Cost estimation as a key component of CCS is then discussed. Various application areas for cost estimation techniques are discussed with a comprehensive literature review in the area. The rationale for developing a cost estimation methodology in a batch type manufacturing environment is established. The chapter ends with conclusions.

2.1

Introduction

Chapter 2 deals with background information in the chosen area of study and provides a comprehensive literature review in the area with a focus on cost estimation techniques applications.

Our day to day lives are full of instances of buying and selling goods and services. The amount paid to buy a commodity reflects the incurred cost from a buyer’s perspective. The same amount is perceived a selling price from the seller’s view point. The commodity may be resold with a higher amount making a profit. Cost can therefore, be defined as: 39

Chapter 2: Background and Related Work

“The amount of money paid or required as a payment to buy a goods or service”

The original commodity may often be altered or modified before being resold and is said to have been added with a value. The value addition process thus incurs further costs. The incurred costs could be the result of tangible and/or intangible values. The process of determination of the final cost of the modified commodity before being resold is referred to as costing.

Costing determines selling price. Setting prices in turn is called ‘pricing’. As costing normally refers to considering all the costs already incurred for a commodity, any unexpected costs at the beginning of the value addition process are discovered and accounted for. For the same reason, however, its role is normally limited to pricing and price adjustments. Cost control may, therefore, not be its domain.

Since selling price is one of the major factors of gaining competitive advantage in the consumer market, cost control can not be ignored. Cost accounting also known as management accounting could provide solutions to cost control by recording cost values and providing opportunities to minimize them in future.

Operational matters requiring aspects of cost control within the framework of a project execution, service delivery or manufacturing set up may be different. The aspects relating to manufacturing environment come under the scope of the current study.

40

Chapter 2: Background and Related Work

2.2

Manufacturing and cost control

Manufacturing involves converting materials from one form to another by adding value to them. This often requires a series of specific treatments or processes to be carried out on different materials. These processes accomplish the desired final product form and shape specified by a design engineer prior to actual manufacturing. Selection of a particular process among various alternatives is closely linked with many factors including the associated costs. Incorporating certain features (from available alternatives into a product design) that require costly processes is often a result of poor product design. Therefore, the final product cost reflects the design quality and also determines selling price. The latter is also governed by consumer demand and is crucial in gaining competitive advantage. Maximizing profits (while remaining competitive in the market) requires an effective CCS alongside keeping high quality standards. An effective CCS monitors various aspects of the final product cost.

Productivity (P)

P Increasing product variety

Increasing production volume

F

Flexibility (F)

Figure 2-1: Relationship between productivity and flexibility

41

Chapter 2: Background and Related Work

In a manufacturing environment, where high volumes of products are produced without making many changeovers in production setup, the aspects of cost control are a routine task. The effectiveness of a CCS, however, is more strongly required within a manufacturing setup of routine changeovers in production setup.

The ability to

changeover to a new production setup economically and quickly to produce new products in response to market or engineering changes is called Product Flexibility. For example, the automobile industries are subject to tough competitions and in order to remain competitive, develop different car models and introduce them at shorter intervals. On the other hand, Productivity is a measure of the extent to which the resources of an organization are consumed effectively in transforming inputs to outputs. The overall productivity of a firm is greatly influenced by flexibility. The productivity of a manufacturing system remains in conflict with flexibility where increasing productivity compromises the system’s flexibility. The relationship is elaborated in Figure 2-1 between flexibility and productivity. An increased flexibility of a manufacturing system demands higher changeover time thereby reducing its productivity. Increased productivity also refers to higher production volumes whereas; an increased flexibility is a reflection of an increased product variety.

Business goals for a manufacturing enterprise are set within the framework of the organizational corporate planning structure. Strategic planning framework in return ensures that a manufacturing system be in place in order to achieve those objectives. For example, the level of flexibility and productivity required to achieve business objectives would need a specific set up for a manufacturing system. High production volumes and low flexibility are the attributes for mass production and can be achieved by setting up transfer lines. Such systems make use of automated assembly lines using industrial 42

Chapter 2: Background and Related Work

robots etc. The investment needed for such a manufacturing set up is high. However, both labour skills and labour costs are relatively low. Small production quantities with a high flexibility, on the other hand, can be achieved by conventional job shops. However, the level of skill required to operate general-purpose machines in such a set up is high. Since the production rate is low, the unit cost in job shops is usually high. Conventional flow line, flexible manufacturing system, manufacturing cells, numeric control systems etc. can be effective in achieving a desired combination of flexibility and productivity and normally result in batch production. As a result multi-skilled labour (low, medium, high) is generally employed to handle tasks for varied levels of flexibility and productivity. Small to medium size batches can be produced on machines ranging from general-purpose with computer controls to equipment with specifically designed fixtures and tools. Figure 2-2 elaborates various levels of productivity and flexibility achievable through different manufacturing systems. The overlap between the systems is due to the various levels of technical attributes (automation, computer control etc.) achievable in each system. Due to the impact of the changeovers on product costs, the need for an effective CCS in a batch manufacturing set up is wider in its scope. Job shop, although, highly flexible can be partly covered by batch production cost control strategies. Both mass production and a job shop system are, therefore, left with little scope for comprehensive CCS.

43

Increasing Productivity

Chapter 2: Background and Related Work

Transfer Line Mass Production

Batch Flow Line

Flexible Manufacturing System

Batch Production

Manufacturing Cell

NC Production

Job Shop System

Job Shop Production

Increasing Flexibility Figure 2-2: Flexibility and productivity of different manufacturing systems

Whether a manufacturing system is based on mass, batch or job shop production, an effective CCS makes sure at every stage of the execution process that the planned budget is adhered to. Accountancy laws are easier to apply once the plans are executed and actual costs are available. The aim is to minimize the difference between the planned budget and the actual costs. In a highly competitive business environment, any non-compliance to planned budgets could seriously jeopardize the accomplishment of an enterprise’s business objectives. Setting realistic budgets in turn is, therefore, also an important element of a CCS and requires accurate predictive tools. A carefully devised cost estimation methodology based on sound engineering principles serves as a reliable tool for predicting accurate costs likely to be incurred during an execution phase.

44

Chapter 2: Background and Related Work

2.3

Cost estimation

Cost estimation is the process of determining a combination of tangible & intangible values associated with the expected and unexpected cost occurrences linked with a set of activities prior to their execution. Accurate cost estimation is essential whether the end product is a project, manufactured goods, or a service. The cost estimated close to the accounting cost should serve as a valuable decision aid tool at the early stages of an execution plan.

Different cost estimation approaches have been developed to best suit the needs of end users or customers. One approach may require the evaluation of uncertainty as an intangible value associated with the loss of goodwill owing to delayed job completion, whereas another may necessitate the estimation of expected cost tied with the development or manufacture of a product. The use of risk assessment and uncertainty evaluation techniques is quite common in project proposals and bidding processes. PCE techniques, on the other hand, generally tend to consider the effect of expected cost occurrences.

Cost estimation affects certain organizational functions. The following is a list of functions or processes in a manufacturing company where cost estimation is involved. The list is not exhaustive but provides a good idea of the impact of cost estimation in the operational and corporate planning structure of an organization. The functions include:

•

deciding whether to produce in-house, purchase, or out-source; 45

Chapter 2: Background and Related Work

•

selecting material, manufacturing processes, and routings;

•

evaluating different design alternatives;

•

setting economic lot sizing for batch production;

•

assessing suppliers’ quotations as a trade-off between customer needs (quality) and available budget (cost);

•

quoting prices to customers before actual manufacturing starts;

•

allocating enterprise-wide resources (man, machinery, tooling, etc.) and budgeting to different technical attributes of a design in proportion to their desirability (extent of customer requirements);

•

manufacturing cost control and hence overall control of production cost.

Good cost estimation has a direct bearing on the performance and effectiveness of a business enterprise as overestimation can result in loss of business and goodwill in the market whereas underestimation may lead towards financial losses to the enterprise. Due to this sensitive and crucial role in an organization, cost estimation has been a focal point for design and operational strategies and a key agenda for managerial policies and business decisions. As a result, a substantial research effort has been expanded in exploring design implications, new techniques and methods for producing accurate and consistent cost estimates not only to generate optimum design solutions but also to achieve the maximum customer satisfaction in terms of low cost, high quality and intime product delivery.

46

Chapter 2: Background and Related Work

2.4

Cost estimation in the early design stages

The key to thrive for a manufacturing enterprise in the 21st century is based on product quality, competitive cost, fast delivery, and flexibility. On the other hand, factors like globalisation and mass customisation put an extra pressure to a business enterprise to survive and remain profitable at the same time. Whereas, an innovative approach and a new product development process may attempt to deal with issues such as flexibility and product quality, they may still be time consuming and less cost effective. In addition, the prospective end user of a would-be product often demands a price quote as soon as possible, sometimes even unconcerned and oblivious of factors such as the extent of the customisation, the nature of the data required and the design complexity. To make matters worse, often a manufacturer ignores the significant factors like design module availability, manufacturability and the level of accuracy required for processing time estimation. The overall situation, therefore, could either lead to an underestimation resulting in a profit loss and a blow to operational targets or a more profound strategic damage caused by overestimation leading towards the loss of customer goodwill and market share. All the above highlights the ever-increasing importance of devising methods to forecast the cost for a new product in the early design and development phases with accuracy.

Since most of the product costs sustained during later in the production life cycle are determined during the conceptual design phase [2], the cost estimation in the early phase of the design cycle is crucial. Many researchers have emphasized the importance of cost estimation at the early design stages when 70 to 80 percent of a total product cost is determined [3-6]. Some researchers have developed methodologies with a special

47

Chapter 2: Background and Related Work

emphasis on early cost estimation [7, 8]. A framework for developing a cost database was suggested by Sheldon et al. [9] and aimed to serve different groups of design for cost (DFC) system users to determine appropriate cost structures by analysing the information provided by a cost accounting system. Knowledge representation in such a way facilitated the generation of cost estimates at an early design stage. A framework to integrate design costs into Quality Function Deployment (QFD) was used by Bode and Fung [10]. The approach adopted is a helpful tool for designers at the early stages of product design for making trade-off decisions between quality and cost prioritising the attainment of technical attributes based on customer requirements. All the above mentioned highlights the significance of not only estimating a product cost accurately but as early as possible.

2.5

Cost estimation for specific applications

A number of cost estimation methods and techniques were developed with reference to particular applications. The techniques only suit the conditions for which they were tailored and can only be effective for their application areas. These techniques range from the evaluation of certain manufacturing and machining processes to the dedicated techniques designed to suit specific manufacturing systems, from composite material costing to the cost analysis of parts and assemblies and from dealing with specific segments in a production cost cycle to covering a product life cycle cost. The section is aimed at providing a comprehensive review of the available techniques for cost estimation with an emphasis on their application areas. This not only leads to develop better understanding of the application areas but could also be helpful in providing a

48

Chapter 2: Background and Related Work

platform for any future exploration within a specific application area of the cost estimation.

2.5.1

Cost estimation for a specific segment in a production cycle

Different costs are associated with various stages in a production cycle starting from the ones incurred during the early phases of a design cycle to those linked with the manufacture of an actual product on the shop floor. Many researchers devised methods to evaluate the costs associated with a specific segment in a production cycle. For example, if a methodology is applicable at the QFD stage [10] the other is developed for the costs associated with the design and development phase of a product [11]. Methods for process planning cost evaluation and optimization can also be found in [12-14]. Aldrich [15] estimated the cost associated with the bill of materials (BOM) using MRPII software. Cost calculation in manufacturing and machining can be found in [16]. Costs associated with conventional manufacturing processes [6], non-conventional manufacturing processes [17] and the machining accuracy [18] can also be found.

Some researchers developed methodologies that could be used for cost estimating in several stages of a product design cycle. For example, Weustink et al. [19] developed a framework for product cost control by estimating the various cost elements and storing the data in a generic way. The methodology allows cost estimation on different aggregation levels, e.g. feature level, component level, assembly level etc. Koonce et al. [20] developed a system capable of generating cost estimates in all phases of the design stage. The system, which was prototyped in JAVA, used simple parametric cost relations in the early stages of a design, when detailed design was not available to 49

Chapter 2: Background and Related Work

produce cost estimates for a product. When the design was developed, estimates could be produced using design features, manufacturing features or a process plan.

2.5.2

Cost estimation for specific machining and manufacturing processes

The selection of suitable manufacturing processes is governed by an accurate estimation of the costs associated with them among other factors. Methods have been devised to predict the costs of specific machining and manufacturing processes. These include the assembly costing techniques [21, 22] and the cost models for die-casting [23]. Further models were developed for a hole-making process [24], welding [25] and milling and drilling [26].

2.5.3

Cost forecasting for specific parts and products

Many researchers focussed on the application of the cost estimation techniques to specific products ranging from standard parts and components to a particular product group. Schreve et al. [27] presented a cost model using mild steel fabricated parts, whereas the one for machined components can be found in [28]. Hicks et al. [8] developed four cost modelling approaches for various classes of engineering components. These components were defined as standard selected, standard designed and bespoke designed. French [29] used a function cost modelling methodology to estimate the costs of mechanical components whereas Ulrich and Eppinger [30] used previous orders and procurement records to estimate the cost of similar components. Kendall et al. [31] presented cost information for automotive components using a 50

Chapter 2: Background and Related Work

simulation technique. Gutowski et al. [32] presented a process-oriented cost model to estimate manufacturing cost of advanced composite aerospace parts. Cost models for injection-moulded components can also be found in [33-35]. On the other hand, cost models for specific product groups include those for PCB manufacturing [36-38], developmental equipment [39], packaging products [40, 41], injection moulding tool [42] and gear drive manufacturing [6].

Another type of products covered by cost estimation techniques is based on composite material. For example, cost and consolidation model for commingled yarn based composites was presented in [43]. Process flow simulation techniques to evaluate manufacturing costs for composite products were discussed in [44]. Cost analysis of thermoplastic composites using different techniques can also be found in [45, 46], whereas Walls and Crawford [47] used historical data to produce cost information for continuous fibre-reinforced thermoplastic products.

2.5.4

Cost estimation for generic systems

Cost estimation models to suit the needs of a generic system were also developed by many researchers. For example, cost models for job shop manufacturing systems can be found in [48, 49]. On the other hand, a mathematical and simulation model to estimate the manufacturing and product cost in material requirement planning (MRP) and just-intime (JIT) systems was proposed in [50]. Similarly, a simulation model to estimate the cost in a flexible manufacturing environment was proposed in [51], whereas the one for cellular manufacturing configuration was proposed in [52].

51

Chapter 2: Background and Related Work

Cost estimation techniques were further developed for specific industry sectors [53]. For instance, work has been carried out for airplane manufacturing industries [54], electronics industries [55], automotive industries [56], aerospace and defence industries [57], telecommunications [58], and ship building industries [59].

Table 2-1 summarizes the discussed literature references for various applications of PCE. It is clear that the techniques have been designed to suit the conditions for a given application area and may not be suitable for any other applications. For example, a methodology designed to predict machining costs may not be applicable for other areas of manufacturing due to the differences in the requirements of the parameters for the two conditions. There is, thus, a need to develop a method that can cover a number of application areas without compromising accuracy yet furnishing estimates in the early stages of a design cycle or even before. Such a system could eliminate or minimize the need for a methodology selection under varying conditions. The techniques designed to work for a specific generic system usually do not have the limitations for other application areas. For example, a methodology developed for a job shop system, although, may not be suitable to work in a batch manufacturing environment but can provide estimates for manufacturing parts and be applicable in the different phases of a design cycle. Maximizing the application areas for a methodology could, therefore, be achieved by originating it from the applications for generic systems. In other words, if an estimation methodology is designed to suit the needs of a generic system, it could work well for the other application areas.

52

Chapter 2: Background and Related Work

Table 2-1: Summary of the published literature references for various applications of PCE

S. No. Application area

References

1.

Cost estimation for a specific segment in a production cycle

[6], [10-20]

2.

Cost estimation for specific machining and manufacturing processes

[21-26], [75-79]

3.

Cost estimation for specific parts and products

4.

Cost estimation for generic systems

Parts and components

[8], [27-35]

Special products

[6], [36-42]

Composite material products

[43-47]

Specific manufacturing system

[48-52]

Specific industrial sector

[53-59]

It was already established in Section 2.2 that the scope of a batch manufacturing system is wider in terms of not just encompassing a range of manufacturing set ups but for a realistic need of a CCS. The effectiveness of such a CCS was then linked with the effectiveness of a cost estimation methodology. Now, that the need to develop a cost estimation methodology for a generic system is evident from the view point of maximizing the application areas already mentioned, the only manufacturing system left for exploring the possibilities for a methodology development is a batch type environment.

2.6

Conclusions

This chapter presented a comprehensive survey of literature in the area of cost estimation in order to establish a background in the research area and to develop an 53

Chapter 2: Background and Related Work

understanding of the problems. The techniques used for cost estimation in various application areas were investigated.

The chapter started with defining basic concepts of cost and costing. Manufacturing systems were discussed with cost control implications. Flexibility and productivity were discussed and their relationship was detailed. It was noted that various combinations of production volumes and product varieties resulted in three main categories of manufacturing environment: mass, batch and job shop production. It was found that batch production environment demanded an effective CCS and was suggested as a desirable area for developing an estimation technique. Cost estimation, its functions and the significance of early estimation were discussed.

A comprehensive literature review with a focus on four main application areas was presented. Techniques from each application area were thoroughly analysed. They included techniques for specific segment in a production cycle, techniques for specific machining and manufacturing processes, techniques for specific parts and products and finally the techniques for generic systems. It was noted that techniques developed for generic systems did have the potential to fulfil the demands of the other application areas. In order to maximize the scope of an estimation methodology, it was deemed necessary to develop a technique for a generic system. Batch manufacturing environment was considered as a viable generic system for which a cost estimation technique could be developed. Finally, the published literature references mentioned for various applications of cost estimation were summarized for any useful research in future.

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Chapter 3 provides a technique classification system based on the state of the art on product cost estimation. PCE techniques are classified to form an extensive hierarchical classification system. The developed classification system is further used to form a decision support system for methodology selection. A case-based model is also developed for effective utilization of past product details. Key advantages and limitations of the techniques are discussed along the course. The chapter concludes with the suggestion of developing a methodology for cost estimation based on combining concepts from both qualitative and quantitative techniques for early and accurate estimation of a product’s cost.

3.1

Introduction

Product cost estimation refers to predicting all the costs associated with manufacturing a product from raw material to a finished product. Accurate product cost estimates are important in establishing a good CCS and help in setting competitive price plans. The role of PCE is, therefore, to predict the overall product cost likely to be incurred throughout the

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entire production phase. The accuracy of the predicted costs will determine the effectiveness of the technique employed and, combined with the information access, can help the entire production enterprise achieve its corporate goals. It, therefore, not only serves operational matters (such as cost control, resource allocation, price setting etc.) but is also deemed as a key component for strategic production planning and control system.

The published literature on PCE covers a wide variety of issues ranging from manufacturing cost estimation of standard mechanical components to cost analysis of highly customized assembled products, from process cost optimisation techniques to specific methods for overhead costing, from unique approaches for estimation at the conceptual design stage to general costing rules designed for use at a later stage in the design cycle and also from classical costing methods to highly novel cost estimation techniques. Several textbooks [60-62] can be found on some of the subjects.

Due to the significance of the cost estimation process in the organizational structure of an enterprise, the influence of an effective estimation methodology can not be underestimated. On the contrary, the availability of an extensive range of estimation techniques makes the selection of an appropriate methodology to suit the prevailing conditions a daunting task. The classification of these techniques based on certain criteria is a step towards overcoming the issue. A number of researchers have attempted to categorize the PCE techniques using certain criteria. Zhang et al. [40] categorized some techniques into traditional detailedbreakdown, simplified breakdown, group-technology based, regression-based and activitybased cost estimation techniques. Ben-Arieh and Qian [11] classified cost estimation 56

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methods into intuitive, analogical, parametric and analytical methods. Shehab and Abdalla [63] mentioned intuitive, parametric, variant-based and generative cost estimating approaches without defining them clearly. The same authors [64] later classified cost modelling approaches at the design stage into knowledge based, feature based, function based, and operations based approaches. Cavalieri et al. [2] identified three approaches for cost estimation: analogy-based, parametric and engineering approaches. However, a comprehensive hierarchical classification of the estimation techniques has not been exploited.

3.2

Development of hierarchical classification system (HCS)

The availability of a wide range of PCE techniques demands an extensive classification system in order to facilitate the selection of a suitable methodology for a given condition. The existing classifications fall short of furnishing a complete framework for methodology selection. These classifications group together the techniques with similarities in separate categories but do not consider the differences within the respective groups. Filtering a methodology is, therefore, constrained. The development of HCS is aimed at providing a framework for not only classifying the PCE methodologies but facilitating their selection to suit different problems. The developed system comprising an extensive hierarchical classification is based on grouping the techniques with similar features into various categories. The methodologies discussed in different categories are distinct and reflect the nature of that category. An effort is also made to elaborate each group or category with

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reference to published work. Meanwhile, mathematical models are presented on occasions with particular references in order to better understand the nature of a given category. The hierarchical classification expands due to the identification of the variations within a group. The PCE techniques are broadly classified into qualitative and quantitative techniques followed by an extensive sub-classification.

Qualitative cost estimation techniques are primarily based upon a comparison analysis of a new product with the products that have been manufactured previously in order to identify the similarities in the new one. The identified similarities help to incorporate the past data into the new product so that the needs to obtain the cost estimate from scratch are greatly reduced. In that sense the past design and manufacturing data or previous experience of an estimator can provide a useful help to generate reliable cost estimates for a new product which is similar to a past design case. Sometimes, this can be achieved by making use of the past design and manufacturing knowledge encapsulated in a system based on rules or decision trees etc. Historical design and manufacturing data for products with known costs may also be used systematically to obtain cost estimates for new products. For example, regression analysis models and neural network approaches could provide an efficient way to predict costs for new products by using historical cost data. In general, qualitative techniques help obtain rough estimates during the design conceptualisation. These techniques can further be categorised into Intuitive and Analogical Techniques, which are discussed in detail in Sections 3.3 and 3.4 respectively.

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Quantitative techniques, on the other hand, are based on a detailed analysis of a product design, its features and corresponding manufacturing processes instead of simply relying on the past data or knowledge of an estimator. Costs are, therefore, either calculated using an analytical function of certain variables representing different product parameters or as the sum of elementary units representing different resources consumed during a whole production cycle of a given product. Although, these techniques are known to provide more accurate results, their use is normally restricted to the final phases in the design cycle due to the requirement of a detailed product design. Quantitative techniques can be further categorised into Parametric and Analytical Techniques, which are discussed in detail in Sections 3.5 and 3.6 respectively.

These techniques categorised as qualitative and quantitative can be illustrated in a tree diagram in Figure 3-1 showing the preliminary classification of PCE techniques.

Product Cost Estimation Techniques

Qualitative Techniques

Quantitative Techniques

Intuitive Techniques

Parametric Techniques

Analogical Techniques

Analytical Techniques

Figure 3-1: PCE Preliminary Technique Classification

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3.3

Intuitive cost estimation techniques

The intuitive cost estimation techniques are based on using the past experience. A domain expert’s knowledge is systematically used to generate cost estimates for parts and assemblies. The knowledge may be stored in the form of rules, decision trees and judgments etc. at a specific location, e.g. a database, to help the end user to improve the decision making process and prepare cost estimates for new products based on certain input information. The present study identified three sub-categories under intuitive techniques.

3.3.1

Case-based methodology

This approach also known as case-based reasoning (CBR) attempts to make use of the information contained in previous design cases by adapting a past design from a database that closely matches the attributes of a new design. This often requires making necessary changes to parts and assemblies of previous design cases and incorporating missing details to it. Figure 3-2 shows a complete framework for the case-based approach with the dotted lines representing the cost interfaces to the system. The process starts by outlining a new product’s design specifications followed by retrieving a closest design match from a design database. The system then attempts to find the changed assemblies and subsequently changed parts in the assemblies. Changes are incorporated in the design either by retrieving similar parts and/or similar assemblies from the design database or by designing the new ones altogether. All the necessary changes are incorporated in a similar way until the new design conforms to the outlined design specifications.

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Figure 3-2: Flow Diagram of the Case-Based Approach for Cost Estimation

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The new design is later stored in the design database. This technique allows the cost estimation for a new product by combining the past results with those for the newly designed components and assemblies, thereby greatly reducing the need to design from scratch. The approach is, therefore, helpful in making good estimates at the conceptual design stage, since the use of the past cost data to generate new estimates greatly minimizes the estimation time. However, the methodology is applicable only when similar past designs are available to incorporate the relevant cost data during cost estimation for new products.

A typical example can be seen in the methodology presented by Rehman and Guenov [3] in which an attempt is made to predict design features from incomplete design descriptions based on past designs and production knowledge. In their work, a system allows the retrieval of past design cases that match the new problem description. The cost modeller detects necessary modifications in the retrieved designs and the cost data is updated accordingly using the adaptation rules stored within the design models. The method, thus, allows the cost estimation and evaluation for innovative designs. The method applied by LiHua and Yun-Feng [65] evaluated costs for new products by implementing the functions of CBR. These functions included organizing case bank, indexing case, initializing case, seeking and searching case and adapting case. The method was useful for rapid costing to satisfy customers’ demands on pricing. Ficko et al. [66] conceived a CBR system for predicting total cost of the tool manufacture. The system is based on extracting geometrical features from CAD-models stored in a database and calculating the similarities with the problem description of a new product’s features.

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Although, the developed system is only limited to tools for manufacture of sheet metal products by stamping, it provides good-quality predictions based on enough similar cases. Balarman and Vattam [67] analyzed other applications of CBR in the domains of helpdesks, diagnosis, cost estimation and design based on its functions such as representations, indexing, matching, adaptation and process of problem solving. Their work is an effort towards building a general-purpose case-based problem solver.

3.3.2

Decision support systems (DSS)

These systems are helpful in evaluating design alternatives. The main purpose of these systems is to assist estimators in making better judgments and decisions at different levels of the estimation process by making use of the stored knowledge of experts in the field. This is illustrated in Figure 3-3. One such system incorporating expert rules has been developed by Kingsman and De Souza [68] for cost estimation and price setting in versatile manufacturing companies dealing with make-to-order (MTO) systems. The developed system not only focused onto different factors that influence the decision making process in handling a customer enquiry but discussed the rules that cost estimators apply when making decisions about these factors.

To incorporate experts’ experience, the artificial intelligence (AI) philosophy is used to represent and utilize a domain expert’s knowledge in a way that is oriented towards problem solving and serves as a decision aid tool. In the particular context of the PCE, for example, it may constitute a segment of the system containing information about machining

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processes, manufacturability analysis and constraints, product characteristics with design functions and relationships with each other set out in logical statements. It may also incorporate rules about the actions to be taken or more conventional mathematical formulae. It can point outside to external programs and databases that can be associated with it including some that can cope with uncertain or conflicting judgments.

Figure 3-3: Decision support system approach to cost estimation

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Shehab and Abdalla [69] developed knowledge-based cost models for the PCE in early design stages whereas Luong and Spedding [24] developed a knowledge-based system by integrating process planning into cost estimation. Another approach adopted by Gayretli and Abdalla [4] focussed on developing a prototype system for manufacturing process optimization. The system assisted designers to create real-time cost estimates and feasible process plans by retrieving manufacturing form features and parameters from the feature database.

One of the most common ways to represent DSS is based on storing design, manufacturing or other constraints as a set of rules. Since many practical situations deal with uncertainty and non-availability of heuristic data, fuzzy logic techniques are used to some extent to overcome such problems. Another non-conventional approach makes use of Expert systems (ES) or Expert Support Systems in the domain of DSS.

Rule-based systems These systems are based on process time and cost calculation of feasible processes from a set of available ones for the manufacture of a part based on design and/or manufacturing constraints. Such a system reflects these constraints in a respective rule class with the information encapsulated in it by an expert in the area. A rule-based algorithm is an example of one such approach, which helps to establish design and manufacturing constraints. This approach is shown diagrammatically in Figure 3-4. Based on a set of user constraints, manufacturing processes are selected, which are then used to calculate the

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product cost. The set of constraints may need to be changed to obtain a different set of manufacturing processes to obtain an acceptable product cost estimate. This methodology is helpful for cost optimization based on process evaluation criteria. However, obtaining the optimized results can be very time-consuming especially, when there are a large number of processes to be evaluated.

Figure 3-4 Cost Estimation Process Model Based On User Constraints

Gayretli and Abdalla [70] developed a rule-based algorithm for the selection and optimization of feasible processes to estimate process time and cost based on parts features.

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A detailed description of part features with possible processes and constraints was given. Process times were calculated using a standard formula as follows:

Pr ocessTime =

FormFeatureVolume Material Re movalRate

(3-1)

The process time is then used to calculate Lot Time, which is based on a form feature quantity. The total process cost is subsequently calculated as follows:

Total Process Cost = Lot Time × PHC

(3-2)

Where, PHC is the Productive Hour Cost given by a cost estimation database [71]. The total cost is then calculated as follows:

Total Cost = Material Cost + ∑ [(Lot Time × PHC) + Tool Cost + Setup Cost]

(3-3)

The proposed system allowed the selection of a combination of feasible processes from the possible ones and hence the calculation of process time and cost based on the user input constraints, e.g. maximum allowable cost and process time for a particular feature. A criterion of feasibility was judged against the level of satisfaction for input constraints. The process allowed flexibility based on user constraints. Another example of this category can be found in [3] where manufacturing and assembly rules were used to update cost data in

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the proposed system, whereas, an object-oriented and rule-based system can also be found in [64] for product cost modelling and estimation.

Fuzzy logic approach This approach to cost estimation is particularly helpful in handling uncertainty. Fuzzy rules such as those for design and production are applied to such problems to get more reliable estimates. However, estimating the costs of objects with complex features using this approach is quite tedious and requires further research in the area. Shehab and Abdalla [63] used fuzzy rules with linguistic expressions and assigned truth-values to them. They used several steps to develop a fuzzy logic model. These steps were fuzzification of input variables followed by fuzzy inference based on a set of rules and finally defuzzification of the inferred fuzzy values. A fuzzy technique consisting of a decision table providing a means for system rules and indicating the relationships between the input and output variables of the fuzzy logic system, is used to handle the uncertain knowledge on cost estimation. The construction of a set of rules from the decision table enables the estimation of the machining time (Ti) for a given feature, which is multiplied by the unit time cost (Ri) to get the machining cost (Cm) for that feature, i.e.:

Cm = Ri Ti

(3-4)

The developed fuzzy logic based system was capable of estimating the total product cost apart from enabling the material selection and estimating the assembly cost. The same

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investigators [64] carried out a similar but more comprehensive study by considering other essential costs such as non-productive and set up costs.

Expert systems This approach is based on storing the knowledge in a database and manipulating it on demand to infer quicker, more consistent and more accurate results based on an attempt to mimic the human expert thought process with the help of an automated logical reasoning approach, normally achieved by rule based programming. Within the specific context of cost estimation, the expert system approach refers to a model and associated procedure exhibiting a degree of expertise comparable to that of a human expert in generating or to help in generating reliable cost estimates. Expert systems applied to the PCE have mainly focussed on formalising the theoretical techniques largely from textbooks etc. rather than encapsulating the practical knowledge (e.g. the expert conceptual estimator developed by Musgrove [72]). Further research in the area considering the human contemplating process of an estimator has a better potential to exploit the typical characteristic. Cost estimation methods for various applications using expert systems or expert support systems can be found in [73, 74].

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3.4

Analogical cost estimation techniques

These techniques employ similarity criteria based on historical cost data for products with known cost such as regression analysis models or back propagation methods. The following sub-sections describe these methods in detail.

3.4.1

Regression analysis models

These models make use of the historical cost data to establish a linear relationship between the product costs for the past design cases and the values of certain selected variables so that the relationship can be used to forecast the cost of a new product. The regression analysis approach based on the similarity principle was adopted by Hundal [75] and Poli et al. [42] to use a basic cost value and consider the effects of variable cost factors by assuming linear relationships between the final product cost and the cost factors. Lewis [76] further used existing designs to provide cost estimates for similar new designs whereas Pahl and Beitz [5] provided more general costing approaches based on similarity.

3.4.2

Back-propagation neural network (BPNN) models

These models use a neural network (NN) that can be trained to store knowledge to infer the answers to questions that may even not have been seen by them before. This means that such models are particularly useful in uncertain conditions and are adaptable to deal with non-linearity issues as well. The back-propagation neural network (BPNN) is the most

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common of all network types and also suits better the nature of the PCE. The application of neural network in cost engineering is discussed in [77].

Shtub and Zimerman [78] compared the cost results obtained with the regression model and the back-propagation neural network model and observed the superiority of the latter in many ways. In another study [40], a featured-based methodology was proposed using BPNN to estimate the cost of packaging products. Cost-related features of packaging products were used in conjunction with historical cost data to obtain a relationship between cost and cost-related features based on BPNN. The proposed method overcame the limitations of regression analysis models such as the assumption of non-linear relationships between product cost and its variables as well as those of traditional breakdown approaches, e.g. the requirement of detailed cost information like process planning cost. Zhang and Fuh [41] proposed a similar approach for early cost estimation, whereas Chen M-Y and Chen D-F [79] proposed a BPNN model for strip-steel coiler. Further, a backpropagation algorithm [2] was used with momentum and a flat spot elimination term for a Multilayer Perceptron (MLP) Neural Network, in which neurons are organized in several layers including an input layer, a number of hidden layers and an output layer.

3.5

Parametric cost estimation techniques

Parametric models are derived by applying the statistical methodologies and by expressing cost as a function of its constituent variables. These techniques could be effective in those

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situations where the parameters, sometimes known as cost drivers, could be easily identified. Parametric models are generally used to quantify the unit cost of a given product. Cavalieri et al. [2] developed a parametric model for the estimation of unit manufacturing costs of a new type of brake disk using the weight of the raw disk, unit cost of raw material and the number of cores as parameters in their model, which is expressed as follows:

C TF   C = FC +  C co N co + rm W 1 − SC  

(3-5)

where, C = Unit cost of disk brake, FC = Fixed Cost Factor (Coefficient), Cco = Core Cost per Kg of Cast iron (Coefficient), Nco = Number of cores, Crm = Unit cost of raw material, SC = Scrap rate (Coefficient), TF = cast iron / steel conversion factor (Coefficient), W = weight

A simple linear regression model using one of the cost drivers would not be effective because of variances between the data. However, the developed model overcame this problem by using more parameters. Validation analysis of the model by comparing the estimated costs with the actual ones of the brake disks demonstrated the superiority of the proposed parametric model over the linear regression model.

A wide range of parametric models can be found in the literature. For example, Hajare [80] modelled parametric costing of components using the product specifications. Roberts and 72

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Hermosillo [81] used approximate tool paths and process parameters from available factory resources to estimate time and cost for small surface units. Boothroyd and Reynolds [82] adopted a parametric costing approach using the volume of typical turned parts as a parameter to estimate the cost in the early design stages. Unlike the detailed-breakdown approach, the method adopted by them could be used in the early design stage without the need of a process plan. Similar work can be found in [83].

3.6

Analytical cost estimation techniques

This approach requires decomposing a product into elementary units, operations and activities that represent different resources consumed during the production cycle and express the cost as a summation of all these components. These techniques can be further classified into different categories, which are discussed in detail below.

3.6.1

Operation based approach

This approach is generally used in the final design stages due to the type of information required and is one of the earliest attempts to estimate manufacturing costs. The approach allows the estimation of manufacturing cost as a summation of the costs associated with the time of performing manufacturing operations, non-productive time, and set-up times. Several techniques have been developed to select the alternative manufacturing operations that optimise the machining cost.

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The cost model proposed by Jung [84] estimated the manufacturing cost by considering three different times including set up time, operation time and non-operation time. Formulation was provided. The total cost was given by:

Mfg cost = (Ro + Rm)[( Tsu/Q)Tot + Tno] + material cost + factory expenses.

(3-6)

where, Ro = operator’s rate, Rm = machine rate, Tsu = set-up time, Q = batch size, Tot = operation time, Tno = non- operation time.

The model could not be used to evaluate design alternatives due to its availability only in the final stages of design cycle. Feng et al. [12] presented a digraph based mathematical model that uses the geometric features including cylinder, rectangular block, chamfer, flat surfaces and hole, and developed an algorithm to estimate the minimum cost using an operation-based approach. The process plans of alternative design solutions with explicit modelling of the machining time of various features represented the criteria of estimating manufacturing costs. Gupta et al. [13] developed a similar methodology using manufacturing features for the evaluation of alternative process plans to estimate the manufacturing cost of the part. Wei and Egbelu [85] used geometric design data and developed a method based on a tree representation of alternate processes to estimate the product manufacturing cost. Although the approach focussed on obtaining the optimum results, it did not consider direct labour cost. Further, Kiritsis et al. [14] proposed a method for the cost estimation of the machining of parts based on the description of given features and associated alternative manufacturing operations. The proposed methodology was based 74

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on Petri nets to determine overall costs including machining cost, moving cost, setup cost and tool change costs. However, getting the optimised results using the proposed methodology was time consuming.

3.6.2

Breakdown approach

This method estimates the total product cost by summing all the costs incurred during the production cycle of a product, including material costs and overheads. The method requires detailed information about the resources consumed to manufacture a product including purchasing, processing and maintenance details.

The cost model developed by Son [86] included labour costs, machining cost, tool cost, set up cost, space occupied cost, computer software cost and material cost. The model also separated the raw material cost and the labour cost into different categories. The proposed model included insurance, utility, maintenance, repair and property costs. The machining cost (Cm,), is hence represented in the following equation as

Cm= (utility cost) + (maintenance cost) + (repair cost) + (insurance cost) + (property cost)

= Σ (CuTm + CmtTmt + CrTr + aFk + bFk)

(3-7)

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where, Cu = utility cost per unit time, Tm = machining time, Cmt = maintenance cost per unit time, Tmt = total maintenance time, Cr = repair cost per unit time, Tr = total repair time, a = insurance premium, Fk = initial investment, and b = property tax.

Further, equations for other cost elements including labour costs, tool cost, set up cost, space occupied cost, computer software cost and material cost were also provided. The requirement of such detailed information restricted the use of the model in the final design stage. Further, manufacturing costs were considered by Bernet et al. [43] as the sum of material, labour and overhead costs and Ostwald [60] estimated product cost as the summation of material cost, manufacturing cost, labour cost and overhead expenses based on hourly usage of machinery or direct labour. Such traditional cost estimation and cost accounting techniques were also discussed in detail in [61].

3.6.3

Tolerance-based cost models

The objective of such models is to estimate product cost considering design tolerances of a product as a function of the product cost.

Singh [87] presented a framework for the concurrent design of product and processes considering the criteria of minimum cost, maximum quality and minimum manufacturing lead time. Three models were presented to jointly design the products and processes. They are unit cost of production model, the quality model and the lead time model. The unit cost model was expressed as follows:

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X0 (d, j) = Ki (d, j) [Xi + f(j)] – Ks (d, j)Xs

(3-8)

where, Ki and Ks are technology coefficients that can be found from the following equations:

Ki = 1/ [1- SC (d, j)]

(3-9)

Ks = SC (d, j)/ [1-SC (d, j)]

(3-10)

SC is the scrap rate given by the following equation:

SC (d, j) = Ø[-d / σ (j)] + 1 – Ø[d / σ (j)]

(3-11)

where, j = jth manufacturing process selected for producing a product, Xo (d, j) = the unit cost with tolerance d, Xi = the unit raw material cost, f(j) = the unit processing cost for jth process, Xs = the unit salvage value, Ki = technology coefficient (input), Ks = technology coefficient (scrap), SC (d, j) = scrap rate, σ (j) = standard deviation, Ø (x) = Cumulative distribution function of probability distribution with the mean equal to 0 and the standard deviation equal to 1.

The modelling methodology was based on obtaining the optimal tolerances and hence setting up the acceptance regions for the design variables meeting certain criteria. The

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objective of the cost model was to select the process and design variables that minimize the cost function. However, the modelling methodology eliminated the needs for design changes because it considered various design and manufacturing factors at the early stage of the design. The cost-tolerance relationships and relevant models can also be found in [88, 89].

3.6.4

Feature-based cost estimation

The feature-based cost estimation methodology deals with the identification of a product’s cost related features and the determination of the associated costs. A considerable research has been carried in order to extract and quantify representative product features that contribute to the total cost. These features can either be design related such as the type of material used for a specific product, geometric details, etc. or process oriented, i.e. a particular process required for manufacturing the product, e.g. machining, casting, injection-moulding etc. The methodology allows the selection of a particular design or manufacturing form feature for DFC system users. However, the approach can have limitations for complex or very small geometric features especially if machining processes are used to produce these features.

Zhang et al. [40] proposed a feature-based cost estimation system for packaging products extracting 32 cost related features in both the design and manufacturing domain. These features were then quantified based on a relative cost influence among the various possible states of a particular feature. However, no attempt was made to quantify these features

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objectively. Ou-Yang and Lin [6] looked into the feature-based costing by focussing on the machining type features and developed a manufacturing cost estimation model based on feature shapes and precision. With the process planning information and geometrical data, the machining time of a feature was estimated. One limitation of their proposed framework was that it only considered conventional machining processes. Further research work in the area of feature-based cost estimation can be found in [90-92].

3.6.5

Activity-based costing (ABC) system

The ABC system focuses on calculating the costs incurred on performing the activities to manufacture a product. The method was first discussed by Cooper and Kaplan [93]. They presented the ABC system as a useful means to distribute the overhead costs in proportion to the activities performed on a product to manufacture it. Hundal [94] presented similar methods. The ABC system proved a good alternative to traditional estimation techniques since it provided more accurate product manufacturing cost estimates [95].

Various information sources for the implementation of the ABC system within a specific context can be found in [96-101]. The effectiveness of the ABC system was discussed by Kaplan [102] in providing helpful cost information to product designers for developing economic designs. The capabilities of the ABC were investigated by Tornberg et al. [103] with a particular emphasis on providing useful cost information to product designers. The study focused on modelling product design, purchasing and manufacturing processes with graphic flow charts in the form of activity chains. With the help of the process models and

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the activity-based cost calculations, product designers were able to estimate the effects of different design options on product costs. The work of Tseng and Jiang [104] attempted to combine the feature-based costing methodology with the ABC approach. Their ABC analysis model could evaluate different manufacturing costs for multiple feature-based machining methods. Yang et al. [105] used process planning, scheduling and cost accounting information to estimate manufacturing and machining cost through an activitybased method. Other examples of manufacturing and machining cost estimation using the ABC approach can be found in [106, 107].

Some other researchers used the ABC approach to model the manufacturing costs in a specific manufacturing set-up. For example, Koltai et al. [108] estimated costs for flexiblemanufacturing systems based on the ABC analysis, whereas Aderoba [48] developed an ABC model for job shops. The latter was based on the classification of all the activities into machine-based

production,

labour-intensive

production,

technical

services

and

administrative services. Cost rates for all such activities were provided which were then used to estimate the cost of a new order. For example, the cost of a machine-based production activity (C) was given as follows

C = [(M+m)tm + (L+l)tl + btb + utu]

(3-12)

where, M = cost rate for machines in the activity per hour, m = periodic rate for complimentary tools in the activity, L = labour rate for direct worker on machine activity, l = labour rates for ancillary worker on machine activity, b = building space rate for machine 80

Chapter 3: PCE Technique Classification System activity, u = utility rate for machine activity, tm = machining time, tl = labour working time, tb = time spent on building space occupied by activity, tu = time of utility being used.

Expressions were also provided for the cost rates for machines and tools, the labour rates for direct and ancillary worker, the building space rate, and the utility rate, which are not described here for brevity of presentation. The proposed method proved useful in highlighting high cost elements; however, its accuracy depended on how reliable the activity time estimates for a new product were.

3.7

Conclusions

This chapter extensively reviewed the pertinent literature on manufacturing and product cost estimation along with a critical evaluation of some of the techniques developed in the area. An extensive classification scheme is developed. A pictorial representation of the classification system adopted in the present study is given in Figure 3-5. The horizontal dotted lines are used to show the different levels in the hierarchical tree diagram proposed.

The techniques were classified into two main groups as qualitative and quantitative, which were then subdivided into two categories each. The chapter examined all the categories in detail with references to the published literature. Mathematical models were presented on some occasions to illustrate certain techniques. In addition, the PCE techniques discussed

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in the chapter are tabulated together with the key advantages, limitations and corresponding published literature in Table 3-1.

The study of individual techniques also revealed the key conditions under which they can be applied. The conditions can be grouped together to form a decision support model (DSM) for cost estimation methodology selection and is presented in Figure 3-6. The developed model is a helpful tool for estimators in making decisions about selecting a suitable estimation methodology. It can be observed that a particular technique linked with a specific class is more applicable in certain situations. During the early phases of the design cycle, when limited data is available, qualitative cost estimation techniques are more appropriate and provide a helpful starting point for a detailed analysis at a later stage. For example, the proposed case-based methodology systematically makes use of available past data to generate estimates for a similar new product. One problem linked with such techniques is the limited availability of past data, which is overcome to some extent by making use of the past experience or knowledge of the estimator generally encapsulated in the form of decision rules. Qualitative techniques, therefore, are helpful either in furnishing rough cost estimates or serve as a decision aid tool for designers or estimators especially during the early phases of design process. However, when the detailed design becomes available, quantitative techniques provide more accurate estimates, which are necessary for factors like design rationalization and determination of profit margins etc. The data requirements restrict the use of such techniques in the final phases of design and development process. Techniques such as the ABC systems overcome the problem to some extent by making use of the pre-determined activity rates to calculate the total amount of

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activities consumed to manufacture a product rather than requiring any detailed design and manufacturing information. This, however, requires lead times for individual products in the early design stages, which may be obtained using methodologies such as the case-based approach. Therefore, a combination of the two approaches, the qualitative and the quantitative techniques, could play an important role in developing a cost evaluation system capable of providing useful cost information on various stages of design and development phases.

The proposed classification system and the developed decision support model are aimed at supporting the decision making process of the estimators and designers. The two elements are formulated to provide guidelines to the users for the selection of an effective estimation methodology. A rightful selection is eventually an aspect of a CCS.

83

Product Cost Estimation Techniques

Level 1

Level 2

Level 3

Qualitative Techniques

Intuitive Techniques

Analogical Techniques

Regression Analysis Model Decision Support Techniques

Quantitative Techniques

OperationBased Approach Breakdown Approach

Rule-Based System

Analytical Techniques

Back-Propagation Neural Network Model

Case-Based Technique

Level 4

Parametric Techniques

Fuzzy Logic System

ToleranceBased Cost Models

Activity-Based Cost Estimation

Feature-Based Cost Estimation

Expert System

Figure 3-5: Classification of the PCE Techniques

84

Chapter 3: PCE Technique Classification System

Innovative design approach

Dependence on past cases

Rule-based Systems

Can provide optimized results

Time-consuming

Fuzzy logic systems

Handles uncertainty, reliable estimates

Estimating complex features costs is tedious

Expert Systems

Quicker, more consistent and more accurate results

Complex programming required

[72-74]

Regression Analysis Model

Simpler method

Limited to resolve linearity issues

[5], [42], [75, 76]

Back Propagation neural network model

Deal with uncertain and non-linear problems

Completely datadependant, Higher establishment cost

[2], [41], [77-79],

Utilize cost drivers effectively

Ineffective when cost drivers can not be identified

[2], [80-83]

Operation-based cost models

Alternative process plans can be evaluated to get optimized results

Time-consuming, require detailed design and process planning data

Breakdown cost models

Easier method

Detailed cost information required about the resources consumed

Cost tolerance models

Cost effective design tolerances can be identified.

Require detailed design information

Feature-based cost models

Features with higher costs can be identified

Difficult to identify costs for small and complex features

Activity-based cost models

Easy and effective method using unit activity costs

Require lead times in the early design stages

[4], [24], [68-69]

Case-Based Systems

Decision Support Systems

Limitations

Intuitive Cost Estimation Techniques

Product Cost Estimation Techniques

Qualitative Cost Estimation Techniques

Key Advantages

Analogical Cost Estimation Techniques

Table 3-1: The PCE techniques; key advantages, limitations and list of discussed references

Analytical Cost Estimation Techniques

Quantitative Cost Estimation Techniques

Parametric Cost Estimation Techniques

References [3], [65-67] [3], [64], [70] [63, 64]

[12-14], [84, 85]

[43], [60, 61], [86]

[87-89]

[6], [40], [90-92]

[48], [93108],

85

Input for selected methodology

Start

Selected methodology Decision Node / Available alternatives NO

1

Apply quantitative techniques

Estimates at conceptual design stage?

YES

Back propagation algorithm

Apply qualitative techniques

YES NO

Parametric relation available?

Past experience available?

YES

YES

NO

Apply analytical techniques

Process planning details / operation times available

Operation-based models

Cost elements’ breakdown available

Breakdown models

Cost as a function of design tolerances

Tolerance-based models

Individual features cost known Unit activity costs known

Feature-based models ABC models

Past product data available?

Apply parametric model

NO

Apply intuitive techniques

NO

Resolving linearity? Past product cases available?

NO

1

Product parameters. Shape, Size, Weight etc. Past experience stored in AI technology? Rule-based algorithm, Fuzzy logicbased system, Expert system

Apply analogical techniques

YES

Apply regression models NO YES

Linear relationship using historical cost data

Apply casebased technology

YES

Apply DSS

Apply BPNN models

Matching algorithm

Stop

Figure 3-6: Decision Support Model for cost estimation methodology selection

86

Chapter 4

MRO and TRO Estimation Methods

Overhead is a major element of the manufacturing cost. The chapter identifies the need to implement an improved overhead estimation methodology based on dividing manufacturing overheads into time- and material-related costs. New overhead estimation methods called material-related overhead (MRO) and time-related overhead (TRO) are, therefore, introduced, developed and implemented in an electrical engineering company for a four-year period. The results based on a four-year retrospective validation analysis confirm the superiority of the proposed methodology over the existing one, as overheads are more accurately estimated.

4.1

Introduction

The aim of Chapter 4 is to present material-related overhead (MRO) and time-related overhead (TRO) estimation methods. This is essential to lay the foundation for developing a comprehensive methodology for early and accurate estimation of a product cost. It has already been considered in previous analysis that early and accurate estimation would require adopting a hybrid approach combining the elements from qualitative and quantitative techniques. It has also been shown that developing a methodology for estimating a product’s cost in a batch type manufacturing environment 87

Chapter 4: MRO and TRO Estimation Methods

is in conjunction with a greater need for the system than for either mass production or job shop system. Further, the development of a methodology to predict an entire product’s cost rather than part or component costs demand a careful analysis of the developed classification system. Breakdown approach presents the entire product cost by summing up all the costs incurred during the production cycle of a product and could, therefore, hold the key to start the development process. In a broader sense, the development of a hybrid system for product cost estimation in a batch type manufacturing environment is, therefore, congruent to the research area.

Developing such a system, however, requires identifying the elements from the qualitative and quantitative techniques for hybrid approach. One of the identified elements is from the quantitative techniques and is based on predicting an entire product’s cost. Breakdown approach requires defining the total cost as a summation of the constituent elements. Before these elements and the total cost are defined; there is a need to understand any existing breakdown models and to identify problem areas.

Product cost consists of general administrative costs, engineering costs (costs incurred during design and development phases including those linked with customer requirements, designing of the part, its process planning, and prototyping), and manufacturing costs. The latter is the largest element of the overall product cost and is mostly determined during the product design phase. Better understanding and control of this cost element is a major step towards achieving an effective CCS. Figure 4-1 shows a breakdown of the selling price and manufacturing costs of a typical product [109]. It can be seen that the manufacturing cost accounts for 40 percent of the selling price. Half of this cost is incurred on parts and material, whereas direct labour accounts for 12 88

Chapter 4: MRO and TRO Estimation Methods

percent. Manufacturing overheads (indirect labour, indirect materials, plant and machinery depreciation, energy costs, etc.) account for 38 percent of the manufacturing costs, which is a substantial figure.

Figure 4-1: Break down of Selling Price and Manufacturing costs

Manufacturing overhead is a significant contributor to the overall product cost and refers to all the production support costs incurred on or off the shop floor and generally for the shared benefit of several products within a manufacturing facility. A traditional approach to estimating such costs relies on summing up all the expenses, other than those included in direct material and labour, and ascertaining a cost rate. The rate is then used to estimate the overheads for a new product by multiplying it with the expected manufacturing lead time (MLT) of the new product. A major disadvantage of this methodology is a disproportionate allocation of the total manufacturing overheads to different products with respect to the actual resources consumed by individual products. Furthermore, since the overheads recovery is based only on MLT and ignores material quantities, costs are underestimated for products with higher material requirements and overestimated for those with lower material quantities.

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Chapter 4: MRO and TRO Estimation Methods

Since, overhead is a major element of the overall product cost and estimating it accurately has a direct bearing on the overall estimated cost value, the current chapter will focus on developing a new overhead estimation methodology. The proposed methodology will then form the basis for the development of a model for the estimation of the overall product cost. The methodology developed in this chapter divides overheads into time- and material-dependent cost elements and overcomes the above mentioned limitations by providing a framework for apportioning the total manufacturing overheads to individual products based on the product’s degree of consumption of manufacturing activities and resources.

Product cost depends greatly on the geographical location of an enterprise owing to factors (such as governmental policies, taxation, political situation, weather, labour cost, and material availability) that could significantly alter the manufacturing cost of a product on different locations around the globe. The contributions of individual subelements (material costs, direct labour, and overheads) towards the overall manufacturing cost also vary within this context. It is not surprising that many western manufactures have moved their operations to Asian countries.

With this in mind, the present study analysed manufacturing cost and its various subelements in an electrical engineering company in South Asia. It is also important to note that any validation through industrial trials will not only make an attempt to endorse the model but help to understand the implications of geographical locations. The developed mathematical model for overhead estimation is implemented retrospectively in the company for a comparative analysis covering a four-year period.

The study sets

precedence for similar studies on other geographical locations with the aim of providing 90

Chapter 4: MRO and TRO Estimation Methods

a good foundation for comparative analysis in order to better understand manufacturing costs and develop an effective CCS.

4.2

Cost estimation methodology at the selected company

A well-established ISO9001 certified electrical engineering company was selected for the study as a representative case of the industrial sector in South Asia because it follows the standardized industrial code of practises acknowledged internationally. Because of the sensitivities around the confidentiality issues related to competitive cost data provided by the company, the company’s name is not mentioned here. The company designs, develops, manufactures, and markets a wide range of technologically advanced electrical and electronic products and provides after sales services. The transformers manufacturing unit of the Power Transmission & Distribution (PTD) division of the company was chosen for the study, as it is the largest manufacturing unit of the company based on a batch type manufacturing set up. The unit deals with the manufacturing of distribution transformers (DT) and power transformers (PT). One of the major reasons for selecting the company in general and the transformer unit in particular is the unit’s existing method of cost estimation that estimates the entire product’s cost based on a cost breakdown approach. Three major cost elements make-up the total manufacturing cost of transformers at the company: material costs, direct labour costs, and overheads. These are discussed in more detail below.

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Chapter 4: MRO and TRO Estimation Methods

4.2.1

Material cost estimation

The material costs are estimated using the material quantities obtained directly from BOM (see example in appendix A) which is developed based on the engineering design details. Scrap margin is accounted for based on past trends. In most of the cases standardized transformers are manufactured and thus engineering designs are already established and so are BOMs. Even when a non-standard transformer is designed and developed, the quantities of different materials required are similar to a closest standard match even though the technical design of the product may be significantly different. Thus, the match provides a good starting point for the non-standard transformer to estimate material cost. As a result, material cost estimation is possible in the early stages of the design and development stage. In such circumstances, material cost calculation, based on past trends and certain commercial indicators, becomes standard. The following commercial indicators were used based on past trends in order to calculate material cost for the year 2003-2004:

•

15 percent increase in purchase price of locally sourced material;

•

10 percent increase in price of materials bought from foreign suppliers;

•

Exchange rate = US $61.4 and 71 Euro (i.e. US $1.0 = Rupees (Rs) 61.4 and Euro 1.0 = Rs 71.0).

The cumulative material requirements (CMR) for transformer manufacturing for a given period of time change in accordance with planned orders. Thus, the factory-wide changes in material consumption over different time intervals can be used to reflect changes in production levels.

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Chapter 4: MRO and TRO Estimation Methods

4.2.2

Direct labour costs

Work centres in both DT and PT comprise operators and machines. Direct Labour here accounts for the cost incurred on wages for total man-hours required for production. The total manufacturing lead time (MLT) for a transformer is calculated using standard routings and process times. These process times are established either by using standard formulas or by deploying time and motion studies. The lead time for a non-standard transformer is determined from the results for the closest standard match. In this way, the total number of man-hours required for manufacturing a transformer can be determined in the early stages of the design process and are subsequently multiplied by the wage rate to give the labour cost incurred. Setting the wage rate for a particular period of time is an organizational policy matter which is influenced by various factors (such as minimum wage rate set by the government, geo-political conditions, economic growth, etc.).

4.2.3

Overheads estimation

Overheads here refer to manufacturing overheads and account for costs other than direct material and direct labour. Since such costs represent more than a third of total manufacturing costs (see figure 4-1), estimating it accurately can significantly enhance the accuracy of the overall PCE process. The new methodology proposed in the study is implemented retrospectively for a four-year period starting from 1999-2000. The methodology employed by the company is discussed below in order to facilitate comparisons between the two methods and provide insight into the optimisation achieved through the implementation of the proposed methodology.

93

Chapter 4: MRO and TRO Estimation Methods

The existing method is based on summing up all the expenses other than those incurred on direct labour and material. For example, the costs incurred on handling, transportation, inspection, storage, inventory control, and purchasing of different materials are classified as overheads. Energy and other utility costs necessary to run different workstations are also included in this category. Several small components such as nuts, bolts, washers, etc. are classed as indirect materials and the costs incurred on these items form part of the overheads as well. By summing all the above-mentioned costs and dividing by the capacity hours, the overhead rate for the following year is calculated. Capacity hours in this context are the hours available for production. The rate is then used to estimate the overheads for a new transformer by multiplying by the MLT of the transformer. The total transformer manufacturing cost is finally estimated by adding the three cost elements: material cost, direct labour cost, and overheads.

The major drawback of this methodology is that the allocation of overheads to an individual transformer in most cases is not in proportion to the material and energy consumed for its production. For example, a transformer with a comparatively lower lead time is allocated lower overheads even though the quantity of material required for its manufacture is higher. Thus, the amount of material required for the manufacture of a transformer is ignored with respect to overheads allocation. This results in underestimation for transformers with higher material requirements and overestimation for those with lower material requirements.

94

Chapter 4: MRO and TRO Estimation Methods

4.3

Proposed methodology for overheads estimation

A careful analysis of the overheads at the selected company revealed that they were largely driven by either material quantities or lead times. In some cases, however, material quantities and lead times may interchangeably influence the same overhead cost element. For example, the cost incurred on tools and equipment is greatly affected by lead times which in turn may be linked with the amount of material to be processed. However, based on consistency, a more direct and stronger link can be established only between tooling costs and lead times as in some cases lead times may be independent of material quantities. The proposed methodology for overheads allocation and estimation is, therefore, based on dividing the overheads into MRO and TRO. This allows more realistic allocation of overheads to individual products by taking care of not only their lead times but their respective material quantities. Mathematical models are developed for the estimation of these overheads in the present study and are validated against transformer data obtained from the selected company.

4.3.1

MRO estimation model

MRO include the costs incurred on material handling and transportation, material

inspection, material storage and inventory control, material purchasing etc. It is important to note that activity times (such as time consumed for material handling, inspection etc.) are not same as MLT that form the basis for TRO. These activity times are effected by variations in material quantities and hence any costs associated with them are considered MRO. The costs incurred on indirect materials are also included in MRO. As the material consumption increases, MRO also go up. Total MRO consumed

95

Chapter 4: MRO and TRO Estimation Methods

during a certain period of time, therefore, can be expressed as a percentage of total direct material cost. A fraction can be set to express the same at the end of the (n-1)th year based on total MRO and the cumulative direct material cost obtainable at the end of the (n-1)th year from the cost accountancy data. The resulting MRO fraction (which is a reflection of the MRO as a percentage of the direct material cost) is then multiplied by the total material cost of an individual product to calculate the MRO for a new product (OM) in the nth year. Total material cost for the product is based on the estimated

material quantities for that product obtained from the BOM and their respective unit costs, i.e.

Om = (C d 1 m1 + C d 2 m2 + .... + C dn mn ) ×

(C imn−1 + C nft−1 + C Pn −1 + C in −1 + C sin −1 − S ) n −1 C dmt

(4-1)

Where,

Cd1, Cd2, …., Cdn = Unit costs of direct material 1, direct material 2, …., direct material

n respectively used in the manufacture of the new product; m1, m2, …., mn = amounts of material 1, material 2, …., material n consumed; Cimn−1 = overall indirect material costs in the (n-1)th year, C nft−1 = overall freight & transportation costs in the (n-1)th year, C Pn −1 = overall purchase department costs in the (n-1)th year, Cin−1 = overall inspection

costs in the (n-1)th year, Csin−1 = overall stores & inventory costs, S = Sale proceed of n −1 scrap, Cdmt = overall direct material costs in the (n-1)th year.

96

Chapter 4: MRO and TRO Estimation Methods

It can be observed that the model can easily accommodate any other MRO to adapt to the system where it is implemented. For example, if a system’s quality control costs are material dependent, equation (4-1) can easily accommodate such costs to adapt to the new system. The percentage fractions of MRO calculated based on cost data (PT & DT) provided by the company for the year 2003-2004 are shown in Table 4-1. All the values given in the table are in (000) Rs. and the scrap value is given in brackets to denote subtraction in the model. The MRO for a new transformer can then be calculated using the percentages obtained and the amount of material used for its manufacture.

Table 4-1: MRO for power and distribution transformers (2003-2004)

Material Related Overheads for Transformers (2003-2004) Power

Distribution

Total

Transformers

Transformers

Transformers

(PT)

(DT)

6,500

19,500

26,000

(1,000)

(3,000)

(4,000)

500

1,500

2,000

1,478

4,433

5,910

790

2,370

3,160

Stores & Inventory Control

1,350

4,050

5,400

Total MRO

9,618

28,853

38,470

203,000

445,700

648,700

5%

6%

Indirect Materials Sale Proceeds of Scrap Freight & Transportation Purchase Department Costs Incoming Inspection

Total Material Consumption MRO (2003-2004)

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Chapter 4: MRO and TRO Estimation Methods

4.3.2

TRO estimation model

TRO refers to the overheads other than the MRO and are proportional to MLT. For

example, energy and other utility costs rise when the lead times increase. Different workstations are identified and all the costs incurred on running these stations are gathered together. For example, energy and other utility costs, repair and maintenance costs, costs incurred on special tools and spares, financing expenses, etc. are grouped under TRO. The total TRO can easily be obtained from cost accountancy data at the end of the (n-1)th year and are divided by the total capacity hours to yield the budgeted TRO rate for the nth year. The TRO for a new product (OT) can then be estimated by multiplying the TRO rate with the MLT of the new product. i.e.

OT = MLT ×

n −1 TROtotal n −1 C total

(4-2)

Where,

n −1 n −1 TROtotal = total TRO in the (n-1)th year; C total = total capacity in the (n-1)th year

TRO rates calculated based on cost data (PT & DT) provided by the company for the year 2003-2004 are shown in Table 4-2. All the cost figures given in the table are in (000) Rs. Since, the workstations running costs obtained from accounts include wages they are excluded from the rates calculation. The TRO for a new transformer can be calculated using the rates in Table 4-2 and the MLT for the transformer.

98

Chapter 4: MRO and TRO Estimation Methods

Table 4-2: Budgeted time related overhead rate calculation (2003-2004)

Power

Distribution

Total

Transformers

Transformers

Transformers

8200

9,989

29,966

39,954

8210

31,110

13,333

44,443

126,631

126,631

Cost Centre No.

8220 8230

2,032

6,097

8,129

8240

915

392

1,307

8250

2,248

963

3,211

8260

4,580

4,580

8290

3,126

3,126

46,293

185,088

231,381

-4,400

-11,900

-16,300

41,893

173,188

215,081

587

1,760

2,346

General Administration

1,665

4,994

6,658

Total (Rs. in 000)

44,145

179,941

224,086

Total Normal Capacity Hours

91,616

291,017

382,633

Budgeted TRO rate ≅

482

619

Total Less; Wages

Add; Financing Expenses

The estimated MRO and TRO for the new product can be added together to give the overall overheads for the new product. i.e.

O = OM + OT

(4-3)

The total transformer cost is finally estimated by adding the three cost elements discussed: i.e. material cost, direct labour and overheads (MRO and TRO).

99

Chapter 4: MRO and TRO Estimation Methods

Table 4-3: Summary of TRO rates, MRO percentage fractions and overhead rates for 4 years

Material Capacity Year consumed Hours (Rs.)

DT

PT

Proposed Methodology TRO

TRO Rate

Existing Methodology

MRO Total Overhead MRO Fraction Overheads Rate (%)

99-00 206,200

511,591

104,400

506

13,114

3

117,514

570

00-01 206,200

440,000

103,000

500

30,000

7

133,000

645

02-03 291,017

407,392

175,800

604

31,371

8

207,171

712

03-04 291,017

445,700

180,000

619

28,853

6

208,853

718

99-00 84,000

237,337

28,350

338

6,629

3

34,979

416

00-01 84,000

182,000

31,000

369

5,986

3

36,986

440

02-03 91,616

112,608

41,300

451

7,359

7

48,659

531

03-04 91,616

203,000

44,145

482

9,618

5

53,763

587

In a similar way, TRO rates and MRO percentage fractions can be calculated for the remaining three years of the validation period by using the data provided by the company. Table 4-3 summarizes the TRO rates and the MRO percentage fractions for the four-year period for both DT and PT obtained by the application of the proposed methodology. The table also determines the overhead rates for the same duration using the existing methodology for overheads estimation. The cost figures in the table are given in (000) Rs. except the final rates. The values can be effectively used to calculate the TRO, MRO and the overheads (company’s method) for a given product by using MLT and material cost of the product as mentioned in Table 4-4 for 25kVA transformer.

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Chapter 4: MRO and TRO Estimation Methods

4.4

Model implementation and validation

Data were collected for a period of 4 years to test the proposed methodology for overhead estimation. Results were systematically analysed using the cost elements breakdown discussed earlier. Costs were estimated for a selected range of products using both the existing and the proposed method for overheads estimation. The results were compared with actual manufacturing costs obtained from the cost accountancy data, and superiority of the proposed methodology was demonstrated.

As opposed to the two methods for cost estimation mentioned earlier, the actual manufacturing costs are based on cost calculation after the actual production and at the end of the financial year. Although, the precise methodology for the actual cost calculation is unknown due to confidentiality issues involved, the cost results and a brief guideline for the methodology involved was provided by the company. The actual costs of the individual transformers are the results of the redistribution of the plant-wide total costs incurred during the financial year in which they were manufactured. The actual costs are based on the actual MLT and materials (including the actual scrap material) consumed for the manufacture of a product. Total actual overheads are allocated to individual products based on a combination of factors including order related costs, tools and equipment utilization for specific products, traceable utility units to individual products, exclusive packaging, etc. Measurable activities (such as testing, inspection, quality control etc.) are accounted for by setting activity rates and determining activity units. A single cost rate is determined for all the other costs based on total production time. This cost is then allocated to individual products based on their MLT.

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Chapter 4: MRO and TRO Estimation Methods

% Variation from actual cost

257

24662 4949 29868 4199 1973 31092 31682 5.74 1.88

03-04

257

27622 4989 32868 4300 1657 33836 34877 5.78 3.01

New method

02-03

Old method

21825 4484 26559 3472 1528 27075 28121 5.55 3.72

Total estimated costs (Rs.)

250

MRO (Rs.)

00-01

TRO (Rs.)

19400 3962 23612 3520 582 23752 24290 2.79 2.22

Total estimated costs (Rs.)

250

Overheads (Rs.)

99-00

Material Costs (Rs.)

Direct Labour Costs (Rs.)

New Method

Year

Old method

Actual manufacturing costs (Rs.)

Table 4-4: Cost estimation for 25kVA transformer

Table 4-4 presents cost estimates for the 25kVA transformer. The costs are based on a MLT of 417 minutes and a wage rate of 36 Rs./hr for 1999-00 and 2000-01 and 37 Rs./hr for 2002-03 and 2003-04. A pictorial representation of the cost estimates produced using the two methods against the actual costs is shown in Figure 4-2 (a and b). It is apparent that the estimates obtained by applying the proposed methodology for overhead estimation are closer to the actual manufacturing costs than those obtained by the previously employed methodology. For example, the difference between the actual and estimated costs based on the previously employed methodology is on average 5% whereas the one resulting from the proposed methodology is on average 2.5%. This is attributed to the fact that the previous method ignores material quantities in the calculation of overheads and thus underestimates overheads and subsequently manufacturing cost.

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Chapter 4: MRO and TRO Estimation Methods

Similar results were obtained for 100kVA, 200kVA, 500kVA and 1000kVA transformers as shown in Figure 4-2 (c to j).

(a)

36 34

25 kVA Transformers

32 30 28 26 24 22 20 1999-00

2000-01

2002-03

2003-04

estimated cost (old method) actual cost

5.78

5.00 3.72

4.00 3.00

3.01

2.79 2.22

1.88

2.00 1.00 0.00 1999-00

2000-01

2002-03

2003-04

Year

estimated cost (new method)

old method

100 kVA Transformers

(c)

new method

100 kVA Transformers

55

(d)

6.00

% Variation from actual cost

Cost Value (Rs in 000)

5.74

5.55

6.00

Year

50 45 40 35 30 1999-00

2000-01

2002-03

2003-04

estimated cost (old method) actual cost

4.44

4.00

2.00

2.70

2.58

3.00

1.73

1.61 1.03

1.00 0.00 1999-00

2000-01

2002-03

2003-04

Year

estimated cost (new method)

old method

200 kVA Transformers

5.48

5.60

5.00

Year

(e)

new method

200 kVA Transformers

60

(f)

7.00

% Variation from actual cost

Cost Value (Rs in 000)

(b)

7.00

% Variation from actual cost

Cost Value (Rs in 000)

25 kVA Transformers

55 50 45 40 35 1999-00

2000-01

2002-03

2003-04

Year estimated cost (old method) actual cost

estimated cost (new method)

5.96

6.00

5.10

5.00

4.52

4.00 3.00 2.00

2.66 2.09

2.11

2.31

1.51

1.00 0.00 1999-00

2000-01

2002-03

2003-04

Year old method

new method

Figure 4-2 Contd.

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Chapter 4: MRO and TRO Estimation Methods

(g)

500 kVA Transformers

120 110 100 90 80 70 1999-00

2000-01

2002-03

2003-04

estimated cost (old method) actual cost

5.00 4.00 3.00 2.00

3.04 2.54

2.40 1.82

2.04

1.00 0.00 1999-00

2000-01

2002-03

% Variation from actual cost

120 110 100 90 80 2000-01

2002-03

2003-04

Year estimated cost (new method)

new method

1000 kVA Transformers

(i)

130

2003-04

Year old method

140

estimated cost (old method) actual cost

5.33 4.89

estimated cost (new method)

1000 kVA Transformers

1999-00

5.89

6.00

Year

Cost Value (Rs in 000)

(h)

7.00

% Variation from actual cost

Cost Value (Rs in 000)

500 kVA Transformers

7.00

(j)

6.11

6.00

5.41

5.19

5.00 4.00 3.00 2.00

3.34 2.62

2.26

2.01 1.43

1.00 0.00 1999-00

2000-01

2002-03

2003-04

Year old method

new method

Figure 4-2: Cost estimation results for 25, 100, 200, 500 and 1000kVA transformers

These results clearly demonstrate the superiority of the proposed methodology in the estimation of overheads and subsequently manufacturing costs. It can thus become an important part of an effective CCS. Indeed, following the analysis presented in this study, the company has adopted the proposed methodology since 2005-06.

The methodology can be further optimized and fine-tuned by considering the following points. The gradual yearly increase in the overall estimated and actual costs shown in Figure 4-2 is due to inflation. Since, the overheads for a particular year are used to determine the rates for the following year; the rates are slightly underestimated due to the effects of inflation which are not accounted for resulting in the underestimation of

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the overall manufacturing costs. This explains why the estimated costs shown above are lower than the actual costs. In addition, capacity hours are used to determine the overhead rates instead of the actual manufacturing hours. This means, if the production system remains under capacity for a particular year, the overhead rates are under estimated for the following year and the same is true for the overall manufacturing costs. Conversely, if the production works over capacity, overestimation may be observed. Since the production for the observed period of four years remained under capacity, underestimation is observed in all the cases presented in the study. To refine the proposed method, the use of normal capacity hours during TRO rate estimation can be replaced by the actual manufacturing hours followed by an adjustment to account for inflation in the following year. If the actual material cost for a product is higher than the estimated one, the actual MRO for the product would also be higher than the estimated ones resulting again in an underestimation of the product cost. This is especially true when the actual wastage on the shop floor exceeds the estimated one. The case-based approach developed by Niazi et al. [110] could prove a useful tool for more accurate material cost estimation.

The contribution of each of the three cost elements to the total manufacturing costs company wide were also analysed in order to ascertain the manufacturing cost breakdown statistics needed to better understand an effective CCS. Figure 4-3 shows the breakdown of the overall manufacturing cost for DT and PT in a diagrammatic form and illustrates the variation in the values of each cost element over the four-year period. The peak values represent the total manufacturing costs for each year which can also reflect the variation in production output over the four-year period examined. For example, the lowest peak value observed in years 2003-04 for PT reflects the lowest level of 105

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production during the four-year period. It can be seen clearly that direct labour cost contributes the least to the total manufacturing cost (owing to the geographical location of the company) whereas material cost is the most prominent cost element. The overheads values shown in Figure 4-3 include both TRO and MRO.

Figure 4-3: Cost element values in DT and PT

The values can be expressed in percentages. For example, the material cost accounts for about 65-85 percent of the total manufacturing cost whereas, labour cost is an insignificant, almost negligible cost contributor (1-2 percent of the total cost). Indirect

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labour and indirect material costs are included in overheads. Overheads that combined both TRO and MRO varied between 13 and 33 percent.

The overheads breakdown showing MRO and TRO is plotted in Figure 4-4 for both DT and PT over the four-year period investigated. The TRO turns out to be the dominant component out of the two. One of the reasons is that the material handling costs that are part of MRO are significantly lower than the workstation running costs that come under TRO.

Figure 4-4: TRO and MRO values breakdown for DT and PT

Since the labour cost is insignificant, a comparison is only made between material costs and overheads in the form of cost trends over the four-year period. Figure 4-5 (a) illustrates the cost trends for DT. It can be seen that the total overheads kept on increasing despite a decline in material consumption until 2002-2003. However, this increase reflects an increase in TRO rather than MRO. The decline in material

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consumption indicates the decline in productivity. The lower productivity, thus, resulted in increased overhead rates due to the allocation of company wide overheads expenditure towards the under capacity manufacture of transformers. Another factor that resulted in increased overheads was an inefficient cost control during the low productivity period.

It can be seen that MRO also increased but their effect on the total overheads was minimal. This was attributed to the fact that energy and other utility costs which are elements of TRO jumped up during that period. Figure 4-5 (b) shows a similar trend for PT. However, the TRO does not exhibit a steep increase as in DT despite a much sharper decline in material consumption compared to DT. This is because the lead times for the PT transformers are much higher than those for DT and so are the TRO. The variation in production levels, therefore, has more profound effect on TRO in PT than in DT. As a result, the decline in production in PT led to low figures for TRO.

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Cost trend over time (DT)

(a)

Cost Figure (Rupees in million)

600 500 400 300 200 100 0 1999-00

2000-01

2002-03

2003-04

Year

time related overheads

material related overheads

Total Overheads

Parts and material cost

Cost trend over time (PT)

(b)

Cost Figures (Rupees in million)

300

200

100

0 1999-00

2000-01

2002-03

2003-04

Year

time related overheads

material related overheads

Total overheads

Parts and material cost

Figure 4-5: Cost trends in (a) DT and (b) PT

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Figure 4-6 compares the cost trends for both DT and PT by considering material costs against overheads. Because of the reasons discussed earlier, more irregularities are found in DT than in PT.

Material Cost against Overheads

Cost Value (Rupees in million)

600 500 400 300 200 100 0 1999-00

2000-01

2002-03

2003-04

Year Material Cost in DT

Overheads in DT

Material Cost in PT

Overheads in PT

Figure 4-6: Cost

trends comparison in DT and PT

The cost element breakdown analysis and the discussion presented above highlight some key points that are useful for establishing an effective CCS. This is particularly relevant where manufacturing cost is calculated using material cost, direct labour costs and overheads. These points are listed below:

•

Estimating direct material cost of a product accurately is vital as this is the most dominant cost element with a significant impact on the overall manufacturing cost 110

Chapter 4: MRO and TRO Estimation Methods

•

Material cost of a product can be estimated precisely using an effective estimation methodology such as the case-based approach [110]

•

Material cost is directly linked with the product design; however, minimising wastage on the shop floor is an important aspect of an effective CCS because it not only reduces direct material costs but also minimizes overheads

•

Direct labour cost is affected by factors like MLT, wage rate, geographical locations, etc.

•

Unlike material costs, overheads are not an integral part of product design and hence play an important role in controlling the overall product cost

•

Controlling overheads during low productivity periods is especially crucial to minimizing product costs

•

Identifying overheads correctly and adopting an effective estimation methodology can significantly alter product cost estimates

•

Determining overhead rates based on material and time consumed to manufacture a product and using the rates to estimate overheads for a new product is an easy, effective and accurate method to produce product cost estimates and is applicable in the early stages of the design and development process.

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4.5

Conclusions

This chapter laid foundation for developing a PCE modelling methodology by establishing an overhead estimation method. In order to predict the entire product cost instead of only part or a component cost, breakdown approach was considered. The chapter considered the existing breakdown of a product cost from a published model in order to portray the potential areas of importance. This led to the identification of overheads as an area worthy of exploration. Problems with the existing methods of overhead estimation were then identified. Some of the existing methods that partially resolved the problems were also discussed. However, this led to the identification of possible solutions for estimating overheads more accurately. It was decided to validate the developed model for overhead estimation through industrial trial. A batch manufacturing set up with the estimation methodology based on a breakdown approach was chosen for the implementation and validation purposes.

The manufacturing costs in an electrical engineering company in South Asia were systematically analysed with emphasis on the estimation of overheads which contribute about a third of total manufacturing costs. The analysis identified problems with the previous practise of estimating overheads and a new methodology was proposed. The new methodology was retrospectively implemented for a four-year period in the company and a cost analysis was carried out. The estimates obtained with the previously employed and the proposed methodologies were compared against the actual costs. It was found that the proposed methodology leads to more accurate manufacturing cost estimation results.

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The study identified irregularities in the cost trends of the selected products over the period of observations, especially during low productivity periods. Recommendations were made to improve the proposed methodology further such as the use of actual manufacturing hours instead of normal capacity hours during TRO rate estimation followed by an adjustment for inflation in the following year. Job shops and batch manufacturing set up based on flexible manufacturing and MRP based systems are some of the examples of potential candidates for the proposed methodology.

The study also revealed that material cost accounts for 75 percent, labour costs for only 2 percent and overheads for almost 23 percent of the overall manufacturing costs at the company. This cost breakdown, however, is representative of that region characterized by lower wage rates. Thus, extensive testing of the proposed methodology in other geographical locations is ongoing in order to further fine-tune it and make it an integral part of an efficient CCS.

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Chapter 5

PCE Hybrid Model

The aim of the Chapter 5 is to develop mathematical models for accurate product cost estimation with a focus on batch manufacturing systems. The modelling methodology presented is a hybrid approach consisting of a breakdown technique and an activity-based costing system and focuses on an effective utilization of cost data obtained at the end of a given period to predict a product’s cost for the following phase. The modelling framework proposed is based on time- and material-dependent cost elements.

5.1

Introduction

Chapter 5 is aimed at modelling the overall product cost from the foundation already provided in the previous chapter. It was established that the development of a hybrid system for PCE in a batch type manufacturing environment is a viable research option in the area. Breakdown approach was then selected as one of the hybrid element. The other elements from the classification system for the hybrid approach will now be identified in this chapter. However, since, the breakdown approach was selected and a complete overhead analysis was already carried out in the previous chapter, the focus is first given here to establish the breakdown elements for the proposed model. This would require an indepth analysis of what constitutes a product’s cost.

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Manufacturing is a transformation process that consumes material and resources. The degree of consumption of these resources is reflected in a product’s cost. The origin of the consumed resources and those of the factors influencing a product’s cost may not only be traced to the shop floor but outside it. The emerging picture of a product’s cost is, therefore, a complex blend of distinct and indistinct contributions made to the product. The contributions or the cost elements are often easier to be allocated to individual products once they are produced. However, predicting these cost contributions even beforehand requires efficient and accurate predictive tools.

The ever-increasing pressure on estimators to predict the cost early (sometimes even before the conceptual phase) and accurately is also accentuating the need to develop innovative techniques combining knowledge, experience, resources and historical data. Often the techniques are customized to suit the needs of a system and/or a product. Whether, the methodology is customized or generic, the final product cost determines selling price. An effective cost estimation methodology, therefore, bears a potential of setting competitive price without compromising profits yet securing commercial advantage to the enterprise.

In a batch manufacturing environment, where the available facilities are effectively utilized to carry out a wide range of operations, estimating manufacturing costs accurately requires an in-depth analysis of the shop floor resources and the way they are consumed. For this reason, determining manufacturing cost in addition to the overall product cost does not often receive enough attention. The estimation techniques available, although predict the overall product cost, fail to yield accurate estimates of the manufacturing cost component. 115

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An opportunity to make any optimization into the same or other components may, thus, be lost. The chapter presents a comprehensive model for the estimation of manufacturing cost and its sub-elements in addition to the overall product cost. However, before developing the mathematical models for PCE, an analysis of the product cost and modelling methodology is drawn.

5.2

Product cost and modelling approach

The previous chapter considered manufacturing cost as a combination of direct material, direct labour and overheads (also termed as indirect manufacturing costs). Manufacturing cost, on the other hand, is a sub-element of the overall product cost which is a combination of engineering costs (costs incurred during design and development phases starting with customer requirements, design of the part, its process planning and prototyping), manufacturing costs and production overheads. Manufacturing cost is the largest element of the overall product cost and is largely determined during the product design phase. This element accounts for all the costs associated with the resources that can be traced to the manufacturing floor where the actual production takes place.

Overall product cost can also be divided into direct and indirect costs incurred on a product during its transformation from raw material to finished entity. Direct costs refer to the cost elements that can be directly traced to a product and are generally incurred for the benefit of the individual product. For example, direct material costs incurred on a product refer to

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the costs incurred on material that is integral to the product design. Similarly, direct labour costs refer to the costs incurred on labour spent purely on manufacturing the product and is easily determined using lead times obtainable from process planning details. Direct material and labour are the elements of manufacturing cost. Indirect costs refer to all the production support costs incurred on or off the shop floor and generally for the shared benefit of several products within a manufacturing facility. These refer to all the costs other than those included in direct costs. These include manufacturing overheads, production overheads and engineering costs.

From the analysis presented in the previous chapter, it was found that manufacturing overheads (part of indirect costs) can be divided into time– and material–dependent cost elements. However, after the implementation and validation analysis, areas for further optimization were discovered. It was found out that a further two classes of manufacturing overheads can be identified. Some of the indirect costs depend on both processing time and material quantities to be produced. Cost spent on tooling, for example, depends on both processing time and the amount of material to be processed and can not be grouped with either time– or material–dependent cost groups. Some of the other indirect costs, on the other hand, are spent on keeping the manufacturing shop floor in a running condition. A realistic approach to allocate such costs on different products is required that is based on the product’s level of consumption of resources from the manufacturing shop floor. If a product stays for a longer period of time and occupies a larger space on the manufacturing floor, it is highly likely to consume more resources than a product that stays for a shorter duration and occupies little space. Such indirect costs can be termed as building space cost

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and are, thus, based on lead times and occupied spaces for individual products. Yet another set of indirect costs are those that can not be directly traced to a manufacturing shop floor or only partially. For example, costs incurred on building security, general administration costs and financing expenses etc. can be grouped together. These costs need to be allocated to individual products using a pragmatic approach. It is highly likely that a product with higher manufacturing costs should incur these costs in greater proportion than those with lower manufacturing costs. It is because a product with a higher manufacturing cost consumes more resources on the manufacturing shop floor and is thus likely to incur higher proportions of other costs also. Such indirect costs can, therefore, be allocated to individual products in proportion to their manufacturing costs. These indirect costs refer to the only set of overheads not directly traceable to the manufacturing shop floor and can be termed as production overheads. The other four indirect costs can be traced to the manufacturing shop floor and can be termed indirect manufacturing costs. These include: time–dependent cost (also referred to as processing cost), material–dependent cost, tooling cost and building space cost. Engineering cost is also a form of indirect cost and refers to the costs incurred during design and development phases starting with customer requirements, designing of the part, its process planning and prototyping.

Based on the breakdown approach, product cost can now be expressed as a summation of the individual cost elements (manufacturing cost, engineering cost and production overheads). A pictorial representation of the detailed product cost breakdown followed in the present study is shown in Figure 5-1 together with the cost distribution for a typical product [109]. The estimated cost for a new product, C pn+1 , can thus be expressed as the 118

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n +1 sum of the three cost elements: estimated manufacturing cost , CGp , estimated engineering n +1 , and estimated overheads, O pn +1 : cost, C Ep

n +1 n +1 C pn +1 = C Gp + C Ep + O pn+1

(5-1)

Selling Price Selling Price 20%

Product Cost

25%

Profit 15%

40%

Manufacturing Cost

Engineering Cost

Production Overheads

Manufacturing Cost

38%

Direct Material Cost

Direct Labour

Indirect Manufacturing Cost

50%

12%

Processing Cost

Material – Dependant Cost

Tooling Cost

Building Cost

Figure 5-1: Pictorial representation of the mathematical model for product cost estimation

Manufacturing costs refer to the costs associated with the activities taking place on the manufacturing shop floor and the cost elements that can be traced to it. The manufacturing

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n +1 cost, CGp , for an individual product, p, can be estimated by summing the direct cost n +1 n +1 , and labour cost, C Lp ) and the indirect manufacturing cost elements (material cost, Cmp n +1 n +1 elements (processing cost, Ctdp , material-dependent cost, Cmdp , tooling cost, CTpn+1 , and n +1 building cost, C Bp ) for the product, i.e.:

n +1 n +1 n +1 n +1 n +1 n +1 C Gp = C mp + C Lp + C tdp + C mdp + CTpn +1 + C Bp

(5-2)

Determining indirect costs accurately and early for an individual product in a manufacturing environment where resources are shared between several different products is challenging and requires sound engineering knowledge of product design, planning, production and costing. A traditional approach to estimating such costs relies on summing up all the expenses other than those included in the direct costs and ascertaining a cost rate. The rate is then used to estimate the indirect costs for a new product by multiplying it with the expected manufacturing lead time (MLT) of the new product. However, a major drawback of this methodology is a disproportionate allocation of indirect costs to different products. Furthermore, since the indirect costs recovery considers only MLT, the amount of material required for the manufacture of a product is ignored. This often results in cost underestimation for products with higher material requirements and overestimation for those with lower material quantities.

The ABC system was presented [93] as a useful means to distribute the indirect costs in proportion to the activities performed on a product during manufacturing. The system 120

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proved a good alternative to the traditional estimation techniques since it provided more accurate manufacturing cost estimates [95]. However, the effectiveness of the methodology depends on the way the activity rates are determined and the accuracy of the estimated activity units. Moreover, time-based activity units are generally employed ignoring material related costs during PCE using the ABC system. For example, the ABC model developed by Aderoba [48] only considered activity times ignoring material quantities for the cost estimation of a new product. Material dependent costs such as transportation, packaging, storage and inventory, etc. may, therefore, not be accurately estimated for the new product.

The model presented in the current chapter overcomes the limitations of the existing methodologies, as mentioned above, by providing a framework for PCE based on time– and material–dependent cost elements. The modelling methodology is a hybrid approach combining a breakdown model (including manufacturing costs, engineering costs and production overheads) with a modified ABC system and skilfully exploits the already validated models in Chapter 4. The above mentioned limitations associated with determining activity rates and activity units using the conventional ABC system are overcome based on an effective utilization of the cost data obtained at the end of a given year ‘n’ to predict a product’s cost in the beginning of the following year ‘(n+1)’ by determining the rates for cost elements. It means that the developed method incorporates the attributes of a case-based system into the ABC system by making use of past data. The modified ABC system, therefore, forms second element of the Hybrid Model. Figure 5-2 is a pictorial representation of the overall modelling framework within the context of the developed technique classification system. It is evident that the developed model is also

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hybrid at the top level of the classification system by making use of the attributes of the qualitative and the quantitative techniques. The breakdown approach helps to estimate the overall product cost. The ABC takes care of the accuracy of the results and the use of the case-based approach helps to produce early results. Although, at the lower levels of the classification system, three elements appear to contribute towards the proposed model, the modified ABC system and the breakdown elements are the two elements of the Hybrid Model. The modified ABC component is itself hybrid in nature. The developed model is a comprehensive and an integrated costing tool that not only estimates the overall product cost but predicts the essential individual cost elements. A low to medium volume batch type production environment where various indirect costs are involved is a highly suitable environment for the application of the proposed methodology.

5.3

Direct cost elements

Direct costs refer to the costs associated with the elements directly identifiable to and linked with a product and are generally incurred for its exclusive benefit. Costs associated with material and labour are largely considered direct manufacturing costs. These are examined in more detail below.

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5.3.1

Direct material costs

The material costs can be estimated using the material quantities obtained directly from the BOM developed on the basis of the product structure and engineering design details. A scrap margin is usually accounted for in BOMs based on past trends. In a manufacturing environment where products are standardized, their engineering designs and BOMs are also established. Even when a non-standard product is designed and developed, the required quantities of different raw materials are similar to those in a closest standard match even though the technical designs of the two may be different. Thus, the closest match provides a good starting point to estimate material cost for the non-standard product. As a result, material cost estimation is possible in the early stages of the design and development stage. n Under such circumstances, the material cost calculation, based on past product cost, Cmp ,

(already stored in a database) and certain commercial indicators termed as material cost deviation index (MCDI), φ n +1 , (such as inflation rate, foreign exchange rate, price increase etc.) for the following year, becomes a standard practice. i.e.,

n +1 n C mp = (1 + φ n +1 ) × C mp

(5-3)

Past product costs can be established using the unit cost, Ckn , of the kth material in the product and its corresponding quantity, mk , i.e.

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n C mp = ∑ (C kn )(mk )

(5-4)

k

n The total cost based on the cumulative material requirement, Cmt , for manufacturing, p,

products for a given period of time changes in accordance with the number of units produced, N pn , for a given product. Thus, the factory-wide changes in material consumption over different time intervals can be used to reflect changes in production levels and can be obtained by the following equation.

n C mtn = ∑ (C mp )( N pn )

(5-5)

p

The total planned cost, Cmtn+1 , based on cumulative material consumption can be obtained from the planned orders, N pn+1 .i.e.

n +1 C mtn+1 = ∑ (C mp )( N pn +1 )

(5-6)

p

124

Product Cost Estimation Techniques

Quantitative Techniques

Qualitative Techniques

Intuitive Techniques

Analogical Techniques

Regression Analysis Model

Decision Support Techniques

Parametric Techniques

Analytical Techniques

Back-Propagation Neural Network Model

Operation-Based Approach

Breakdown Approach Feature-Based Cost Estimation

Case-Based Technique Expert System Rule-Based System Fuzzy Logic System

ToleranceBased Cost Models

Activity-Based Cost Estimation

Hybrid Model for PCE Figure 5-2: Development of the Hybrid Model within the framework of the technique classification system

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5.3.2

Direct labour

The manufacturing shop floor layout consists of work centres which can be either labourintensive or machine-intensive centres or both. Fabrication, manual assembly and painting are examples of labour-intensive centres sometimes referred to as labour centres also. CNC machines, automatic assembly lines, industrial robots are examples of machine-intensive centres. A combination of the two is also common and can be termed as hybrid centres; examples include lathes, mills, semiautomatic assembly lines, etc. More commonly the term machine centre is also used to refer to either machine-intensive or hybrid centres i.e. any work centre that is not a labour centre can also be termed a machine centre. Figure 5-3 illustrates the three different work centres.

Work Centre

Labour Centre/ Labour-intensive centre Fabrication, manual assembly, painting etc.

Machine Centre

Machine-intensive centre CNC machines, automatic assembly lines, industrial robots etc.

Hybrid centre Lathes, mills, semiautomatic assembly lines etc.

Figure 5-3: Types of work centres

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The direct labour cost incurred on a product accounts for the fraction of the wages of the workers in the work stations through which the product is routed. The time spent by the workers to manufacture individual products and their respective wage rates (generally set on the basis of their skill levels) can be used to determine this cost. However, in a batch manufacturing environment where multi-skilled workers are placed on work centres intermittently and handle multiple tasks, a more pragmatic approach is required to ascertain these costs.

The direct labour in the proposed methodology is based on the shop floor wide aggregate labour rate and the labour units spent to manufacture a product. Thus, the direct labour cost n already incurred on an individual product, C Lp , can be obtained as a product of the actual

n n , and the labour units consumed, U Lp , to manufacture it, i.e. labour rate, RLA

n n n C Lp = ( RLA ) × (U Lp )

(5-7)

n +1 The estimated labour cost, C Lp , can be given as a product of the estimated labour rate, n +1 n +1 RLE for a given period and the estimated labour units, U Lp , for a given product.

n +1 n +1 n +1 CLp = ( RLE ) × (U Lp )

(5-8)

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Total planned labour units, U Ltn+1 , can be used to estimate the total labour cost, C Ltn+1 , for planned orders, i.e.

n +1 C Ltn +1 = ( R LE ) × (U Ltn +1 )

(5-9)

Labour units The MLT of a product is the summation of the individual lead times in the relevant work centres. The lead time for a job on an individual work centre (sometimes referred to as work centre cycle time WCCT) is the time spent by the job on the work centre before moving on to the next work centre. The lead time is different from the man-units consumed which are referred to as the total time spent by all the workers on the job in that work centre. The man-units on an individual work centre can be converted into labour units by considering the output levels (skilled, semi-skilled and non-skilled levels) of the individual workers. The total time spent by skilled labour, tx, semi-skilled labour, ty and non-skilled labour, tz, can be expressed in a unified form of labour units, Lnjp , by applying skill indices,

α, for semi-skilled labour with ranging from 0.4 to 0.8 and, β, for non-skilled labour with ranging from 0.25 to 0.4.

Lnjp = ∑ t x + α ∑ t y + β ∑ t z x

y

(5-10)

z

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The values for skill indices can be set based on feedback form shop floor supervisors. For example, the value of α = 0.6 can be set for a semi-skilled labour whose skill or output level is almost 60 percent of a standard skilled-labour. Wages of a worker on the shop floor may also be a criterion to set the indices as variations in wages of the workers can be in accordance with their skill or output levels.

This approach is particularly helpful in a computer integrated manufacturing (CIM) environment where time cards are filled at individual work centres with job codes, employee numbers, etc. Based on the relative skill levels of semi- and non-skilled labour compared to those of the skilled ones, line supervisors are generally in a good position to ascertain skill indices for individual workers. If an individual lead time, t njp , is taken as the time spent by all the workers working on a job in a work station, then the number of skilled, x, semi-skilled, y, and non-skilled, z, labour can be used to obtain labour units on the work centre, using the formula:

Lnjp = t njp ( x + αy + βz )

(5-11)

The total labour units consumed for the product can then be given as:

n U Lp = ∑ Lnjp

(5-12)

j

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This in turn allows the estimation of the shop floor wide labour units consumed, U Ltn , for a given period of time based on the number of different products produced during that period:

n U Ltn = ∑ (U Lp )( N pn )

(5-13)

p

The determination of labour units for a product, therefore, requires lead times at individual work centres and number of different workers with their skill levels working on the product. The lead times can be obtained from standard routings and are established either by using standard formulas or by deploying time and motion studies. For example, a range of time estimation models and time standards can be found in [111]. In a CIM environment, a feedback mechanism ensures that the actual lead times are standardised for future use. The lead time for a non-standard or a new product can be established from the results for the closest standard match and incorporating the changes in consultation with the shop floor supervisors and planning engineers. The labour units required to manufacture the product can then be estimated based on the number of operators required on individual work centres.

Labour rate The shop floor-wide direct labour cost incurred during a given period, C Ltn , reflects the wages paid to the shop floor workers during that period and is the summation of all the total wages in the individual work centres, Gtjn , i.e.:

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C Ltn = ∑ Gtjn

(5-14)

j

The total wages and the total labour units consumed in a given period can be combined to calculate the actual labour rate, i.e.:

∑G

n tj

n RLA =

j

U Ltn

(5-15)

The labour rate calculated in this way differs from the conventional wage rate for a given worker. The wage rate for a particular period of time is a matter of organizational policy and is influenced by various factors (such as minimum wage rate set by the government, geo-political conditions, economic growth, and an individual worker’s skill level etc.). The actual labour rate during a period n can be used to ascertain an estimated labour rate for period n+1 based on the expected variance called labour cost deviation index (LCDI), ε n +1 , (such as the effects of inflation, forecasted wage differential, etc.):

n +1 n RLE = (1 + ε n +1 ) × RLA

(5-16)

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5.4

Indirect cost elements

These are costs associated with contributions that can be traced to the manufacturing shop floor but not to a specific product or only partially. The costs incurred on indirect material (material shared for the benefit of many different products), utilities, machine repair and maintenance, quality control, tooling and equipment, building space, etc. comprise indirect costs. The indirect cost elements for an individual product can be determined by adopting a suitable methodology for apportioning the total indirect costs based on the product’s degree of consumption of manufacturing activities and resources. The study identifies four kinds of indirect costs that can be linked with manufacturing shop floor and presents comprehensive models to estimate them for a specific product.

5.4.1

Processing cost

The processing costs incurred during a given period on the manufacturing shop floor, Ctdn , refer to all the processing-time-dependent costs (excluding labour costs) that contribute to the smooth running of the machine centres on the shop floor. Thus, this cost can be expressed as a summation of all the individual time-dependent cost elements, Cdn , (such as utility cost, maintenance cost, repair cost, machine depreciation, machine insurance etc.) for a given period:

Ctdn = ∑ Cdn

(5-17)

d

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n +1 The processing cost for an individual product, Ctdp , can be determined from the estimated n +1 n +1 , and processing units for the product, U Mp : processing rate, RME

n +1 n +1 n +1 C tdp = ( RME ) × (U Mp )

(5-18)

Processing units The job processing time, tipn , on the, ith, machine centre (time spent by a job between its arrival and departure from a machine centre while the machine is running) can be used to determine processing units consumed by the job, M ipn , on the centre by applying a machine index, ηi .

M ipn = η i × t ipn

(5-19)

The machine index accounts for repair, maintenance, utilities etc. and takes values ranging from 1.25 to 2.0 [9]. Older machines requiring more maintenance, repair, etc. will have a higher index value. The job processing time is generally the same as lead time and can be obtained directly from time cards in a CIM environment. By summing up all the processing n units at individual machine centres, the total processing units for the product, U Mp , can be

obtained:

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n U Mp = ∑ M ipn

(5-20)

i

n The shop floor-wide processing units consumed, U Mt , for a given period of time can be

calculated based on the number of different products produced during that period:

n n U Mt = ∑ (U Mp )( N pn )

(5-21)

p

The job processing times for a new product can be estimated using closest standard matches allowing the estimation of the processing units for the new product.

Processing rate n A shop floor-wide aggregate processing rate, RMA , is proposed from the processing cost

data collected during a given period and the corresponding processing units consumed:

R

n MA

C tdn = n U Mt

(5-22)

However, the same methodology can be used to establish separate rates for individual machine centres if their corresponding processing costs can be traced and cumulative processing units obtained easily. The estimated rate for the following period can be set

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based on a processing cost deviation index (PCDI), µ n +1 , that reflects the effects of inflation, utility costs variations, maintenance and insurance forecasts, etc.:

n +1 n RME = (1 + µ n+1 ) × RMA

5.4.2

(5-23)

Material dependent cost

Several indirect costs incurred in a manufacturing enterprise can be attributed to material quantities used to manufacture different products, called material-dependent costs (MDC). Examples of such costs include: indirect material, purchasing, stores & inventory, freight & transportation, material inspection, packaging, and quality costs, etc. These costs do not depend on the lead times or processing times but on the quantity of materials consumed. Thus when the direct material quantities go up, MDC also go up. As a result, MDC is also a significant contributor to the manufacturing costs. The total material-dependent costs for a n given period, Cmd , can be expressed as:

  n C md =  ∑ C wn  − S n  w 

(5-24)

Where, C wn refers to the total cost incurred on an individual MDC element (such as packaging) and S n is the salvage value for scrap material. Since the MDC increase with the rise in direct material quantities, the fraction based on the total MDC and the cumulative

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direct material cost for a given period can be used to estimate the MDC for a specific n +1 n +1 product, Cmdp , using its estimated direct material cost, Cmp and MDC deviation index

(MDCDI), ρ n+1 (the effect of inflation, variations in material, freight and transportation prices etc.):

 Cn n +1 C mdp =  md n  C mt

5.4.3

 n +1  × (1 + ρ n+1 ) × C mp 

(5-25)

Tooling cost

Tools range from manual equipments to jigs, fixtures, moulds, dies etc. The total tooling cost incurred on the manufacturing floor for a given period, CTtn , comprises the cost n incurred by tools utilization and replenishment in machine centres, CMT , and labour n centres, CLT .

n n CTtn = CMT + CLT

(5-26)

Tooling cost depends not only on the amount of material processed on the manufacturing floor but also on the job processing times on machine and/or labour centres. The proposed methodology, therefore, allocates the total tooling cost incurred on the shop floor to individual products on the basis of their material costs and corresponding processing and/or labour units. Tooling cost rates in labour and machine centres for a given period n are

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determined for this purpose. Estimated tooling cost rates for the following period n+1 n +1 n +1 based on machine centres, RMT , and labour centres, RLT , can then be effectively utilized to

predict the tooling cost for an individual product, CTpn+1 , i.e.:

(

) [(

)(

) (

)(

n +1 n +1 n +1 n +1 n +1 CTpn +1 = C mp × RMT U Mp + RLT U Lp

)]

(5-27)

Determining the tooling cost for an individual product based on an aggregate shop floorwide tooling cost rate often results in disproportionate allocation. This is due to the cost variances between the tools at machine centres and labour centres and the different time spent by the product on the respective centres. The proposed model overcomes this problem by providing separate rates for tools used at machine and labour centres respectively.

Machine tool rate n The machine tool rate, RMT , is associated with the total tooling cost incurred in machine n centres, C MT , during a given period. It is given by the formula:

n RMT =

n (CMT ) n (U Mt ) × (Cmtn )

(5-28)

The total machine tool cost for a given period can be expressed as the sum of total depreciation, DMn , of M’ number of machine tools during that period. The costs associated

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with number of b machine tools that are broken down can be incorporated by considering their initial purchase prices, Pb , and respective depreciated values, Db .

    n CMT =  ∑ DMn  +  ∑ ( Pb − Db )  M   b 

(5-29)

Standard techniques can be applied to ascertain the depreciation values for individual tools. The estimated machine tool rate for the following period can then be set based on a machine tool cost deviation index (MTCDI), ψ n +1 , to account for the effects of inflation, expected variation in tool utilization, life expectancy factor of the current tools, etc.:

n +1 n RMT = (1 + ψ n +1 ) × RMT

(5-30)

Labour tool rate n n The labour tool rate, RLT , considers the total tooling costs incurred in labour centres, C LT ,

for a given period. It is determined using the formula:

n R LT =

n (C LT ) n (U Lt ) × (C mtn )

(5-31)

The total labour tool cost for a given period can be expressed as the sum of total depreciation, D Ln , of L number of labour tools during that period. Similarly to the machine 138

Chapter 5: PCE Hybrid Model

tools, the costs linked with number of a broken labour tools with their initial purchase prices, Pa , and respective depreciated values, Da , can be incorporated as follows:

    n CLT =  ∑ DLn  +  ∑ ( Pa − Da )   L   a 

(5-32)

A labour tool cost deviation index (LTCDI), σ n +1 , is then employed to account for inflation, expected variation in tool utilization, life expectancy factor of the current tools, etc. and thus the labour tool rate for the following period will be:

n +1 n RLT = (1 + σ n +1 ) × RLT

5.4.4

(5-33)

Building space cost

The building space cost includes all the essential costs incurred to keep the manufacturing shop floor and the overall plant in a usable condition. Plant depreciation, building insurance, maintenance, repair, and utilities (excluding those supplied to the shop floor) are some of the examples of building space cost elements. The number of h building space cost elements, Chn for a given period can be added together to determine the total building space cost, C Btn , for that period.

C Btn = ∑ C hn

(5-34)

h

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The proposed methodology allocates the total building space cost to individual products based on the areas they occupy on the manufacturing shop floor and their lead times. Products requiring bigger spaces and higher lead times incur larger proportion of building space costs. Building space rate for a given period is determined for this purpose. An estimated building space rate, RBn +1 , can then be set for the following period. This allows the estimation of the building space cost for an individual product by multiplying the n +1 estimated rate with the manufacturing space, SGp , and units (processing and labour) for the

product, i.e.:

(

) (

) (

n +1 n +1 n +1 n +1 C Bp = RBn +1 × S Gp × U Mp + U Lp

)

(5-35)

Building space rate Building space rate for a given period, RBn , can be set by dividing the total building space n , and cost incurred during that period from the total manufacturing units (processing, U Mt

labour, U Ltn ) and the total area of the manufacturing shop floor, S Gtn .

R Bn =

n (U Mt

C Btn + U Ltn ) × S Gtn

(5-36)

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Again a building cost deviation index (BCDI), δ n +1 , can be defined to account for any variations due to inflation, forecast variations for building maintenance, repair, utilities etc. and the final adjusted rate will be:

RBn +1 = (1 + δ n +1 ) × RBn

(5-37)

Manufacturing space Manufacturing space here refers to the overall area of the manufacturing shop floor and is a combination of the space occupied by all work centres, S otn , and the total unoccupied space on the floor, Sutn .

SGtn = S otn + Sutn

(5-38)

Shop floor cell layout records can be used to find out occupied spaces by individual work centres, O nj , that can be summed together to give the total occupied space.

S otn = ∑ O nj

(5-39)

j

The ratio of the total manufacturing space to the total space occupied can be effectively n +1 used to allocate the manufacturing space for an individual product, SGp .

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 Sn n +1 S Gp = S opn +1  Gtn  S ot

  

(5-40)

Where, S opn +1 , refers to the total occupied space for the product and can easily be obtained by summing up the number of r different work centre spaces through which the product is routed, Orpn +1 .

Sopn +1 = ∑ Orpn +1

(5-41)

r

5.5

Production overheads

Overheads here refer to the production overheads (PO) and are different from indirect manufacturing costs. These include costs incurred on elements like security services, computer software, general administration, financing, sales and marketing, etc. They are not normally traced to manufacturing shop floor. The total PO, Otn , can be found by adding the number of q different PO cost elements, H qn , i.e.:

Otn = ∑ H qn

(5-42)

q

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Since, the POs are incurred to maintain manufacturing activities; they can be effectively allocated to individual products as fractions of their manufacturing costs. The fraction calculated based on the total PO and the total manufacturing cost, CGtn , incurred during a given period can, therefore, be used to estimate the POs for an individual product for the n +1 following period, O pn +1 , using its estimated manufacturing cost, C Gp , and PO deviation

index (PODI), τ n+1 (the effect of inflation, variations in selling expenses, general and administration costs etc.):

 On  n +1 O pn +1 =  nt  × (1 + τ n +1 ) × C Gp  C Gt 

(5-43)

The total manufacturing cost incurred for a given period is a summation of all the individual total manufacturing cost elements, i.e. material, labour, time-dependent, material-dependent, and building space costs.

n n CGtn = Cmt + CLtn + Ctdn + Cmd + CTtn + C Btn

5.6

(5-44)

Conclusions

This chapter presented a comprehensive modelling methodology for PCE in a batch type manufacturing environment. The overhead estimation method developed in the previous chapter formed the basis for extending the modelling framework. The limitations associated 143

Chapter 5: PCE Hybrid Model

with the existing methods of overheads estimation resulted in defining sets of new indirect costs which were modelled later on. The only element that could not be modelled was engineering cost due to the insufficient experience, data and knowledge obtained from the industrial domain. However, the nature and the extent of the theories developed for the other elements and the clarity of the developed models contain the intrinsic characteristics that can serve as guidelines to model the engineering cost.

The adopted modelling methodology is a hybrid approach combining the attributes of a breakdown technique with the ABC system in order to estimate the total product cost. In this respect, the model was presented as a summation of individual cost elements (manufacturing cost, engineering cost and production overheads) which were broken down further to their sub-elements. Activity rates and units were defined and modelled for individual elements based on an effective utilization of historical cost data in order to predict product costs early and accurately. Thus comprehensive models for estimating manufacturing cost and indirect cost elements for individual products were given.

The proposed modelling framework is based on time- and material-dependent cost elements and overcomes the current limitations in cost estimation. The model has been tested and validated using data from a crane assembling unit and the results are presented and discussed in the next chapter.

144

Industrial

Chapter 6

Implementation and Analysis of the PCE Hybrid Model The aim of Chapter 6 is to implement the developed PCE Hybrid Model in a batch manufacturing environment in the UK. The process will focus on developing an implementation algorithm, modelling cost deviation indices and obtaining the estimated cost values from the model’s implementation for a given product range. The estimated results will also be obtained from the company’s own method.

6.1

Introduction

Chapter 6 establishes basis for a thorough validation analysis for the developed PCE Hybrid Model. This is achieved by the industrial implementation and application of the Hybrid Model developed and presented in the previous chapter. When considering the validation process, it is important to determine the criteria for validation and that if the adopted criteria are widely acceptable and recognizable standards within the framework of a specialism. Although, mathematical models can be simulated to validate the results, those designed for industrial applications need to be backed up by industrial trials to best serve

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the purpose. Industrial trials can be time consuming requiring attention to details, the results based on such attempts can only strengthen the confidence in the entire validation process itself.

The developed model as part of the current research study was not only conceptualized with the aim of theoretical development in the field but to serve the wider industrial needs also. The criterion for its validation, therefore, is fittingly set to proceed with the industrial implementation and application. The process involves implementing the model and validating it by comparing the results with those generated by any existing system in place.

Setting the objectives for the validation process and defining how they will be achieved are fundamental to the success of the entire process. Before any of the objectives can be set, the active conditions have to be considered. Within the context, getting the right balance between the duration of the trials and the consistency of the results generated during that time is important. The trial period, therefore, is set for three years (2003 – 2005) retrospective analysis requiring field data from 2001 to 2005 based on the requirement of the developed model. The validation period of three years is a reasonable time to allow the process to generate reliable and consistent results. Since the model is developed to mainly fulfil a batch manufacturing system’s requirements, the selection of such an industrial environment for the implementation and validation analysis is yet another active condition. A careful consideration was given to the conditions to initiate the validation process.

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

The main objective of a PCE process is to predict the likely product cost early and accurately. Accurate estimation refers to minimizing the difference between the actual costs and the predicted values. The developed model should aim to predict product costs more accurately than any of the existing systems in use at the selected company. Although cost estimation has no direct influence on cost control, the estimated results should help the decision-making process to devise cost control strategies. Cost estimation methods that can predict not just the entire product cost but the elemental values can highlight the potential areas for better cost control. The developed model should, therefore aim to present better structured and more elaborate elemental results than those generated by the existing system.

Section 6.2 details the procedure and methodology for the industrial implementation of the PCE Hybrid Model. A comprehensive algorithm is developed to facilitate the implementation process. Section 6.3 details the PCE process at the company. The necessary business information is presented followed by the cost estimation for the given product range using the company’s own method of cost calculation. Section 6.4 deals with the implementation of the PCE Hybrid Model in the selected company with the help of the modelled indices and based on the developed algorithm in section 6.2 in order to ascertain the estimated costs for the given product range for the duration of the trial period. Section 6.5 concludes the chapter.

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

6.2

HMI algorithm and the implementation methodology

The Hybrid Model Implementation (HMI) algorithm is developed and presented in the section to facilitate the industrial implementation of the model. The overall aim of the implementation of the Hybrid Model in return is to facilitate the entire validation process. With this in mind, it is essential to compare the results generated by the implementation of the Hybrid Model against those generated by the company’s own method. The company’s method of cost estimation with the relevant results would, therefore be discussed to support the implementation of the Hybrid Model. But first the necessary steps and the overall procedure of the Hybrid Model’s implementation will be discussed.

The Hybrid Model is implemented in the selected manufacturing company for a retrospective analysis of three years (2003 – 2005). The developed model makes use of the available data at the end of a year (n) and the preceding year (n-1) to predict the costs for the following year (n+1). Data obtained from 2001 to 2004 could therefore be used to predict costs from 2003 to 2005. Since, the comparison of the estimated costs predicted at the beginning of a year is made with the cost data obtained at the end of that year; cost data for 2005 were also required in order to make comparison with the estimated costs for that year. Therefore, the data obtained from 2001 to 2005 were used for the implementation and validation analysis for (2003 – 2005). The estimated results will then be compared against the actual product costs in the next chapter as part of the validation analysis. The current chapter details the entire implementation process. Figure 6-1 to Figure 6-7 represents the Hybrid Model Implementation (HMI) Algorithm.

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

The stepwise preliminary implementation of the Hybrid Model is presented in Figure 6-1. It is clear that the entire PCE process for a product is outlined in 13 different steps starting from material cost estimation to the estimation of a product’s overall cost. The figure cross references relevant sections, figures and equations. The logical sequence of necessary steps is shown with arrows. The dotted arrows follow sub-systems detailed in separate cross referenced figures with step numbers.

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Start Step 1 Step 2 (refer to Figure 6-2) Material Cost Estimation (Section 5.3.1) Step 3

1

1A Step 4 (refer to Figure 6-3)

2

Labour Cost Estimation (Section 5.3.2)

Step 5

2A Step 6 (refer to Figure 6-4) 3

Processing Cost Estimation (Section 5.4.1)

Step 7

3A Step 8 (refer to Figure 6-5)

MDC Estimation (Section 5.4.2)

Step 9

4A

Manufacturing Cost Estimation Equations (5-2), (5-44)

Step 11

4

Step 10 (refer to Figure 6-6) 5

5A Step 12 (refer to Figure 6-7)

Production Overhead Estimation (Section 5.5)

Step 13

6

6A

Product Cost Estimation (Section 5.2) Figure 5-1, Equation 5-1

Stop

Figure 6-1: PCE Hybrid Model implementation phase

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Detailed implementation steps are facilitated with necessary links in the preliminary implementation phase. For example material cost estimation process is presented with links 1 and 1A and is elaborated in Figure 6-2. The logical steps presented in rectangular boxes are connected with arrows. Inputs to the system are presented in parallelograms together with necessary references to the equations developed as part of the Hybrid Model. For example, equation (5-4) can be used to calculate material cost for the ‘pth’ product in the ‘nth’ and the (n-1)th years using the input provided in the same parallelogram. The input in this case refers to material cost data provided by the company from its financial accounts.

1 Material cost data for the nth and (n-1)th years

Material cost calculation for pth product in the nth and (n-1)th years

Cumulative material costs in the nth and (n-1)th years

Eq (5-4)

Number of units produced in the nth and (n-1)th years Eq (5-5)

MCDI calculation for the (n+1)th year

Estimated material cost for the pth product in the (n+1)th year

1A

Eq (B-5)

Eq (5-3)

Refer to Figure 6-1 (step 3)

Figure 6-2: Material cost estimation implementation process

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

The inputs to the system are either primary or secondary. Primary inputs are the details provided by the company. Secondary inputs to the system are the results obtained during the implementation phase and are fed to the system to generate further results.

For

example, during the calculation for PCDI mentioned in Figure 6-4, the inputs to equation (B-9) are aggregate processing rates (secondary input) and inflation rates (primary input). Aggregate processing rates are termed secondary inputs because they were calculated in the preceding step using equation (5-22). It is, therefore, fitting to sequence the execution steps in the HMI algorithm to maintain the logical flow and to effectively utilize the secondary data. The algorithm is designed to facilitate the Hybrid Model implementation at the selected company and as such adapts to the system. However, minor changes can make the algorithm more generic. Some of the customizations are considered in light of the requirements mentioned in section 6.4.

The HMI algorithm facilitates the generation of the results by effectively utilizing the primary and secondary inputs and the PCE Hybrid Model. The results include not only the estimated product and manufacturing costs but the elemental values including the estimated material, labour, processing and material-dependent costs. In addition, the cumulative costs and the deviation indices are effectively calculated. All the results generated through the implementation of the HMI algorithm are discussed in detail in section 6.4.

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2 Labour units (LU) calculation for pth product in the nth year LU calculation at jth work centre (WC)

Lead times at jth WC, number of skilled, semi-skilled and non-skilled labour, labour indices Eq (5-10) or (5-11)

No

LU calculated at all ‘j’ WC ? Yes

Total LU calculation for pth product

No

Total LU for all ‘p’ products calculated?

Eq (5-12)

Number of units produced in the nth year for all ‘p’ products Eq (5-13)

Yes

Shop floor-wide LU calculation in the nth year

Total wages paid in the nth year to all workers

Direct labour cost calculation in the nth year

Actual labour rate (LR) calculation for the nth year

LCDI calculation for skilled, semi-skilled and non- skilled labour and then average LCDI for the (n+1)th year

Eq (5-14)

Eq (5-15)

Average per month wages of skilled, semi-skilled and non-skilled labour in the nth and (n-1)th years, inflation in the nth and (n+1)th years Eqs (B-6), (B-7) and (B-8)

Estimated LR calculation for the (n+1)th year Estimated labour cost for pth product in the (n+1)th year

Eq (5-16)

Eq (5-8)

2A

Refer to Figure 6-1 (step 5)

Figure 6-3: Labour cost estimation implementation process

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

3 Processing units (PU) calculation for pth product in the nth year Processing time at the ith MC, machine index

PU calculation at ith machine centre (MC)

Eq (5-19) No

PU calculated at all ‘i’ MC? Eq (5-20)

Yes

Total PU calculation for pth product Number of units produced in the nth year for all ‘p’ products No

Total PU for all ‘p’ products calculated?

Eq (5-21)

Yes

Financing expenses and insurance, maintenance, repair and energy costs incurred in the nth year

Shop floor-wide PU calculation in the nth year

Eq (5-17) th

Processing cost calculation in the n year Eq (5-22)

Aggregate processing rate (PR) calculation for the nth year

PCDI calculation for the (n+1)th year

Aggregate processing rates for the nth and (n-1)th years, inflation in the nth and (n+1)th years Eq (B-9)

Estimated PR calculation for the (n+1)th year Eq (5-23)

Estimated processing cost for pth product in the (n+1)th year

3A

Eq (5-18)

Refer to Figure 6-1 (step 7)

Figure 6-4: Processing cost estimation implementation process

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

4

Total MDC calculation for the nth and the (n-1)th years

Indirect material, stores & inventory, freight & transportation, material inspection, purchasing, packaging and material handling costs and scrap for the nth and (n-1)th years Eq (5-24)

MDCDI calculation for (n+1)th year

Total MDC and cumulative material costs for the nth and (n-1)th years, inflation in the nth and (n+1)th years Eq (B-10)

Estimated MDC for the pth product in the (n+1)th year Eq (5-25)

4A

Refer to Figure 6-1 (step 9)

Figure 6-5: MDC estimation implementation process

5

Manufacturing cost estimation (MCE) for pth product in the (n+1)th year

Estimated material, labour, processing and materialdependent costs for the pth product in the (n+1)th year Eq (5-2)

Cumulative manufacturing costs in the nth and the (n-1)th years

Cumulative material, labour, processing and material dependent costs for the nth and (n-1)th years Eq (5-44)

5A

Refer to Figure 6-1 (step 11)

Figure 6-6: Manufacturing cost estimation implementation process

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

6

Total PO in the nth and the (n-1)th years

PODI calculation for the (n+1)th year

Computer related and general admin costs and selling expenses in the nth and the (n-1)th years Eq (5-42)

Total PO and cumulative manufacturing costs in the nth and (n-1)th years, inflation in the nth and (n+1)th years Eq (B-14)

Estimated PO for the pth product in the (n+1)th year Eq (5-43)

6A

Refer to Figure 6-1 (step 13)

Figure 6-7: PO estimation implementation process

In order to fully appreciate and understand the PCE Hybrid Model, the HMI algorithm and the generated results, it is essential to understand the company’s method of cost estimation and the estimated results. The next section, therefore, details the company’s estimation method and the generated results before elaborating the Hybrid Model’s results.

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6.3

PCE at the company

A well established crane and ship engineering company based in the UK (identity is shielded due to confidentiality issues) was selected for the study as a representative case in the country. The company designs, develops, manufactures, and markets a wide range of cranes and parts for cranes and ships. It also provides after sales, installation and commissioning services. The organizational structure of the company is divided into crane manufacturing division (CMD) and ship engineering division (SED). The structural verticalization within the organization meant that the divisions and sub-divisions carry out their businesses independently. The total industrial output in the year 2005 was reported in excess of £100m with £25m and £75m divided between the CMD and the SED respectively. The CMD is divided into three sub-divisions namely spares & parts (SPSD), assembly & services (ASSD) and installation & commissioning (ICSD) with the respective industrial output in excess of £3m, £12m and £10m in the year 2005.

6.3.1

Information and details

The SPSD of the CMD was selected for the study. The main reason for the selection of this sub-division in particular and the company in general was that the developed model’s scope in terms of its parameters was likely to be covered there. The company was keen on initiating the validation process from a relatively smaller unit. Table 6-1 highlights the industrial output values in (£s) from 2002-2005 for the CMD.

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Design of parts and products at the company takes place at the divisional level. New product designs are normally generated for the ASSD where crane assemblies and subassemblies are manufactured from the outsourced parts and/or procured from the SPSD. The designs for products manufactured at the SPSD are already made, product range being the standard. However, any minor changes are customized to the actual product designs. Table 6-2 outlines the product range for the SPSD for the duration of the study.

The SPSD comprise fabrication and assembly units. There are a total of 20 different machines in the sub-division. During its manufacture a product is first routed on the machines within the fabrication unit before being routed through the assembly unit machines until its final completion. The products route through a set of predetermined machines within each unit based on its processing requirements. On its completion, a product is handed over to the CMD sales from where it is either shipped to the customers or sent to the ASSD.

Table 6-1: Industrial output values for the CMD (2002 – 2005)

Industrial Output Values

2002

2003

2004

2005

SPSD

2,192,384

2,534,222

2,895,843

3,200,353

ASSD

10,983,782

11,625,460

12,098,570

12,595,000

ICSD

9,901,843

9,955,987

9,980,350

10,048,380

Total (CMD)

23,078,009

24,115,669

24,974,763

25,843,733

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Table 6-2: Product range at the SPSD

S. No. Product Number

Product Description

1.

MQ4033

Tripod crane

2.

MQ4030

Tripod crane

3.

MQ4024

Overhead mounted bridge crane gripping manipulator

4.

MQ3522

Overhead mounted gripping manipulator

5.

MQ2538

Overhead trolley mounted gripping manipulator

6.

MQ1033

Overhead mounted linear track gripping manipulator

7.

GQ4026

Column mounted double wire gripping manipulator

8.

GQ4024

Column mounted gripping manipulator

Products within a unit are manufactured either in small batches or independently. Product quantities are planned based on quarterly sales forecast released a quarter in advance of the actual production. For example, the quantities for production in the third quarter are released at the end of the first or the beginning of the second quarter in order to make necessary arrangements for material procurement and production planning and control. Product cost evaluation and review is carried out yearly. Table 6-3 gives out the details of the product quantities produced in the SPSD from 2001 to 2005.

Product cost at the company is made up of material cost, labour cost and overheads. Actual unit product costs are obtained at the end of a financial year from the cost accountancy data

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based on the cumulative production cost of a given product and its respective number of units produced in a given year. The values are given in the Table 6-3 and were provided by the company.

Table 6-3: Yearly production quantities for the product range in the SPSD (2001 – 2005) and Actual unit product cost for the given product range (2002 – 2005)

Product

No of units produced

Actual Product Cost per unit (£)

2001

2002

2003

2004

2005

2002

2003

2004

2005

MQ4033

430

450

400

485

324

1068

1197

1344

1520

MQ4030

265

250

230

200

265

955

1082

1226

1428

MQ4024

145

150

165

190

175

1948

2155

2370

2665

MQ3522

175

150

135

165

185

1267

1388

1551

1740

MQ2538

280

325

360

345

378

1492

1659

1851

2100

MQ1033

432

375

450

319

316

487

540

628

729

GQ4026

265

245

298

335

285

807

911

1005

1174

GQ4024

318

325

350

245

329

386

435

477

555

6.3.2

Material cost estimation

Material cost here refers to the direct material costs. Material quantities are ordered based on the planned orders. The actual material quantities take into account the actual scrap and 160

Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

wastage. The actual material costs are, therefore, only available after the production and can be obtained from the financial data at the end of the production year. Table 6-4 presents the actual material costs in (£s) for the product range during the period of study. The cumulative material costs were obtained at the end of a given financial year and used to furnish the unit material costs for the respective products for that year.

Table 6-4: Actual material cost (Cumulative and per unit costs) Product

Total material cost (Actual) (£)

Unit material cost (Actual) (£)

2001

2002

2003

2004

2005

2001

2002

2003

2004

2005

MQ4033

214140

228100

211200

265780

181440

498

507

528

548

560

MQ4030

110240

105120

101430

92000

129850

416

420

441

460

490

MQ4024

176610

185210

215325

259540

252350

1218

1235

1305

1366

1442

MQ3522

123550

112125

104625

135300

158175

706

748

775

820

855

MQ2538

225400

280520

327600

331200

383670

805

863

910

960

1015

MQ1033

101520

95240

117900

92510

98592

235

254

262

290

312

GQ4026

84535

87620

110856

123950

112575

319

358

372

370

395

GQ4024

52470

54200

59500

40425

56588

165

167

170

165

172

Total

1,088,465

1,148,135

1,248,436

1,340,705

1,373,240

The material cost calculation for a specific product in a given year is based on the amounts of different materials in that product and their respective unit costs for that year. Material quantities are obtainable from BOMs (see example in appendix A). Since the products are

161

Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

standardized, BOMs are established. Actual material costs incurred for a product can vary based on a number of factors and are available after its production and generally at the end of a financial year.

Table 6-5: Estimated unit material costs for the given product range (2003 – 2005)

Product

Estimated unit material cost (£) 2003

2004

2005

MQ4033

530

554

574

MQ4030

439

463

482

MQ4024

1290

1370

1430

MQ3522

781

814

859

MQ2538

902

956

1005

MQ1033

265

275

304

GQ4026

374

391

387

GQ4024

174

179

173

Material cost estimation at the SPSD is based on considering the actual product costs at the end of a given year to predict for the following year. Average inflation values are used to estimate the material costs for the following year. A cost uncertainty index (CUI) value is also used on top of the inflation to account for any uncertainties. The average inflation values of 2.4, 2.5, 3.0, 3.5 and 3.2 percent were used respectively for 2001 – 2005 along 162

Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

with a fixed CUI value of 1.5 percent. For example, the actual material cost value of £507 for MQ4033 obtained at the end of year 2002 was used to estimate for the year 2003 to be £530. Table 6-5 gives out the estimated material cost values for the given product range predicted by the company for 2003 – 2005.

6.3.3

Labour cost estimation

The total labour cost in a given year for the SPSD is the summation of the wages paid to all the workers in both the fabrication and the assembly units for that year. The yearly capacity is given in man-hours and is calculated by multiplying the number of working days in a year, the average number of shifts per day, the number of hours per shift and the average number of workers working per shift. The total labour cost obtained at the end of a given year is divided by the capacity to provide an aggregate shop floor-wide labour rate. Table 6-6 provides the aggregate labour rate values for the respective years.

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Table 6-6: Aggregate labour rate calculation

2001

2002

2003

2004

2005

1

1

1

1

1

250

250

250

250

250

No. of hours per shift

8

8

8

8

8

No. of workers per shift

21

26

26

26

26

Capacity (man hours)

42,000

52,000

52,000

52,000

52,000

Total Wages (£)

240,120

336,600

387,000

460,080

507,600

5.72

6.47

7.44

8.85

9.76

Shifts per day No. of working days per year

Aggregate Labour Rate (£/hr)

Based on the lead times and number of workers working on different products in each of the shop floor units, the total man-hours for individual products can be calculated as shown in Table 6-7. The labour rate available at the end of a given year is used for the following year to estimate the labour costs for individual products by multiplying the rate with the products’ corresponding man-hour values. For example, the labour rate of 6.47 £/hr obtained at the end of 2002 was set as an estimated rate for the following year giving an estimated labour cost value of £337 in the year 2003 for MQ4033. Table 6-7 tabulates the estimated labour costs also.

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Table 6-7: Total man-hours and estimated labour costs (2003 – 2005) for the given product range

Product

Fabrication Unit

Lead

Lead

time

time

(min)

(hr)

MQ4033

240

MQ4030

Assembly Unit

Lead

Lead

time

time

(min)

(hr)

20.0

240

5

27.5

3.0

6

150

2.5

MQ2538

220

MQ1033

No. of

man-

workers

hours

4.0

5

330

5.5

MQ4024

180

MQ3522

Total

No. of

man-

man-

workers

hours

hours

4.0

8

32.0

200

3.3

5

18.0

220

3.7

6

15.0

180

3.7

7

25.7

120

2.0

6

GQ4026

220

3.7

GQ4024

120

2.0

6.3.4

Estimated Labour Cost (£)

2003

2004

2005

52.0

337

387

460

16.7

44.2

286

329

391

4

14.7

32.7

211

243

289

3.0

6

18.0

33.0

214

246

292

180

3.0

6

18.0

43.7

283

325

386

12.0

100

1.7

4

6.7

18.7

121

139

165

6

22.0

230

3.8

5

19.2

41.2

266

306

364

3

6.0

180

3.0

3

9.0

15.0

97

112

133

Overhead estimation

Overhead costs at the company refer to all the costs other than material and labour costs. Overheads incurred in a given year are known at the end of a financial year. The overheads incurred in that year are summed up and divided by the man-hour capacity to give the overhead rate. The rate is used for the following year to estimate the overheads likely to be incurred on individual products by multiplying it with the corresponding man-hour values for the products. Table 6-8 details the yearly overheads in £s obtained at the end of each 165

Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

financial year. Scrap values are presented in negative to show the salvage value. The individual overhead cost elements represent categories with like costs. Indirect material here not only represents the cost on material used for shared benefits of products but the tools utilized. Since the tooling is not heavy with comparatively lower costs, the company has not assigned a separate cost pool for the tooling cost. Insurance costs here refer to the costs of insuring machinery, equipment, building and all other insurable items. However, the costs of insuring the equipment and machinery are higher than any other insurance costs. Any costs not incurred for the direct benefit of the SPSD but for the shared benefit of the company are charged proportionately.

Total actual production cost for a year can be calculated by summing the total material, wages and overheads in that year and are also given in Table 6-8. The estimated values for product costs using the company’s method can now be given by summing the three estimated elements: material, labour and overheads as mentioned in Table 6-9. The table also gives the cumulative values for the estimated production costs (2003 – 2005).

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Table 6-8: Overhead costs for individual elements (2001 – 2005) 2001

2002

2003

2004

2005

Indirect material

55050

56500

64200

75200

75800

Stores & Inventory control

45600

48900

54200

56240

62450

Freight & Transportation

35200

39900

58200

62400

85240

Material Inspection

24500

25600

26500

27000

27560

Purchasing

17800

18970

19250

21130

25360

Packaging

26050

27700

32540

45230

51230

Material handling

16890

17290

19260

19265

21450

Insurance cost

67300

69500

72000

88000

98400

Financing Expenses

24500

28000

36000

42000

45000

Maintenance Cost

20850

25424

38586

51384

62598

Repair Cost

18853

21220

38106

25814

41852

Energy cost

57200

65000

98000

130000

160000

Computer related cost

44280

45550

64870

85925

105425

General admin cost

139660

145650

182560

210220

238954

Selling Expenses

95255

109245

132364

194500

256450

(Scrap)

-34350

-36800

-37850

-39250

-38256

Total Overheads (actual)

654,638

707,649

898,786

1,095,058

1,319,513

15.59

13.61

17.28

21.06

25.38

1,983,223

2,192,384

2,534,222

2,895,843

3,200,353

Overhead rate (£/hr) Total production cost (actual)

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Table 6-9: Estimated product cost values (2003 – 2005) Product

Estimated product cost per unit

Estimated production cost (Cumulative)

2003

2004

2005

2003

2004

2005

MQ4033

1574

1840

2129

629579

892490

689762

MQ4030

1326

1555

1802

305059

311029

477660

MQ4024

1946

2178

2407

321139

413818

421251

MQ3522

1444

1630

1845

194918

268905

341409

MQ2538

1779

2035

2311

640397

702155

873572

MQ1033

640

737

862

288117

234996

272356

GQ4026

1200

1409

1619

357726

471852

461284

GQ4024

475

549

621

166425

134603

204425

2,903,361

3,429,848

3,741,718

Total

6.4

Implementation of the PCE Hybrid Model

The developed model presents the estimated product cost as a summation of manufacturing cost, engineering cost and production overheads. Since the engineering designs for the SPSD are already established, the engineering costs in terms of design and development expenditures are negligible. Any minor costs within the context are incurred at the ASSD and subsequently charged to the SPSD within general administration overheads. These costs were not separately provided by the company. Manufacturing cost and production overheads would, therefore, add up to the estimated product cost for an individual product. 168

Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Manufacturing cost is presented as material, labour and indirect manufacturing costs. Indirect manufacturing costs comprise processing, material-dependent, tooling and building space costs. Any cost incurred on tooling at the company is not separately recorded but combined with the indirect material cost and would form part of material-dependent cost (MDC) estimation. Plant-wide building maintenance, repair and energy costs are allocated in proportion to the industrial output and charged to the division and subsequently combined with equipment & tool maintenance, repair and energy costs respectively. These costs would, therefore, be dealt with part of processing cost estimation. Manufacturing cost estimation in this case would be the sum of material, labour, processing and MDC.

The application of the HMI algorithm presented in section 6.2 can be followed from the following sub-sections in order to facilitate the implementation of the Hybrid Model and generate estimated cost values.

6.4.1

Material cost estimation

Material cost estimation using the presented Hybrid Model required calculation of material cost deviation index, φ n +1 . Material cost deviation trends from the past years could be used to predict the index values for the following years based on the model derived (see appendix B) as follows:

n  C mp  −1− I n  n − 1 C   mp 

φ pn +1 = I n +1 + (1 + I n +1 ) × 

(6-1)

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Where, φ pn +1 is the deviation index for the pth product estimated for the following year. I n n and and I n+1 are the interest rates in the current and the following year respectively. C mp n −1 C mp are the material costs for the pth product in the current and the preceding year

respectively.

Table 6-10: Material cost deviation index and estimated unit material cost values (2003 – 2005)

Estimated unit material cost (£)

Material cost deviation index (%)

(Hybrid Model)

φ pn +1

Product

2003

2004

2005

2003

2004

2005

MQ4033

518

553

567

2.26

4.71

3.50

MQ4030

427

465

479

1.53

5.45

4.03

MQ4024

1257

1387

1426

1.84

6.29

4.41

MQ3522

796

808

866

6.48

4.20

5.58

MQ2538

931

965

1010

7.86

6.01

5.26

MQ1033

276

272

321

8.74

3.67

10.62

GQ4026

404

389

366

12.90

4.55

-0.97

GQ4024

169

174

159

1.53

2.40

-3.45

5.39

4.66

3.62

Average index ( φ

n +1

)

By using all the known values, the model can predict the indices for the product range for the following year. The values can then be used to predict the estimated material cost 170

Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

values. An average index value can also be used for the purpose but it may compromise the accuracy of the individual results. However, the purpose of the average value is best served for a new product with no known past data. The material cost values available at a given time and the average index value can then be used to predict the product cost for the following year. Table 6-10 gives out the indices and the estimated material cost values.

6.4.2

Labour cost estimation

Labour cost estimation using the hybrid method requires the estimation of shop floor-wide aggregate labour rate and the labour units consumed for each product. The lead times for the individual products in the two work centres and the corresponding data obtained from the company for the number of skilled (x), semi-skilled (y) and non-skilled (z) workers required to manufacture the respective products can be used to determine labour units for each product. Skill indices of 0.75 and 0.35 were set for semi-skilled and non-skilled workers respectively based on an average skill level of around 75 and 35 percent with respect to their skilled counterparts. Table 6-11 tabulates the labour units in hours required for the manufacture of the individual products. The table also calculates the total number of labour units consumed in each year using the data for the number of units produced in corresponding years.

The total labour units and the total wages paid in a year can be used to determine the labour rate for that year. The rate can then be used to determine the estimated labour rate for the following year by considering the LCDI, ε n +1 for the following year. The LCDI values can

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

be found by using the equations (B-6), (B-7) and (B-8). Average monthly wages of the skilled, semi-skilled and non-skilled workers obtained from the company were used for that purpose. The average index values as obtained can be used to determine the estimated labour rates. The estimated rates can be used to generate estimated labour costs for individual products based on their respective labour units as shown in Table 6-12.

Table 6-11: Labour units calculation Product

Fabrication

Assembly

Total labour units consumed

Labour Units

x

y

z

x

y

z

(hr)

2001

2002

2003

2004

2005

MQ4033

1

2

2

2

3

3

34.00

14620

15300

13600

16490

11016

MQ4030

2

2

1

2

1

2

32.68

8659

8169

7515

6535

8659

MQ4024

1

2

3

2

1

1

22.02

3192

3303

3633

4183

3853

MQ3522

2

1

3

2

2

2

22.10

3868

3315

2984

3647

4089

MQ2538

2

3

2

1

2

3

28.80

8064

9360

10368

9936

10886

MQ1033

1

2

3

1

1

2

11.18

4831

4194

5033

3567

3534

GQ4026

2

1

3

2

1

2

27.16

7197

6654

8093

9098

7740

GQ4024

1

1

1

1

1

1

10.50

3339

3413

3675

2573

3455

Total

53770

53706

54900

56029

53231

α β

0.75

0.75

0.35

0.35

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Table 6-12: Labour cost deviation index and estimated labour costs Average wages per month (single

Labour cost deviation

employee) (£)

index (%)

2001

2002

2003

2004

2005

2003

2004

2005

Skilled

980

1100

1290

1580

1700

13.04

18.27

22.79

Semi

810

950

1080

1280

1400

18.23

14.56

650

800

910

1050

1200

24.19

18.49

Nonskilled

Average Index ( ε

n +1

)

Labour Rate (Hybrid Model) (£/hr) Actual Estimated

6.4.3

4.47

6.27

Product

Estimated unit labour cost (£) 2003

2004

2005

MQ4033

248

273

326

18.70

MQ4030

248

272

326

14.63

15.46

MQ4024

165

181

217

15.82

18.98

MQ3522

167

183

219

MQ2538

210

231

277

7.05

8.21

9.54

MQ1033

82

90

107

7.43

8.16

9.77

GQ4026

208

228

273

GQ4024

79

86

103

Processing cost estimation

The total processing costs spent on the shop floor refer to the necessary costs to keep the floor facilities in the running condition. Financing expenses, insurance, maintenance, repair and energy costs obtained at the end of the financial year add up to the total processing costs for the year. Processing costs for a product can be estimated by multiplying the estimated rate with the processing units of the product. Processing units refer to the total time the product spends on the work centres while being processed. The combined lead time, therefore, for a given product spent on the fabrication and the assembly units would

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

refer to the processing units for the product. The total processing costs for a given year and the total processing units consumed in that year can be effectively utilized to produce the processing rate for the year.

Table 6-13: Estimation of processing units, deviation indices, rates and costs

Product

Estimated processing

Processing units (Total)

Processing

cost per unit (£)

Units (hr) 2001

2002

2003

2004

2005

2003

2004

2005

MQ4033

8.00

3440

3600

3200

3880

2592

128

198

216

MQ4030

8.83

2341

2208

2032

1767

2341

142

219

238

MQ4024

6.67

967

1000

1100

1267

1167

107

165

180

MQ3522

5.50

963

825

743

908

1018

88

136

148

MQ2538

6.67

1867

2167

2400

2300

2520

107

165

180

MQ1033

3.67

1584

1375

1650

1170

1159

59

91

99

GQ4026

7.50

1988

1838

2235

2513

2138

120

186

202

GQ4024

5.00

1590

1625

1750

1225

1645

80

124

135

Total

14738

14638

15109

15028

14578

Processing costs (Total)

188703

209144

282692

337198

407850

Processing rate (actual)

12.80

14.29

18.71

22.44

27.98

) (%)

12.37

32.42

20.15

16.06

24.78

26.96

Processing cost deviation index ( µ Processing rate (estimated) (£/hr)

n +1

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

However, predicting the rate for the following year would require considering any processing costs deviations. The method for calculating such deviations mentioned earlier can be used to predict the PCDI values, µ n +1 , for the following year by using the equation (B-9). The PCDI values can then be used to generate the estimated processing rates.

Estimated processing costs can then be determined for the range of products. Table 6-13 covers the estimation of processing units per unit and the total processing units required in a given year. It also calculates the rates and the deviation index values and then gives out the estimated processing cost per unit for the given products.

6.4.4

MDC estimation

The total MDC for the SPSD for a given year is obtained by summing up indirect material, stores and inventory, freight and transportation, material inspection, purchasing, packaging and material handling costs and subtracting the scrap value for that year. MDC per unit material consumed can then be used to determine the MDC deviation index ( ρ n+1 ) values using the method described earlier and given by equation (B-10). This allows the estimation of the MDC per unit material cost for the following year resulting in the estimation of the MDC per unit of the corresponding products for that year. Table 6-14 outlines all these values.

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

Table 6-14: MDC deviation index and estimated MDC per unit values

n

Total MDC ( C md ) (£) n

Cumulative material cost ( C mt ) (£) n

n

MDC fraction ( C md / C mt ) MDC deviation index ( ρ

n +1

) (%)

2001

2002

2003

2004

2005

186,740

198,060

236,300

267,215

310,834

1,088,465

1,148,135

1,248,436

1,340,705

1,373,240

0.172

0.173

0.189

0.199

0.226

0.99

10.46

5.06

0.174

0.209

0.209

Estimated MDC fraction ( C md / C mt )x( 1 + n

n

ρ n+1 )

Product

Estimated MDC per unit (£)

MQ4033

90

116

119

MQ4030

74

97

100

MQ4024

219

290

299

MQ3522

139

169

181

MQ2538

162

202

212

MQ1033

48

57

67

GQ4026

70

81

77

GQ4024

29

36

33

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

6.4.5

Production overheads estimation

The total PO for the SPSD in a given year can be obtained by adding selling expenses, computer related costs and general administration costs. The total actual manufacturing costs for the SPSD in a year refers to the summation of the cumulative material costs, total wages, total MDC and the total processing costs incurred in that year.

Table 6-15 PO fractions (actual & estimated) and deviation indices 2001

2002

2003

2004

2005

1,704,028

1,891,939

2,154,428

2,405,198

2,599,524

279,195

300,445

379,794

490,645

600,829

Total manufacturing cost (actual) n

( CGt ) (£) n

Production overheads ( Ot ) (£) n

n

PO fraction ( Ot / CGt ) PO deviation index ( τ

n +1

0.164 ) (%)

0.176 -2.74

Estimated PO fraction ( Ot / CGt )x( 1 + τ n

0.159

n

n +1

)

0.154

0.204 11.79

0.197

0.231 15.81

0.236

The total PO and the total manufacturing costs can be used to establish the PO fractions and subsequently the estimated values of PO fractions. The estimated values of the fractions require the calculation of the PO deviation indices, τ n+1 using the method mentioned earlier for the calculation of the indices and given by equation (B-14). Table 6-15 explains the calculation of the fractions and the indices. By adding the already estimated manufacturing cost elements, the estimated values for manufacturing costs for individual products in a

177

Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

given year can be obtained. These values and the corresponding estimated PO fractions can be used to estimate the production overheads for the individual products. Estimated product cost can then be determined by combining the manufacturing and the PO cost elements estimated for the product. Table 6-16 tabulates the estimated manufacturing, PO and product costs per unit.

Table 6-16: Estimated per unit values for manufacturing, PO and product costs Estimated product

manufacturing cost per unit (£)

Estimated production

Estimated product cost per

overheads per unit (£)

unit (£)

2003

2004

2005

2003

2004

2005

2003

2004

2005

MQ4033

990

1144

1234

153

225

291

1142

1370

1525

MQ4030

886

1048

1136

137

207

268

1023

1254

1405

MQ4024

1747

2022

2120

270

398

501

2017

2420

2621

MQ3522

1187

1293

1411

183

255

333

1370

1548

1745

MQ2538

1414

1567

1683

218

309

398

1633

1875

2081

MQ1033

466

511

596

72

101

141

538

611

737

GQ4026

796

878

911

123

173

215

919

1051

1126

GQ4024

357

420

430

55

83

102

412

503

532

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Chapter 6: Industrial Implementation and Analysis of the PCE Hybrid Model

6.5

Conclusions

This chapter discussed the implementation of the Hybrid Model in a batch manufacturing environment in the UK as part of the validation process for the model. The implementation phase involved the retrospective application of the PCE Hybrid Model along with the company’s method of cost estimation. The implementation of the Hybrid Model was facilitated by the HMI algorithm. Cost data at the end of a given year were effectively used with the help of the proposed deviation indices, resulting in furnishing the estimated costs for the given product range well before the actual manufacturing started.

It was noted that the Hybrid Model with the help of the HMI algorithm generated detailed cost breakdown values for every product. The company’s method was not able to predict such breakdown values. The provision of breakdown values is helpful in identifying high cost elements and subsequently helps in making cost control decisions. The cumulative cost values were also obtained that can be helpful in making statistical and financial analysis of the cost data at the organizational level. Such analyses support key operational and strategic decisions for middle and senior management.

The Hybrid Model attempted to overcome the limitations associated with TRO and MRO models. For example, inflation and other cost deviations were incorporated through the introduction of deviation indices that also optimized the use of past data. The use of normal capacity hours during labour cost and overheads (indirect costs) calculation was replaced by a new method based on calculating labour and processing units etc.

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Deviation indices are crucial to the overall accuracy of the estimated results and as such demand further investigations. For example, there is a need to investigate the effects of more than two years past cost trends. The HMI algorithm can also be made more generic by adding components for tooling and building space costs calculation in line with the Hybrid Model. Care should be taken while categorizing the indirect elements to different subcategories. For example, material handling costs are categorized under material-dependent costs based on its relation with the increasing material quantity. Increased material quantities result in increased handling and thus in increased costs. However, an increased handling time should not be confused with processing time and the resulting costs should not be categorized under processing costs. Because processing costs are based on job processing times at work or machine centres. On the other hand, an increased material handling time is accounted for in increased material quantities. Similar care should be taken for other overheads elements.

In short, previous limitations found in TRO and MRO estimation methods were removed. The obtained results are compared in the next chapter for the validation analysis.

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Comparisons and Validation Analysis

The aim of Chapter 7 is to validate the developed PCE Hybrid Model by comparing the estimated costs obtained in the previous chapter and in the current chapter against the actual costs for a range of products. The process will involve analysing the costs at different levels including the entire product costs, cumulative production costs, overheads for an individual product and overheads at cumulative level. The chapter will also present a breakdown analysis.

7.1

Introduction

The route to successful validation is inscribed in achieving the objectives. This in turn requires outlining the validation method. In Chapter 4, the MRO and TRO estimation methods were presented, implemented and validated by comparing the results obtained from the application of the model with those generated by the company’s method. The model presented in Chapter 5 is more comprehensive and requires more than just scrutinizing it against an in-house methodology. A decision, therefore, was made to implement a published model and obtain the estimated cost results from its application alongside the already obtained results in Chapter 6 from the application of the PCE Hybrid

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Model and the company’s method. The three results will then be compared against the actual product costs. Comparing the estimated product costs from the three methods against the actual costs can only strengthen the argument to justify the superiority of the developed methodology. The newly developed Hybrid Model was therefore, implemented alongside a published model in the selected manufacturing company for a retrospective analysis of three years (2003 – 2005).

Chapter 7 presents the comparisons and validation analysis. This is based on comparing the estimated cost values (2003 – 2005) obtained using the three methods (the company’s method, the selected published model and the Hybrid Model) against the actual cost values provided by the company and given in Table 6-3, Table 6-4, Table 6-6 and Table 6-8. An analysis of the cost variations from the actual costs is presented by not just considering the cumulative production costs but the individual product costs and the cost elements, where possible. Almost every level of the analysis demonstrates the superiority of the developed model. An analysis for cost elements breakdown based on the actual production costs is also drawn. The breakdown results obtained highlight the typical tendencies of the region through the analysis of a representative case. The analysis when compared with the results obtained for the South Asian region presented in Chapter 4 provides the basis for understanding and developing an effective CCS.

The actual product cost values were provided by the company and calculated based on the actual cost figures obtained from the cost accountancy data at the end of each year. These considered the actual material and labour costs. Material costs considered the actual 182

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material quantities and wastage. Labour costs were based on the actual time spent on a product or a batch of products taken from the time cards on the shop floor. Any other costs were allocated to the products based on either activity rates and units or their traceability to the products. For example, material handling, stores & inventory, inspection and quality control costs were allocated based on activity rates and units. Freight & transportation, packaging, financing expenses etc. were in most cases traceable to the products. However, any exact method for their calculation was not given by the company.

Before the validation analysis, the results from a published model would be obtained in order to compare the three estimated results against the actual costs. Section 7.2 details the cost estimation results for the given product range using the selected published model as a representative case from the domain. The section, therefore serves the preparation before comparison analysis. Section 7.3 presents the product cost analysis based on comparing the estimated product costs from the three methods against the actual costs. Section 7.4 compares the estimated and the actual cumulative costs. Section 7.5 analyses estimated and actual overheads at product and production level. Section 7.6 presents a statistical analysis of cost breakdown results. Section 7.7 concludes the chapter.

7.2

Preparations for comparisons

The purpose of the implementation of a published model is to validate the developed model by not just comparing it against the industrially established tool but to present its

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superiority against an already established and recognized representative case from the published research domain. Therefore, the selected model should already have been tested. In order to draw comparison between the developed and the published models, it is essential that the published model should have the necessary parameters to be applicable within the framework of the manufacturing enterprise. The available field data should form the basis for the selection of the model and to further evaluate costs.

The model presented by Jung [84] was selected for the implementation and validation purposes as it not only complied with the above criteria but is established in the field. Jung described major cost elements as material, labour, engineering and burden cost. He did not model engineering costs but manufacturing costs were presented as follows:

Mfg cost = (Ro + Rm)[( Tsu/Q)Tot + Tno] + material cost + factory expenses

(7-1)

where, Ro = operator’s rate, Rm = machine rate, Tsu = set-up time, Q = batch size, Tot = operation time, Tno = non- operation time.

Three different times are considered but refer to the manufacturing lead time (MLT) time for a product. Labour and machine related costs were described using the MLT. Burden cost or factory expenses refer to the costs other than material, labour and machine related costs and can be considered as the overheads spent for the combined benefit of all the products. In an industrial environment where engineering costs are relatively low, negligible or accumulated with the overheads, Jung’s model refers to the overall product 184

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cost. In the given conditions where engineering costs, if any, are part of the general administration costs, the model can predict product costs. The major cost elements, therefore, comprise labour and machine costs, material cost and factory expenses.

7.2.1

Labour and machine cost estimation

Labour and machine cost estimation using Jung’s model requires the operator’s and machine rates calculation. The operator’s rate (Ro) is based on the shop floor’s direct labour cost. The total wages can, therefore, be divided by the shop floor-wide cumulative MLT to obtain the rate. The floor-wide MLT in a given year can be obtained by lead times of the individual products and the respective number of units produced in that year. Similarly, machine running costs (maintenance, repair and energy costs) can be divided by the total MLT to determine the machine rates (Rm).

The obtained rates at the end of a given year can be used for the following year’s labour and machine cost estimation process by considering the effect of inflation in that year. Since, Jung’s model does not describe the ways to consider any cost variances, only the known variation (i.e. average inflation) is considered for the estimation purposes. The summation of the estimated rates can be multiplied by the individual lead times to estimate the labour and machine costs for individual products. Table 7-1 tabulates the lead times (individual and cumulative), machine running costs (the summation of maintenance, repair and energy costs), the rates (operator and machine) and the estimated labour and machine costs per unit.

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Table 7-1: Lead times, machine running costs, rates (operator and machine) and labour and machine costs

Product

Manufacturing lead time (MLT) (total)

Labour and machine cost

(hr)

per unit (£)

Lead time per unit (hr) 2001

2002

2003

2004

2005

2003

2004

2005

MQ4033

8.00

3440

3600

3200

3880

2592

252

308

367

MQ4030

8.83

2341

2208

2032

1767

2341

279

340

405

MQ4024

6.67

967

1000

1100

1267

1167

210

257

305

MQ3522

5.50

963

825

743

908

1018

173

212

252

MQ2538

6.67

1867

2167

2400

2300

2520

210

257

305

MQ1033

3.67

1584

1375

1650

1170

1159

116

141

168

GQ4026

7.50

1988

1838

2235

2513

2138

237

289

344

GQ4024

5.00

1590

1625

1750

1225

1645

158

192

229

14738

14638

15109

15028

14578

16.29

23.00

25.61

30.61

34.82

96,903

111,644

174,692

207,198

264,450

6.57

7.63

11.56

13.79

18.14

Total (hr) Operator's rate (Ro ) (£/hr) Machine running cost (£) Machine rate (Rm) (£/hr)

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7.2.2

Material cost and factory expenses

The amounts of all the material used for the manufacture of a product and their unit prices can be used to ascertain the total material cost of the product. The only known cost deviation (i.e. the average inflation) can then be accounted for in order to predict the total material cost for the product for the following year. For example, the material cost of £522 can be set for MQ4033 for 2003 based on the known value of £507 from 2002 and the inflation rate of 3 percent for 2003.

Ascertaining the factory expenses for an individual product requires the calculation of an expenses rate. The rate can be calculated by dividing the total factory expenses from the cumulative MLT for a given year. The rates after taking into account any deviations effect (inflation in this case) for the following year can be multiplied by the total lead times of the products to furnish their corresponding estimated factory expenses values in that year. Whereas, the total factory expenses for a given year can be obtained by summing all the costs other than material and labour costs. Since, the maintenance, repair and energy costs were considered in the calculation for machine related costs; they would also be excluded from the factory expenses. The estimated product costs can then be given by adding the corresponding factory expenses, material, labour and machine cost components. Table 7-2 calculates the factory expenses rate, the estimated factory expenses per unit and the estimated product costs per unit.

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Table 7-2: The total factory expenses, the expenses rate, the estimated per unit values (factory expenses, product cost) (2003-2005)

Factory expenses (Total) (£) Factory expenses rate (£/hr) Product

2001

2002

2003

2004

2005

557,735

596,005

724,094

887,860

1,055,063 Estimated product cost per

37.84

40.72

47.92

59.08

72.37

unit (£)

Estimated factory expenses per unit (£)

2003

2004

2005

MQ4033

336

397

488

1110

1251

1420

MQ4030

370

438

539

1082

1234

1418

MQ4024

280

331

406

1762

1938

2122

MQ3522

231

273

335

1174

1287

1434

MQ2538

280

331

406

1379

1529

1703

MQ1033

154

182

224

531

594

691

GQ4026

315

372

457

919

1046

1183

GQ4024

210

248

305

539

616

704

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7.3

Comparison analysis for product cost

The estimated product costs using the Hybrid Model (new method), the company’s method and the Jung’s model mentioned in Table 6-16, Table 6-9 and Table 7-2 respectively can be plotted against the actual product costs given in Table 6-3.

Figure 7-1 gives the cost comparison for the entire product range for the three year period (2003 – 2005). The green vertical columns represent the actual costs for respective products. The other three dotted lines represent the estimated product costs. The analysis clearly shows the superiority of the Hybrid Model as the dotted line representing the results from the Hybrid Model remains closer to the green vertical bars (the actual costs). For example, the estimated costs of £1110, £1574, £1142 were given by the Jung’s model, the company’s method and the Hybrid Model respectively for the year 2003 against the actual product cost of £1197 for the same year.

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Figure 7-1: The comparison of the actual costs against the estimated costs

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Any deviation of the estimated cost values from the actual cost represent the estimation error linked with a given estimation method. In addition to the cost analysis presented earlier, there is a need to analyse the estimation errors using the three methods. The estimation error trends using the three methods for the investigation period are given in Figure 7-2. Error estimations are based on deviations from the actual costs and presented in percentages. The actual cost is represented by the x-axis with zero error. It is clear that on almost every occasion the estimated values predicted by the Hybrid Model are closer to the actual values than those predicted by the other two methods. Although on an isolated case (MQ4030), the Jung’s model predicted slightly better values, the Hybrid Model’s prediction was not only within the acceptable limit for that case but the overall accuracy is far more consistent. It can be seen that a cautious approach by the company’s adopted method resulted in not just overestimation on almost every occasion but resulted in as much as 40 percent error. This was mainly due to an effort to avoid under estimating and setting a price more than the actual cost value. However, the loss of goodwill and sales as a result of overestimation could far outweigh any apparent profits as a result of overestimation resulting in net loss of potential profits. A yearly cost rise in the actual values and the estimated values is also visible due to an increase in almost all the cost element values. Jung’s model underestimated on many occasions partly because of no provisions in the model for considering cost variances that could be useful in keeping up with the cost trends. Only the known variances were accounted for. Both under- and over- estimations were observed within acceptable limits using the Hybrid Model. It is also clear that the use of deviation indices has eliminated the problem of underestimation associated with the TRO and MRO methods presented in chapter 4.

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Figure 7-2: Estimation error trends for the three methods (2003 – 2005)

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It is not uncommon in an industrial environment to focus on net error estimation analysis. While some of the products during a given period may be highly overestimated, the others remain underestimated. The net estimation error may be within acceptable limits. However, the approach can be dangerous as some of the products may be priced very low while the others could be highly priced. This could lead to losses on individual products due to underestimation. On the other hand, those overestimated and thus over-priced products could also result in loss of consumer confidence and loss of market. Therefore, instead of relying on net error estimation, there is a need to estimate individual product’s cost accurately.

An analysis based on a yearly consolidated representation for the investigated period considering the entire product range is given in Figure 7-3. Error estimation values are also given. Big error distributions across the product range are seen in a given year using both the company’s and the Jung’s method. The company’s method overestimated for almost the entire product range throughout the investigation period. Jung’s method mostly under estimated for the given product range throughout the investigation period. The values estimated by the Hybrid Model were either underestimated or overestimated within very close range of the actual costs. In any given year, the values were evenly spread across the entire product range.

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Figure 7-3: Percentage cost estimation variations from actual product costs.

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In order to visualise better the error distribution trends across the product range for a given year using the three methods, results are presented in Figure 7-4. The error trends for a given year demonstrate the effectiveness of the Hybrid Model when compared with the other two methods. Huge fluctuations are seen for the estimation error values using either the company’s method or the Jung’s model across the entire product range for the three year period. The Hybrid Model’s estimation trends, on the other hand, are clearly even and stay close to the actual values. In terms of not just the accuracy, but the consistency of the results, the Hybrid Model can be seen as a superior methodology. Estimation errors displayed on various occasions are almost negligible unlike those displayed by the other two methods. The effective use of the past data along with accurate prediction of the various indices is behind the accurate prediction of the overall product costs among other factors. Such precision is mainly down to eliminating the already observed shortcomings in the methodology presented in Chapter 4.

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Figure 7-4: Estimation error trend across the product range

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Due to huge fluctuations of estimation error across the entire product range using the two methods, some of the products may be highly over estimated while the others highly underestimated resulting in unrealistic price settings. Such a situation could have serious implications for the business objectives of an enterprise. Many companies tend to even out the errors by linearizing the error distribution. Even any error linearization could do little to help the situation. For example, the linearization of the errors for the company’s method could help to even out the error distribution across the product range, but the overall error still stays unreasonably high (around 20 percent) as shown in Figure 7-5. Most importantly, such a linearization has little practical implications as such a comparison requires the actual costs which are not discovered until usually the products are produced with price quotes already furnished. However, for statistical analysis and accuracy optimization (based on the rectification of the consistently inaccurate trends) purposes, such results can be helpful. Past error distribution trends, however, may have to be used and relied upon at increased risk of compromising the accuracy for future results.

Similarly, the linearization carried out for both the Jung’s model and the Hybrid Model are shown in Figure 7-6 and Figure 7-7 respectively. The linearization of the errors for the Jung’s model finds the underestimation of up to around 20 percent and an overestimation of around 10 percent. The values for the Hybrid Model, on the other hand, do not exceed 5 percent for both under and overestimation.

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Figure 7-5: Error linearization for the results given by the company’s method

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Figure 7-6: Error linearization for the results given by the Jung’s method

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Figure 7-7: Error linearization for the results given by the Hybrid Model

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Another point noticeable from Figure 7-7 is a changing response for error estimation trend on yearly basis as opposed to the ones presented in Figure 7-5 and Figure 7-6. This is due to the fact that the Hybrid Model takes into account the changing factors to estimate costs. Factors like, inflation rate, expected cost deviations etc. are accounted for very well and by adjusting the response, the estimated values are always kept close to the actual costs. The incorporation of the case-based technique into the modelling framework is also responsible for sensitizing the model by keeping it aligned with the changing trends. While the model is sensitized to the trends, its robustness remains unquestionable. The overall validation analysis spread over a three-year period covering a range of products under varying conditions and huge fluctuations of cost deviations still produced consistent results within acceptable limits of error estimations. The estimated values are, therefore, reliable and can serve the operational purposes (such as price setting, cost control, lot sizing, etc.) well. More strategic decisions can also be relied upon (such as make or buy decisions, business resizing, etc.). The results produced by the other two methods are hugely desensitized to the changing cost trends and consistently produced results with huge estimation errors and unchanged trends. Although, the statistical data analysis can help to exploit the error consistencies to manually adjust the estimated values, the process would not be risk free and the essence of using an estimation method will be lost.

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7.4

Comparison analysis for cumulative costs

In addition to the analysis for individual products, it is essential to carry out the validation for the cumulative cost values. This is also necessary to quell any notion of a possible selfadjustment of individual under and overestimation on the cumulative level. This means an attempt will be made to determine if any under or overestimation at product level even out each other at cumulative level. In other words, the current analysis is aimed at finding out if a methodology less accurate at estimating individual product costs can be more accurate at cumulative level. This would be done by comparing the total actual costs incurred in the SPSD during a given period against the cumulative values for the estimated results obtained by using the three methods.

Figure 7-8 (a) compares the three estimated cumulative costs with the actual costs at the cumulative level. The values are given in million £. The black line representing the actual costs stays closer to the green vertical bars representing the estimated values given by the Hybrid Model (new method). Figure 7-8 (b) quantifies the estimation error. The estimation error values represent the percentage deviations from the actual costs. The estimated values predicted by the Hybrid Model at the cumulative level fluctuated between -3 and 2 percent for the overall period of the investigation. The company’s method overestimated on the cumulative level by as much as around 19 percent despite fluctuating under and overestimation values at individual levels. The Jung’s model, on the other hand, underestimated costs by around 9 percent at the cumulative level despite fluctuating values at the individual products. This demonstrate that even after taking into account any

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adjustments of fluctuating values for individual products at the cumulative level, high degree of under and overestimations were observed using the two methods.

Millions

Cost Values (£s)

Actual Cost Vs Estimated Cost

(a)

4.0 3.5 3.0 2.5 2.0 2003

2004

2005 Production Year

Total Estimated Production Cost (Jung's)

Total Estimated Production Cost (Comapny)

Total Estimated Production Cost (New )

Total Production Cost (Actual)

Estimation errors from cumulative actual costs (%)

(b)

20

Estimation variation (%)

14.57

18.44

16.92

10 1.79 0

-3.01 2003

-10

-7.66

-1.17 2004

2005

-8.40

-9.29

Production Year -20 Estimation error using Jung's model (%)

Estimation error using company's method (%)

Estimation error using hybrid model (%)

Figure 7-8: (a) Cumulative actual costs against total estimated values, (b) estimation errors for cumulative costs

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The Hybrid Model remained close to the actual costs at the cumulative level of prediction. Even if the cumulative results for the two methods were closer to the actual costs after considering any adjustments, the impact of huge under and overestimation on individual products could not be ignored. However, more accurate results for the Hybrid Model even at the cumulative level demonstrate the ultimate superiority of the model over the two methods considered. In addition, the highly accurate values predicted by the Hybrid Model both at the individual and the cumulative levels with consistency would be very difficult for any other method (not considered in the current validation analysis) to rival.

The Hybrid Model gives out optimized values at the cumulative level (i.e. more accurate than those predicted by the other two methods). The quantification of the optimized values against the two methods is shown in Figure 7-9. The results are based on considering the estimation error values for the cumulative costs. Only the error values in the respective years are considered ignoring the symbolic negative signs, if any (meant for showing underestimation), thus allowing the quantification of the deviations from the actual costs. The differences between the estimation error values for a given year using the Hybrid Model and the company’s method resulting in the optimized values are mentioned in the first part of the figure. Those based on the Jung’s model are presented in the second part. A maximum of over 16 and 8 percent optimizations were obtained against the company’s and the Jung’s methods respectively. Linearized trends are also included in both cases showing similar results even after adjusting the errors over the duration of the investigation. The results show significant improvements achieved by the Hybrid Model against the two methods.

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Optimization achieved 2003-2005 (%) 18.00

(a)

16.65 15.75

15.00

Optimization (%)

y = 2.09x + 10.47 12.00 11.56 9.00

6.00

3.00 2003

2004

0.00

2005

Production Year Optimization from company's method (%) Linear optimization trend from company's method (%)

Optimization achieved 2003-2005 (%)

(b)

10.00 8.12 8.00

Optimization (%)

6.61 y = 1.73x + 2.99

6.00 4.65 4.00

2.00 2003

2004 Production Year

2005

0.00 Optimization from Jung's model (%) Linear optimization trend from Jung's model (%)

Figure 7-9: Optimization for the estimation accuracy achieved by the Hybrid Model against (a) the company’s method (b) the Jung’s model

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7.5

Comparison analysis for product and production overheads

An important aspect of the validation analysis is to investigate the effects of the three methods on the accuracy of the breakdown elements. The accurate estimation of the breakdown elements would eventually lead to the accurate prediction of the overall product costs. Identifying the least accurate elements could help to better understand the problem areas in the existing methods and reason why the developed model is more efficient.

Direct and indirect elements are estimated in different ways using the three methods. Direct elements are easier to analyse because they are mainly estimated using the standard procedures. Since, the indirect costs were estimated with different approaches and comprise a larger portion of the overall product cost, it warrants investigation. The company’s method termed indirect costs as overheads. Factory expenses were considered using the Jung’s model and are part of the indirect costs. However, the machining costs have to be considered also for the total indirect costs. Processing cost, material – dependent cost and production overheads comprise the total indirect cost using the Hybrid Model. Since, the three methods divide the indirect costs into different elements; the best way to make an analysis is to consider the overall indirect cost or total overheads instead of considering any sub-levels.

In order to compare the estimated overheads using the three methods, the actual values of overheads incurred by different products are required. The actual values were obtained 206

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from the accountancy data at the end of a financial year and are allocated to individual products based on the ABC method. Activity rates are set and the activity times are based on the recorded values during a manufacturing phase. Although, the exact method was not disclosed by the company, the allocated overhead values for individual products were supplied.

The comparison of the estimated values for overheads using the three methods against the actual values is presented in Figure 7-10. The comparison is based on analysing the estimation error trends for the given product range. The error trends represent the percentage deviations from the actual costs. The solid lines represent the estimation error trends for the Hybrid Model. On almost every occasion, the estimation error produced by the Hybrid Model is not only lower than those presented by the other two methods but remains in acceptable limits. The company’s method largely overestimated overheads for individual products based on a cautious approach, whereas, huge fluctuations can be observed in the estimation errors for the product range using the Jung’s model. It is also noticeable that the estimation errors for overheads are greater than those for the overall product costs using all the methods. This refers to the complexities in predicting overheads accurately. The other elements must also be more accurately predicted such that the overall results stay more accurate than those for just overheads. Despite that the overheads predicted by the Hybrid Model stay within reasonable limits unlike those predicted by the other two methods.

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Figure 7-10: Estimation error trends for overheads using the three methods (2003 – 2005)

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Due to the inconsistent results shown by the two methods for the individual products, the cumulative overhead values are also analysed in Figure 7-11. The results are based on comparing the estimated and actual overhead values at the cumulative level using the three methods. The effects of adjustment result in the overall underestimation of overheads predicted by the Jung’s model by around 15 percent and those for the company’s method result in an overestimation of up to 32 percent. The values for the Hybrid Model varied between -12 and 4 percent. The results clearly demonstrate the superiority of the Hybrid Model over the other two methods for overheads estimation at both individual and cumulative levels of estimation.

Estimation errors for cumulative overhead (%)

Estimation variation (%)

40 30 20 10 0 2003

2004

2005

-10 -20 Production Year Estimation error using company's method (%)

Estimation error using hybrid model (%)

Estimation error using Jung's model (%)

Figure 7-11: Overheads estimation analysis for the cumulative values

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The above analysis leads to the quantification of the optimization achieved in the estimation of overheads as a result of using the Hybrid Model in comparison to the other two methods. The results are presented in Figure 7-12 (a) & (b) along with linearization. The optimization is based on considering the deviation values from the actual costs without considering the negative signs (meant for representing underestimation). The differences in the values of error estimation of the two methods against those shown by the Hybrid Model presented in the respective years result in the optimization values. For example, the overhead estimation values predicted by the Hybrid Model in 2004 were almost 29 percent more accurate as compared to those estimated by the company’s method. The optimization of around 14 percent was also achieved against the Jung’s model estimated values for overheads. For the purpose of statistical analysis, the linearized results are also incorporated and demonstrate linear trends of the optimization for the investigation period.

Every aspect of the validation analysis demonstrated the superiority of the developed Hybrid Model for PCE. Individual product’s estimated costs and the cumulative costs were analysed and checked for not just accuracy but consistency of the results. The analysis for overhead estimation at product’s level and cumulative level also demonstrated the developed method’s superiority.

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Overhead estim ation optim ization based on Com apny's m ethod 28.79

30 24 % Optimization

(a)

23.97 y = 5.58x + 10.70

18 12.82

12 6 0

2003

2004

2005

Production Year Estimation Optimization (%)

Linear estimation optimization trend

Overhead estim ation optim ization based on Jung's m odel

(b)

15 14.10

% Optimization

11.41 10 y = 4.91x + 0.11

5

4.28

0 2003

2004

2005

Production Year Estimation Optimization (%)

Linear estimation optimization trend

Figure 7-12: Optimization achieved for overhead estimation based on (a) the Company’s method (b) the Jung’s model

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7.6

Cost breakdown analysis

One of the advantages of incorporating the breakdown approach in the Hybrid Model is its ability to present a cost breakdown analysis that could lead to the identification of the cost elements requiring better cost control. A cost breakdown analysis is also presented in this study based on the actual costs incurred. All the three methods discussed here consider different breakdown structures. However, since the Hybrid Model is already validated for its accuracy and consistency and found to be superior to the other two models, it will be applied to the actual costs to get the breakdown statistics and for further analysis.

Figure 7-13 shows the production cost (actual) breakdown analysis from 2002 to 2005. Overheads refer to the total indirect costs and are made up of processing costs, materialdependent costs and production overheads. The values are based on the cumulative expenditure in respective years for a given element and are represented in percentages. The breakdown can be considered a typical representation of the UK manufacturing sector based on the analysis of a representative case. Material cost is found to be the highest share (47 percent on the average) of the overall product cost followed by overheads and then labour costs with 37 and 16 percent average values respectively. It can be noted that labour costs in UK are significantly higher than those obtained from the South Asian region. Overhead is a big share of the overall product cost and its accurate estimation is important to the overall accuracy of an entire product’s cost.

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Figure 7-13: Production cost (actual) break down analysis (2002 – 2005) presented in values and percentage

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An analysis of the three elements based on yearly trends is presented in Figure 7-14. The values represent the cumulative costs incurred on material, labour, and overheads. A gradual yearly rise for the direct elements (material and labour) is not surprising and is due to inflation and other variants. A steeper rise in overheads needs further investigation. However, one explanation could be a less-effective control on overheads resulting in a steeper rise. This is due to the company’s adopted cautious approach of overheads estimation resulting in overestimation and thus setting cost control strategies accordingly.

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Figure 7-14: Production cost elements trends

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Before analysing in detail why overheads rose more steeply, it is necessary to see their effect on the overall production and manufacturing cost. Figure 7-15 (a) gives out the yearly production and manufacturing costs in million £. Part (b) considers the effect of elemental costs on these values. It is clear that production and manufacturing costs kept rising relative to a steeper rise in overheads. Although material and labour costs are proportionately higher in the overall product cost, their effect on the overall manufacturing and production costs remained unaffected throughout the duration of the analysis. However, a direct effect of a steep rise in overhead values on production and manufacturing cost necessitates its further analysis.

Material cost is directly associated with design attributes and although cost control aspects consider it, the discussion is beyond the scope of the thesis. Similarly, labour cost control require effective process planning and operations management strategies, the scope of the study (cost estimation) does not cover such discussions. However, an analysis of the overhead values could lead to the identification of the elements with higher cost values in order to keep in place an effective CCS. Figure 7-16 is a breakdown of the actual overheads based on the Hybrid Model application. Production overheads make the largest portion with an average value of 44 percent from 2002 to 2005. Processing cost and MDC make up 31 and 25 percent respectively. The figure also describes the values for the four-year period.

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Figure 7-15: (a) Production and manufacturing costs (b) elemental costs effect on production and manufacturing costs

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Figure 7-16: Overheads break down analysis (2002 – 2005) presented in values and percentage

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The analysis of the three sub-elements presented in Figure 7-17 shows a steeper rise in the values for production overheads after 2003. While the processing costs displayed a steady yearly rise for the four – year period, MDC were more controlled from 2003 – 2005.

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Figure 7-17 Overhead elements trends (2002 – 2005)

A further breakdown of the largest overhead element (production overhead), into its constituent elements is presented in Figure 7-18. General administration costs ranged from 40 to 49 percent of the overall production overheads and mainly remained the largest constituent element. Selling expenses with 35 to 42 percent and computer related costs with 15 to 18 percent of the production overheads were the other two constituents.

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Figure 7-18: Production overheads breakdown (2002 – 2005)

An analysis of the cost trends for the constituents presented in Figure 7-19 clearly shows that selling expenses increased rapidly and became the largest constituent in 2005 leaving behind general administration costs. General administration costs remained the largest value constituent until 2004 but its rise remained gradual throughout four-year period. Similar results were noted for computer-related costs. Although, the analysis revealed the

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selling expenses as a possible area for cost control, a steeper rise in its values in the later half of the trend was partly a result of the business policy decisions to boost sales.

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2003

2004

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Production Year Computer related cost

General administration cost

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Figure 7-19: Production overhead elements trends analysis

A similar analysis can be carried out for the constituent elements for processing costs and MDC. For example, the one carried out for processing costs in Figure 7-20 reveals a sharp rise in energy costs. Repair costs were kept under control and went down between 2003 and 2004. Maintenance costs showed a steadier trend. Financing expenses can also be seen to be kept under control. It is clear that energy costs were a major contributor to the processing cots.

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Figure 7-20: Processing cost elements trends

An analysis for the MDC constituent elements presented in Figure 7-21 shows that freight and transportation costs could have been better controlled especially between 2002 and 2003 and then 2004 and 2005. Packaging costs between 2003 and 2004 could also be controlled more efficiently. Costs associated with material handling, inspection and scrap were largely kept under control.

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MDC Elements Trends 90 80 70

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Figure 7-21: MDC elements trends

The cost element analysis presented is a result of the Hybrid Model’s application and can be effectively used to identify high cost elements providing opportunities for better cost control. In that sense, the developed model can not only furnish early cost estimates for an entire product with accuracy and consistency but provide cost control opportunities by identifying high cost elements.

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7.7

Conclusions

This chapter presented the validation analysis that comprised the comparisons of the actual costs of the given product range against the estimated costs for the same range given by the developed Hybrid Model, the company’s method and a published model. The Jung’s model was selected as a representative case from the published domain being a proven case that could be implemented within the framework of the selected manufacturing set up. Every level of the analysis performed demonstrated the superiority of the developed model.

The cost estimates for individual products given by the Hybrid Model were found to be more accurate and more consistent. The company’s method adopted a cautious approach and as a result overestimated on almost every occasion with as much as 40 percent estimation error on isolated cases. Although the Jung’s model predicted slightly better values for an isolated case, the Hybrid Model’s prediction was not only within the acceptable limit for that case but the overall accuracy was found to be more consistent. The incorporation of the case-based technique into the modelling framework sensitized the model without compromising its robustness. The overall validation analysis spread over a three-year period covering a range of products under varying conditions and huge fluctuations of cost deviations still produced consistent results within acceptable limits of error estimations.

Cumulative cost analysis showed similar results. The company’s method overestimated by as much as around 19 percent and the Jung’s model underestimated by around 9 percent at

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the cumulative level. The Hybrid Model remained close to the actual costs even at the cumulative level of prediction. The quantification of the optimization against the two methods showed that a maximum of over 16 and 8 percent optimizations were obtained against the company’s and the Jung’s methods respectively.

Another aspect of the validation analysis considered analysing the overhead estimation accuracy at product and cumulative levels. On almost every occasion, the estimation error (overheads for individual product) produced by the Hybrid Model was found to be not only lower than those presented by the other two methods but remained in acceptable limits. The cumulative overhead values were also analysed and resulted in the overall underestimation of overheads predicted by the Jung’s model by around 15 percent and those for the company’s method in an overestimation of up to 32 percent. The values for the Hybrid Model varied between -12 and 4 percent.

A cost breakdown analysis was also presented for a four-year period (2002 – 2005) based on the actual costs incurred. Material cost was found to be 47 percent; labour costs 37 percent and overheads 16 percent of the overall production cost. A further analysis of the overheads breakdown values was carried out. The cost element analysis presented was a result of the Hybrid Model’s application and helps to identify high cost elements providing opportunities for better cost control.

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Chapter 8

Conclusions

Chapter 8 concludes the thesis by summarizing the overall work and contributions. The methodology and approaches developed in this thesis are evaluated by comparing the aims and objectives of the work set at the beginning of the study with the outcome of the research. The chapter describes current and future trends in the field of cost estimation and describes how the developed model conforms to those trends. The chapter also identifies future research avenues within the specific context of the established research.

8.1

Summary

The main aim of the study was to develop a comprehensive methodology for product cost estimation in a batch type manufacturing environment. In order to achieve that, a genuine theoretical development in the area was maintained followed by industrial trials and validation. The overall process of the theoretical development was based on identifying problems that the cost estimators face with the existing methods of PCE. This led to an extensive review of the existing methods for PCE and identification of possible solutions. The objectives were set in light of the possible solutions and were followed up with a careful plan throughout the study. New theories, methods, techniques and mathematical models were developed in line with the objectives. The developed models were validated

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through industrial trials due to the practical nature of the overall research area. The overall research work was carefully structured in the thesis.

Chapter 1 described the scope of the research study. To do that, an overview of the research area was provided. It was highlighted that a good pricing system requires the application of cost engineering. The significance of cost estimation on cost control was discussed. The role of cost estimation in the set up of a business enterprise with reference to maximizing its profits was then noted. The chapter outlined and briefly discussed the problems in the area of PCE. The aims and objectives of the research study were set and briefly discussed. Finally, the chapter described the overall structure of the thesis.

Chapter 2 established background information in the area of cost estimation. The concepts of cost and costing were introduced and the implications of cost control on manufacturing systems were discussed. Three kinds of manufacturing systems were discussed: mass, batch and job shop production. The rationale for developing a cost estimation methodology for a batch type manufacturing environment was then presented. The chapter also presented a comprehensive literature review with a focus on the techniques for different applications of cost estimation. One of the application area noted was for generic systems. It was found out that developing a methodology for generic systems could widen the scope of the developed methodology. It was, therefore, decided to develop the methodology for generic systems applications. Since, a batch type manufacturing environment is also a form of generic system, and was already considered a viable option to develop a methodology for; a

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decision was made to develop a methodology to suit the needs of a batch type environment to satisfy the needs of a generic system also.

Chapter 3 extensively reviewed the literature on manufacturing and product cost estimation and provided a detailed survey along with a critical evaluation of some of the techniques developed in the area. Based on the similarities and the differences of the existing methods, a comprehensive hierarchical classification system was suggested. The developed system along with the key conditions for the application of a methodology from a given category helped in developing a decision support model. The support model was developed with the aim of assisting designers and estimators in selecting a methodology. During the course of the classification system development, a framework for case-based methodology was proposed in order to make an effective use of past product details. The proposed classification system was broadly categorized in qualitative and quantitative techniques. Qualitative techniques were found to be useful in providing early estimates and quantitative techniques were noted for their accuracy. The chapter concluded with the suggestion of developing a methodology for cost estimation based on combining concepts from both qualitative and quantitative techniques for early and accurate estimation of a product’s cost.

Chapter 4 formed the basis for developing a PCE modelling methodology by establishing an overhead estimation method. In order to fulfil the objectives of developing a method for predicting an entire product’s cost, a cost breakdown approach was considered. An analysis of the existing breakdown techniques identified overhead as a key element for the overall accuracy of a product cost. Problem identification with the existing method of overhead 227

Chapter 8: Conclusions

estimation led to the development of a new overhead estimation methodology based on material– and time–dependent costs. The proposed methodology was validated in a batch type manufacturing environment in South Asia. The validation analysis was based on comparing the estimated product costs obtained with the application of the proposed methodology and the company’s method against the actual product costs. The proposed model for overhead estimation was found to be superior to the company’s method of overhead estimation as the former allowed more accurate estimation of product costs. The chapter also revealed manufacturing cost breakdown statistics at the company. The cost breakdown can be considered a representative case for that region characterized by lower wage rates. The chapter finally discussed room for further optimization in the proposed method.

Chapter 5 provided a complete framework for estimating a product cost early and accurately in a batch type manufacturing environment. The overhead method developed in Chapter 4 formed the basis for extending the work. The limitations identified in the already developed method were overcome. In order to make use of the attributes of the qualitative and the quantitative techniques, a hybrid modelling approach was considered. Case-based approach from the qualitative techniques was selected to facilitate an effective use of past product details to allow an early estimation of new products costs. This was achieved by making use of the past product costs obtained at the end of a given year to predict the costs in the following year. Two methods from the quantitative techniques were selected. The use of breakdown approach allowed the estimation of an entire product’s cost instead of only part or component costs. The activity-based costing method was incorporated to get

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accurate results. Although, the activity rates and units were modelled, the modelling framework was established on time– and material–dependent cost elements giving the Hybrid Model even better accuracy than the conventional ABC systems.

Chapter 6 was based on the industrial implementation and application of the Hybrid Model in a batch manufacturing environment in the UK selected as a representative case of the manufacturing sector in the country. The implementation presented the procedure of using the Hybrid Model. This was achieved by developing a comprehensive Hybrid Model Implementation (HMI) algorithm. The algorithm provided all necessary steps in logical sequence to implement the model. The provisions of primary and secondary data input to the system were accommodated in the algorithm along with inclusions of the Hybrid Model’s comprehensive set of equations. Equations for cost deviation indices were introduced in order to effectively utilize past data. The algorithm successfully implemented the model and the cost estimate results were obtained. Key benefits of using the algorithm and the Hybrid Model were demonstrated. The cost estimates from the company’s method were also obtained. The implementation phase facilitated the generation of cost estimates and is part of the entire validation process. The estimated results were obtained retrospectively from 2003 to 2005 by using the field data from 2001 to 2004.

Chapter 7 was based on a follow up of the implementation phase and compared the results obtained in the preceding chapter in order to validate the Hybrid Model. The Jung’s model was also selected as a representative case from the published domain based on its already established validity within its domain and its compatibility with the field data and the 229

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selected manufacturing set up. Estimated cost values using the Jung’s model were obtained. All the estimated cost values for the given product range were compared against the actual costs for the same range. The estimated costs for that purpose were obtained by the application of the Hybrid Model, the company’s own method and the selected published model. Every level of the validation analysis demonstrated the superiority of the developed model. For example, the costs for individual products were more accurately and more consistently estimated using the Hybrid Model. Cumulative production costs were also estimated more accurately and more consistently. The optimization of over 16 and 8 percent were obtained against the company’s and the Jung’s methods respectively by using the Hybrid Model. The developed model was also checked for its overhead estimation accuracy at product and cumulative production levels. The optimization achieved for overhead estimation was found to be up to 29 percent against the company’s method and 14 percent against the Jung’s model.

A cost breakdown analysis was also presented for a four-year period (2002 – 2005) based on the actual costs incurred. The breakdown values revealed can be considered a typical representation of the UK manufacturing. A further analysis of the overhead breakdown values was also carried out based on the Hybrid Model’s application. The analysis proved helpful in identifying the high cost elements thus providing opportunities for better cost control. The developed model, therefore, forms part of a cost control system development also.

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8.2

Contributions

In order to evaluate the outcomes from this thesis, the contributions from the overall research work are outlined below.

8.2.1

Development of a technique classification system

Following a comprehensive literature review in the area of PCE, methodologies were categorised into qualitative and quantitative. An extensive analysis of the categorized techniques led to further sub-division of up to four levels and thus resulting in a comprehensive hierarchical classification system. It was found that qualitative techniques mainly focussed on early estimates and quantitative ones delivered accuracy by making use of product design and process planning details. The developed system was found helpful in identifying that an accurate overhead estimation methodology is essential for accurate estimation of a product’s cost. The proposed system is also helpful in visualizing the nature of an estimation technique and comparing it with the other from the same category or a different one.

8.2.2

Development of a decision support model (DSM)

Following a comprehensive literature review and the developed classification system, key conditions for the implementation of a technique from a given category were identified. This led to the development of a decision support model. The aim of the system is to assist

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designers and estimators in selecting an estimation methodology to suit the needs of a system and given conditions. This is particularly necessary when several cost estimation techniques may be applied in a given condition. However, due to the availability of a large number of estimation techniques, estimators either find the selection process timeconsuming or erroneous. The developed model overcomes the limitations by providing consistency in the selection process.

8.2.3

Development of time- and material-based overhead estimation methodology

In order to develop a methodology that could predict an entire product’s cost, breakdown approach was considered. Following the review and the proposed classification system, overhead was identified as an important breakdown element. The significance of accurate estimation of this element led to the identification of any existing methods for its prediction. The ABC system was found to overcome some of the problems but still left few areas for improvement. In light of the identified problems with the existing method of overhead estimation, an improved overhead estimation methodology was proposed based on time– and material–dependant cost elements. The industrial validation based on a fouryear retrospective analysis in a batch manufacturing environment in South Asia revealed the superiority of the developed methodology against a representative method from the manufacturing domain.

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8.2.4

Development of a PCE methodology for batch production

A main objective of the study was to develop a methodology that could predict an entire product’s cost early and accurately. This was achieved by developing the Hybrid Model for PCE in a batch type environment. The model was based on combining attributes from qualitative and quantitative cost estimation techniques from the proposed classification system. Case-based approach from qualitative techniques provided means of utilizing past cost details in order to furnish estimates for similar new products in future. It allowed the early estimation by eliminating the need for product design details necessary to furnish estimates from scratch. The already developed methods for overhead estimation (TRO and MRO) provided basis for further improvement by incorporating the concepts of improved ABC system features. Overheads were sub-divided and calculated based on improved concepts of activity rates and activity units. In this way, the accuracy attributed to quantitative techniques was achieved by making use of the improved and modified concepts of the ABC system. The use of breakdown approach not only allowed the estimation of the entire product cost, but the representation of the cost into elements and sub-elements.

The developed model can also predict manufacturing cost in addition to the overall product cost. The representation of a product cost into its elements and sub-elements allows the identification of any high cost areas. The identification in return facilitates cost control opportunities. The developed model in that sense goes beyond just furnishing early and

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accurate cost estimates for a product. It constitutes a key component of a cost control system.

8.2.5

Development of cost deviation indices

The introduction of the case-based framework in the Hybrid Model was facilitated by cost deviation indices. The indices were based on effectively utilizing past two years data to predict future costs. Inflation and other cost deviations were also incorporated in the indices for optimized use of past data and accurate prediction. This also resulted in overcoming the limitations of TRO and MRO methods. Deviation indices are crucial to the overall accuracy of the estimated results from the developed Hybrid Model.

8.2.6

Development of HMI algorithm and industrial implementation

Development of the PCE Hybrid Model could serve no real purpose if it could not be successfully implemented in industries. One of the objectives was to implement the developed model in an industrial environment. This thesis devised a comprehensive procedure for the industrial implementation of the developed PCE Hybrid Model. This resulted in the development of HMI algorithm to facilitate the implementation procedure. The Hybrid Model was subsequently implemented in the selected UK batch manufacturing industry. The Hybrid Model with the help of the HMI algorithm and deviation indices generated the estimation results for the given product range. The HMI algorithm after minor changes can be made more generic for a wider scope of industrial implementation.

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8.2.7

Comparison and validation

The validity of the developed model could only be established after the comparisons of its generated results against the ones from the already recognized and validated methods. Therefore, the model was validated after a three-year retrospective industrial implementation trial. The cost estimation results that were obtained after a successful industrial implementation were not only compared against an industrially recognized and representative method but against an already established published model. The results from the Hybrid Model were found to be more accurate as the furnished estimated costs were found to be closer to the actual product costs than those predicted by the other two methods. However, the validation analysis went even further ahead by comparing not just the product costs but the cumulative costs and the elemental costs. Every aspect of the comparison analysis validated the Hybrid Model as the costs estimated were not only more accurate but more consistent than those predicted by the other two methods.

8.2.8

By – products

The overall study resulted in not just achieving the set objectives but in delivering valuable by-products.

A comprehensive literature review carried out in the field not only presented a critical analysis of the developed techniques with the key advantages and limitations but provided useful work with reference to the applications in the area. Similarly, the developed case-

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based model serves as a valuable component for not just the Hybrid Model but provides a framework for developing a data retrieval system for other applications of production planning and control system. The developed model makes use of past product details in order to furnish ones for similar new designs. Only the changes in the new designs can be incorporated thereby eliminating the need to furnish details from scratch. Another valuable outcome of the study was the revelation of statistical cost breakdown figures on two different geographical locations that were typical of the regions and reflected contemporary trends. The figures reflect the geographical implications on cost occurrences and are helpful in creating a better understanding for developing an effective CCS.

The overall contributions resulted in theoretical development to the field of PCE. This development was fully backed up by industrial trials and validation analyses. All in all the work presented in the thesis resulted in some pioneering contributions to the field of cost engineering in general and PCE in particular.

8.3

Current Trends and Future Work

Before exploring the possibilities for further research avenues in the already established research domain, it is befitting to analyse how it conforms to the current and future trends in the area.

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With the advent of computers and the advancement in technology, non-conventional approaches such as knowledge-based techniques and neural network models have been applied effectively utilizing past knowledge to predict the future costs in the early design phases. Current trends in cost estimation exploit the feature technology and a simpler trend is based on estimating the costs by calculating the amount of activities performed to manufacture a product. However, more recent works in the field focus on getting quicker and more accurate results by developing integrated systems combining two or more approaches. For example, a mix of neural network approach and feature technology is an emerging trend. Applying neural networks in CBR [112], cost-tolerance analysis using neural networks [113] and fuzzy activity-based costing [114] are also among some of the new concepts. Yet another area of ongoing research activities combines rule-based, fuzzy logic based, and feature-based methodologies together. An approach that blends some of these techniques could provide more promising results. For example, there is a need to combine the feature technology with the ABC method to study the effects in detail. An approach dealing with the ABC systems and neural networks at the same time may yet be another research area.

In line with the recent and ongoing research trends in the area of PCE, the developed methodology exploits the benefits of the three individual techniques from two branches (qualitative and quantitative) to develop a Hybrid Model that conforms to the current and future trends. The established research, therefore, opens new avenues for exploring further in the field. Following are some of the suggested projects.

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Validation and optimization analysis of the Hybrid Model for PCE through simulation

The aim is to analyze and investigate thoroughly the behaviour of different parameters of the models under varying conditions and compare the results. This should lead to further optimization of the Hybrid Model.

Development of a data retrieval system based on the case-based methodology

The aim of the proposed project is to develop a matching algorithm to facilitate the adaptation of a past product design with closest similarities to a new design. The developed algorithm will form part of the overall data retrieval system by interfacing it into the already proposed case-based system.

The development of a comprehensive prototype computer-based cost estimation system based on the developed Hybrid Model

The already established research when combined with the elements from the above mentioned proposed projects could lead to the development of a comprehensive prototype computer-based cost estimation system. The optimization analysis through simulation and the development of a data retrieval system based on the proposed case-based approach would form integral elements for the proposed computer-based system. The project should aim at interfacing the system with product design data-base. The aim of such an integrated 238

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system would be to generate product cost estimates for new product designs at design conceptualization stages. Such a system would facilitate designers, estimators, planners and managers to make necessary decisions from design changes and price quotes to devising production planning and control strategies. More strategic decisions like make or buy and business resizing etc. would also be possible.

8.4

Concluding remarks

The validation of the Hybrid Model demonstrated through various aspects of the analyses can be attributed to a number of factors. A comprehensive study of the available techniques through a well-structured literature review helped to identify the problem areas. This led to the identification of ways to develop solutions based on an effective utilization of strengths of some of the best known methods and eliminating their shortcomings. The initial methods proposed as part of this thesis that were already found to be more accurate than some of the existing techniques, were further analysed. As a result, a framework for a more comprehensive methodology based on further optimizations was presented. The selfassessment procedure fine-tuned the developed methodology.

The work presented in the thesis resulted in contributions to the field of PCE and forms part of the pioneering work at King’s College London. The encouraging results from the industrial validation analysis open avenues for further exploration in the field. The established work is also an attempt to provide a platform for researchers and practitioners

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alike to explore further in the field. For example, Professor Frank J Fabozzi of Yale School of Management (USA) and editor of the Journal of Portfolio Management not only cited the published work as excellent but incorporated the article as a basic chapter of his recently published book [115]. Finally, the overall work, therefore, provides contributions to the field of applied engineering and opens up new channels for further explorations.

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Publications Arising from the PhD Study

The research carried out as part of the current PhD study and covered in the thesis has resulted in the following leading journal publications:

•

Niazi A, Dai JS, Balabani S, and Seneviratne L. Product cost estimation: Technique classification and methodology review. Transactions of the ASME. Journal of Manufacturing Science and Engineering, May-2006, 128(2), 56375, Publisher: ASME, USA, 2006.

•

Niazi, A., Dai, J. S., Balabani, S., and Seneviratne, L. D. A new overhead estimation methodology: A case-study in an electrical engineering company. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Jan-2007, 221: 699-710, 2007.

•

Niazi, A., Dai, J. S., and Balabani, S. PCE Hybrid Model for cost estimation in a batch type manufacturing environment. Transactions of the ASME. Journal of Manufacturing Science and Engineering, 2007, (submitted).

•

Niazi, A., and Dai, J. S., HMI Algorithm and industrial implementation framework for PCE Hybrid Model. Transactions of the ASME. Journal of Manufacturing Science and Engineering, 2007, (submitted).

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Publications Arising from the PhD Study •

Niazi, A., and Dai, J. S., Methodology comparisons and validation analysis for PCE Hybrid Model. Transactions of the ASME. Journal of Manufacturing Science and Engineering, 2007, (submitted).

242

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260

Appendix A

Bill of Material (BOM)

The purpose of appendix A is to elaborate BOM. This is carried out by taking the example from a hammer drill. The drill is gradually dismantled and assemblies, sub-assemblies and parts & components are identified. Material and material quantities for different parts are identified. The information along the process is recorded and helps to establish BOM for the drill.

A.1 Introduction Bill of material (BOM) is a representation of different material with their respective quantities used in a product. Such details are extracted from product design documents. Details contained in design documents help in establishing a product structure based on creating sub-assemblies, assemblies and eventually product levels.

In order to better understand BOM and product structure a hammer drill presented in Figure A-1 is selected and dismantled gradually. The process of dismantling the product identifies assemblies and sub-assemblies and hence results in the overall product structure as presented in Figure A-2. Figure A-3 shows the dismantled drill with the assemblies and sub-assemblies. The other assemblies and sub-assemblies mentioned in the product structure are shown from Figure A-4 to Figure A-7. 261

Appendix A: Bill of Material (BOM)

Figure A-1 Hammer drill

A.2 BOM for Hammer Drill Product structure is a result of design specification and is a helpful tool in identifying assemblies, sub-assemblies and parts & components. The information when presented in tabular form with parts and assemblies names and their respective material quantities constitute BOM. BOM presents product design details by exploding assemblies and sub-

262

Appendix A: Bill of Material (BOM)

assemblies to part and component level and identifying the required materials with their respective quantities as shown below for the selected hammer drill in Table A-1.

263

Figure A-2 Product structure (Hammer Drill)

264

Appendix A: Bill of Material (BOM)

Figure A-3 Dismantled drill with assemblies and sub-assemblies

265

Appendix A: Bill of Material (BOM)

Figure A-4 Parts and components in product structure

Figure A-5 Winding (Stator and rotor) and drive assembly

266

Appendix A: Bill of Material (BOM)

Figure A-6 Driven assembly (with gear and shock absorber) and Drill/Hammer switch

Figure A-7 Trigger assembly

267

Appendix A: Bill of Material (BOM)

The BOM for the drill at product level comprise parts & components and the drill assembly. The drill assembly can be considered a phantom assembly. Phantom assembly represents a group of components or parts that cannot be assembled together unless some other parts and/or assemblies are added to it. This type of imaginary assembly adds to no operation/processing cost. Respective material and material quantities are also shown in Table A-1 for each component used. BOM explodes the drill assembly into electrical and mechanical assemblies with further explosions later on. Material quantities at the part and component levels add up to sub-assemblies and assemblies level and eventually the overall product level.

Table A-1 Hammer Drill (product level) 1.6 Kg

Component

Quantity per item

No of items

Material

Depth gauge

1

Plastic

10 (10)

Chuck key

1

Steel

40 (40)

Chuck

1

Steel

120 (120)

Shell

2

Plastic

50 (100)

Front support handle

1

Thermoplastic

150 (150)

Chuck screws

2

Steel

0.5 (1)

Body screws

6

Steel

0.5 (3)

Drill Assembly

1

-

1176 (1176)

(total quantity) gm

Drill Assembly (phantom assembly) 1176gm

268

Appendix A: Bill of Material (BOM)

Electrical Assembly

1

-

629 (629)

Mechanical Assembly

1

-

547 (547)

Electrical Assembly (phantom assembly) 629gm Winding

1

-

325 (325)

Connections

1

-

304 (304)

Winding (assembly level) 325gm Stator

1

-

207 (207)

Rotor

1

-

118 (118)

Stator (sub-assembly level) 207gm Shell

1

Electrical steel

87 (87)

Stator winding

1

Copper

52 (52)

Insulators

8

Plastic

3 (24)

Pegs

4

Thermoplastic

2 (8)

Holding strip

2

Steel

12 (24)

Cables

4

Copper

3 (12)

Rotor (sub-assembly level) 118gm Shell

1

Electrical Steel

28 (28)

Core

1

Plastic

12 (12)

Copper plate

1

Copper

15 (15)

Rotor winding

1

Copper

63 (63)

Connections (phantom assembly) 304gm 269

Appendix A: Bill of Material (BOM)

Rotor Connection

1

-

28 (28)

Fuse

1

-

5 (5)

Trigger Assembly

1

-

31 (31)

Mains

1

-

240 (240)

Rotor Connection (phantom assembly) 28gm Brush Assembly

1

-

14 (14)

Plastic cover

2

Plastic

2 (4)

Plastic end

2

Plastic

2 (4)

Wire holder

2

Copper

3 (6)

Brush Assembly (sub-assembly level) 14gm Spring

2

Steel

2 (4)

Copper Wire

2

Copper

1 (2)

Copper plate

2

Copper

1 (2)

Brush

2

Coal

3 (6)

The Trigger Assembly (assembly level) 31gm Spring

1

Steel

1 (1)

Screw

4

Steel

0.5 (2)

Clamp

2

Steel

1.5 (3)

Connector type I

2

Copper

1.5 (3)

Connector type II

2

Copper

1.5 (3)

270

Appendix A: Bill of Material (BOM)

Plastic Mould

1

Plastic

5 (5)

Trigger

1

-

10.5 (10.5)

Lock assembly

1

-

3.5 (3.5)

Trigger (sub-assembly level) 10.5gm Spring

2

Steel

1.5 (3)

Plastic shell

1

Plastic

3 (3)

Clamp

1

Plastic

2 (2)

Trigger frame

1

Plastic

2.5 (2.5)

Lock assembly (sub-assembly level) 3.5gm Spring

1

Steel

1.5 (1.5)

Plastic Press

1

Plastic

2 (2)

Mains 240gm Cable

1

Insulated Cu Wire

155 (155)

Plug

1

-

85 (85)

Mechanical Assembly (phantom assembly) 547gm Drive Assembly

1

-

281 (281)

Driven Assembly

1

-

167 (167)

Drill/Hammer Switch

1

-

99 (99)

Driven Assembly (assembly level) 167gm Driven shaft

1

Carbon Steel

55 (55)

271

Appendix A: Bill of Material (BOM)

Driven gear

1

Carbon steel

23 (23)

Fastening spring

1

Steel

12 (12)

Shock absorber

1

-

77 (77)

Shock Absorber (sub-assembly level) 77gm Spring

1

Steel

15 (15)

Shell

1

Alloy steel

62 (62)

Drive Assembly (assembly level) 281gm Driving shaft

1

Steel

86 (86)

Fan

1

Plastic

35 (35)

Journal bearing

1

Stainless steel

32 (32)

Ball bearing

1

Stainless steel

26 (26)

Gear holder assembly

1

-

102 (102)

Gear Holder Assembly (sub-assembly level) 102gm Static gear

1

Steel

24 (24)

Gear ring

1

Brass

24 (24)

Holding shell

1

Alloy steel

54 (54)

Drill-Hammer Switch (sub-assembly level) 99gm Steel strip

1

Steel

35 (35)

Sphere

1

Steel

38 (38)

Plastic Mould

2

Plastic

13 (26)

272

Appendix A: Bill of Material (BOM)

From MRP point of view, BOMs are maintained at the cumulative level for a product and represent combined quantities of similar materials at the lowest level as shown in Table A-2. These quantities are helpful in procuring the material based on the product manufacturing quantities.

Table A-2 Cumulative material quantities at the lowest level for the hammer drill

S. No.

Material

Quantity (gm)

1

Plastic

229.5

2

Thermoplastic

158

3

Steel

406.5

4

Electrical steel

115

5

Carbon steel

78

6

Alloy steel

116

7

Stainless steel

58

8

Copper

158

9

Brass

24

10

Insulated copper wire

155

11

Coal

6

12

Screws

12 Pcs

273

Appendix B

Deviation Indices

The appendix B is aimed at deriving the equations for cost deviation indices. The indices form part of the PCE Hybrid Model.

B.1 Material cost deviation index Material cost deviation index value refers to the amount of deviation in the cost of a material from its original cost. For example, material cost deviation index for the pth product in the nth year represented by φ pn can be given in terms of material cost for that n n −1 product in the nth year ( Cmp ) and the (n–1)th year ( C mp ) as follows:

φ pn =

n n −1 C mp − C mp n −1 C mp

=

n C mp n −1 C mp

−1

(B-1)

Any deviation in the costs is a result of not just inflation but other factors. If I n is the deviation index due to inflation in the nth year and J pn represents the index due to other factors for the pth product in the same year, then φ pn can also be given as follows:

274

Appendix B: Deviation Indices

φ pn = I n + J pn ⇒ J pn = φ pn − I n

(B-2)

The above equation (B-2) can be converted in a similar way for the (n+1)th year.

φ pn +1 = I n +1 + J pn +1

(B-3)

Where, φ pn+1 is the material cost deviation index for the pth product in the (n+1)th year, I n+1 is the deviation index due to inflation in the (n+1)th year and J pn+1 represents the index due to factors other than inflation for the pth product in the (n+1)th year. The value of J pn+1 is based on J pn and can be obtained by taking into account I n+1 i.e.

J pn +1 = J pn (1 + I n +1 )

(B-4)

Therefore, the value of J pn+1 can be replaced in the equation (B-3) as follows:

φ pn +1 = I n +1 + J pn (1 + I n +1 ) ; Now replacing the value of J pn from equation (B-2):

φ pn +1 = I n+1 + (φ pn − I n )(1 + I n +1 ) ; and now replacing the value of φ pn from equation (B-1):

275

Appendix B: Deviation Indices

n  C mp

φ pn +1 = I n +1 + 

C

n −1 mp

 − 1 − I n (1 + I n+1 )  

(B-5)

Equation (B-5) can be used to determine material cost indices for number of ‘p’ products in the (n+1)th year using their respective material costs in the nth and the (n–1)th years and the inflation values in the nth and the (n+1)th years. Therefore, the known cost data can be used to predict the indices for the product range.

B.2 Labour cost deviation index Let average per month wages of non–skilled, semi–skilled and skilled labour in the nth year be W0n ,

W1n and W2n respectively and for the (n–1)th be W0n −1 , W1n −1 and W2n −1

respectively. If labour cost deviation index for non–skilled, semi–skilled and skilled labour in the (n+1)th year are represented by ε 0n +1 , ε 1n +1 and ε 2n +1 respectively, equation (B-5) can be used in a similar way to give these indices as follows:

 W0n  − 1 − I n (1 + I n +1 ) n −1  W0 

(B-6)

 W1n  − 1 − I n (1 + I n +1 ) n −1  W1 

(B-7)

ε 0n +1 = I n +1 + 

ε 1n +1 = I n +1 + 

276

Appendix B: Deviation Indices

 W2n  − 1 − I n (1 + I n +1 ) n −1   W2

ε 2n +1 = I n +1 + 

(B-8)

In order to determine the estimated labour rate value for the (n+1)th year, an average labour cost deviation index value ( ε n +1 ) can be determined.

B.3 Processing cost deviation index The aggregate shop floor wide processing rate in the nth and the (n–1)th years represented as n n −1 RMA and R MA respectively can be used in a similar way to predict the processing cost

deviation index value for the (n+1)th year ( µ n +1 ) as follows:

 Rn  µ n +1 = I n +1 +  MA − 1 − I n (1 + I n +1 ) n −1  R MA 

(B-9)

B.4 MDC deviation index n If MDC fraction values ( C md / C mt ) in the nth and the (n–1)th years are represented as RMDC n −1 and R MDC respectively, the above method can be used in a similar way to predict the MDC

deviation index value for the (n+1)th year ( ρ n +1 ) as follows:

277

Appendix B: Deviation Indices

 Rn  ρ n +1 = I n +1 +  MDC − 1 − I n (1 + I n +1 ) n −1  R MDC 

(B-10)

B.5 Tool cost deviation index Machine tool cost deviation index value for the (n+1)th year (ψ n +1 ) can be presented using n n −1 actual machine tool rates in the nth and the (n–1)th years (i.e. RMT and RMT respectively) as

follows:

 Rn  ψ n +1 = I n +1 +  MT − 1 − I n (1 + I n +1 ) n −1  RMT 

(B-11)

Similarly, labour tool cost deviation index value for the (n+1)th year ( σ n +1 ) can be given by n n −1 using the actual labour tool rates in the nth and the (n–1)th years (i.e. R LT and R LT

respectively) as follows:

 Rn  σ n +1 = I n +1 +  nLT−1 − 1 − I n (1 + I n +1 )  R LT 

(B-12)

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Appendix B: Deviation Indices

B.6 Building cost deviation index Again an index value for building cost deviation in the (n+1)th year ( δ n +1 ) can be obtained by using the actual building space rates in the nth and the (n–1)th years (i.e. RBn and R Bn−1 respectively) in the following way:

 Rn  δ n +1 = I n +1 +  nB−1 − 1 − I n (1 + I n +1 )  RB 

(B-13)

B.7 PO deviation index If production overhead fraction values ( Ot / C Gt ) in the nth and the (n–1)th years are n n −1 represented as R PO and R PO respectively, the PO deviation index value for the (n+1)th

year (τ n+1 ) can be given as follows:

 Rn  τ n +1 = I n +1 +  PO − 1 − I n (1 + I n +1 ) n −1  R PO 

(B-14)

279