40,41,42_textile Indusrty Or Final Draft.docx

Anil Surendra Modi School of Commerce, NMIMS University, Mumbai

Operations Research

Systematic Application Of Operations Research in production planning and Profit Optimization in the textile-clothing industry for Imperial Dyeing Ltd

Submitted By : Manan Sanghai (40) Shailja Sultania (41) Ashmi Sharma (42)

Abstract: This paper aims for profit optimization of a textile dyeing company – ‘Imperial Dyeing ltd’ which is located in Surat. Developing a linear programming model and using quantitative techniques in ‘Imperial Dyeing ltd’ is very essential for maximizing profit and developing various factors that can be utilized for decision making. The first process involved data gathering. Physical interviews of the concerned managers were conducted to obtain the data. The reports given by the company was also used to obtain the necessary data. The data collected and quantitative techniques applied here are unreservedly subjective. The data collected is then analysed to formulate a decision making factor. An objective function is created in terms of the concerned decision variables, i.e. the profit per meter of different materials that are produced. Machine hours in every process that is required to produce each material is used to formulate constraints in the model. A linear programming model for the company is then developed for profit optimization. The model equations with sufficient restrictions considering manufacturing impediments are comprehended using MS-Excel solver. To conclude, some irrefutable observations have been drawn to help the company identify its loss making products and hence maximize their profits. Keywords: Profit optimization, linear programming model, simplex method, dyeing industries.

India’s textiles sector is one of the oldest industries in Indian economy dating back several centuries. It is one of the largest contributors to India’s exports with approximately 13 per cent of total exports. The Indian Textile Industry contributes approximately 2 per cent to India’s Gross Domestic Product (GDP). The textile industry has two broad segments. First, the unorganised sector consists of handloom, handicrafts and sericulture, which are operated on a small scale and through traditional tools and methods. The second is the organised sector consisting of spinning, apparel and garments segment which apply modern machinery and techniques such as economies of scale (Foundation, n.d.). In our research paper we have collected data about Imperial Dyeing Limited which is an Indian textile manufacturing and dyeing company incorporated on 31 January 1995. It is involved in Spinning, weaving and finishing of textiles. It is a testing task for the manager of the company to identify the type and quantity of products which guarantee more gross income with efficient resource utilization at a minimum cost for the company. The problem addressed here is to determine the type and quantity of dyed fabrics to be produced by the company for efficient resource utilization that can enhance the returns of the company through the application of linear programming technique. Linear programming is an operational research technique used to allocate optimally production resources for a firm’s best practices. The linear programming problem (LPP) technique will be used to determine the product mix that will maximize the total profit at a specified time. It is the best method for determining an optimal solution among alternatives to meet a specified objective function limited by various constraints and restrictions. (Gera Workie, 2016)

The main objectives of the study are to formulate a linear programming model that would suggest a viable product- mix to ensure optimum profit for Imperial Dyeing Ltd. and to highlight the peculiarities of using linear programming technique. Our paper aims to encourage the selected company to adopt the application of linear programming technique in determining their product- mix. Bearing these objectives in mind, a post optimal analysis of the established profit maximization model would be attempted to help the management in adjusting its decisions in the face of increases or decreases in demand, resource prices and or availability of raw materials. Finally, from the findings of the study, suggestions of how linear programming method could be widely applied in business decision making in Imperial Dyeing Ltd. would be offered.

Review of Literature We found similar researches done by various authors which relate to our objective and methodology of profit optimization using Linear Programming Model. A Case Study on Profit Planning of Textile Industry Using Linear Programming Approach (Eshetie Kassegn, 2016) studies about the development of linear programming model for Almeda Private Limited, Ethiopian Textile Industry. The main objective of study was to maximize profit by using linear programming technique and minimize production cost. Almeda Textile Factory faced problems in earning the maximum possible profits because of lack of good profit planning techniques. Solution for this problem was found by development of linear programming model for major products of the company. A similar research was done in determining the Production Amounts in Textile Industry with Fuzzy Linear Programming (Çağatay Teke, 2017) which discussed the use of FLP for solving a production planning problem in a textile industry. It can be concluded that this method introduced is a promising method for solving such problems. Because the FLP model has fuzziness in both objective function and constraints, it was solved by using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gave the amount of production for each cloth type in order to gain maximum profit. The study illustrated how particular problems of real production systems can be treated by the theory on fuzzy sets. Another research on Application of Linear Programming Techniques to Determine the Type and Quantity of Textile Dyed Fabrics (Gera Workie, 2016) solved the problem of how to determine the optimal number of textile dyed fabrics to be produced by LPP. The strategies obtained by using LPP yield more dyed fabrics and more gross income than strategies obtained from trial and error methods. The company could make a production quantity and gross income differences of 703923.9654 meters dyed fabrics and Birr 35412071.47 correspondingly if it uses LPP. The production quantity and gross income of the company could be improved by 72.63% and 65.91% respectively. A study by Woubante & Gera Workie on The Optimization Problem of Product Mix and Linear Programming Applications considered an apparel industrial unit in Ethiopia as a case study. Apparel manufacturing firms profit mainly depends on the proper allocation and usage of available production time, material, and labour resources. The findings of the study suggest that the profit of the company can be improved by 7.22% by applying linear programming models. (Woubante, 2017). Another study on Profit Optimization Using Linear Programming Model: A Case Study of Ethiopian Chemical Company aimed at profit optimization of an Ethiopian chemical company located in Adama (Ethiopia). Linear programming model was

applied and the maximum profit Birr 107,353.17 per day for company was found. It was found that the company was left with an idle filtration and evaporation time of 5 and 7 hours per day respectively and un-utilizing demand for sulphuric acid of 44.52 tons per day which was corrected after the LPP modelling was done. Thus, the optimal feasible solution was 20 tons of aluminium sulphate per day, 6.98 tons of sulphuric acid per day. (Vishwa Nath Maurya, 2015)

Methodology The relevant data in this research paper was gathered from a textile manufacturing and dyeing company – ‘Imperial dyeing ltd’ which is located in Surat. The data hereon is gathered with the objective of identifying the methods of decision making for profit maximization and develop the model to do the same. From this case company, four types of products the company is producing, the amount of products sold by the company, a profit per unit that can be generated from the sale of each product and the total amount of product produced per meter have been obtained. Relevant data regarding the daily production, annual production, annual demand for each product, machine hour required in each process of daily production, machine hour required per meter of cloth and total machine hour is also essential for developing the linear programming model.

Data Collection Techniques A physical interview was conducted with the manufacturing manager and the sales manager of the ‘imperial dyeing ltd’ to gather the required data for developing the linear programming model. The workers working in the factory were observed to ascertain the daily working hours of the appointed work force. Certain secondary sources of data collection was also used to get accurate information. Annual reports uploaded by the company was analysed and reviewed to attain relevant data. This technique was essential as alternate strategies in gathering accessible data for directing effective and reality based research. Facts about the sector were gathered through accessing books related to the research.

Data Analysis Techniques The relevant data collected was scrutinized using linear programming model. The data was transformed into a linear programming model and solved the model (problem) using simplex algorithm by applying MS-Excel solver in order to determine the optimal combination of the products of the organization that can maximize its profit within the accessible rare resources.

LPP Model and its Application Linear Programming is a mathematical technique for generating and selecting the optimal or the best solution for a given objective function. Technically, linear programming may be formally defined as a method of optimizing (i.e. maximizing or minimizing) a linear function for a number of constraints stated in the form of linear inequalities. (Vishwa Nath Maurya, 2015)

Z = c1x1 + c2x2 (Objective function), Subject to the linear constraints:

a11 x1+ a12 x2(≤ or≥) b1,a21 x1+ a22 x2(≤ or≥) b2,...... , am1 x1+ am2x2(≤ or≥)bm,x1, x2(≤ or≥) 0. LPP OF DYEING COMPANY: Imperial Dyeing Ltd. Manufactures and dyes four major materials – Saree material, Polyester Dress material, Cotton Dress Material and Shirting Material which undergoes through five processes: Bleaching, Dyeing, Print, Stentering and Packing. Material bleaching is one of the phases in the production of materials. All raw materials, when they are in common shape, are known as 'greige' material. The process of decolourization of greige material into a suitable material for next processing is called bleaching. Then comes the dyeing process which is the application of dyes or pigments on textile materials such as fibres, yarns, and fabrics with the objective of achieving colour with desired fastness. Dyeing is regularly done in a special arrangement containing dyes and particular compound material. After the dyeing process printing of colour to fabric in definite patterns or designs is carried out. After this Stentering is carried out in which heat setting is done by the stenter for Lycra fabric, synthetic and blended fabric and the shrinkage property of the fabric is controlled. Curing treatment for resin, water repellent fabric is done by the stenter. After completing the entire manufacturing task, apparel is required to be packed. According to data collection the company was dyeing 35000 metres of saree material per day (35000*330 = 11550000 metres annually), 28000 metres of polyester dress material per day (28000*330 = 9240000 metres annually) , 22000 metres of cotton dress material per day (22000*330 = 7260000 metres annually) & 21000 metres of shirt material per day (21000*330 = 6930000 metres annually). The annual demand for these four materials is 13200000 metres, 9900000 metres, 8300000 metres, 7600000 metres respectively. The two major constrains for dyeing in the company is the demand of the materials and the availability of the machine hours on the five processes of dyeing.

Constraint of machine hours on 5 processes of dyeing Products

Machine Hours on bleaching material 18

Saree (35000m/day) Polyester dress 18 material(28000m/day) Cotton dress 18 material(22000m/day) Shirt 18 material(21000m/day) 7920 Total Available Time (assuming 330 working days per year)

Annual Demand (in metres)

dyeing 22

print 21

stenter 24

packing 16

13200000

20

20

22

12

9900000

20

20

22

12

8300000

18

20

20

8

7600000

7920

7920

7920

7920

According to sales department of the company the dyeing of saree material costing Rs.13/metre is sold for Rs.15/metre. The polyester dress material costs Rs.10/metre & is sold for Rs.11 whereas the cotton dress material costs Rs.15 and is sold for Rs.17. The dyeing of shirt material costing Rs.12/metre is sold for Rs.13.50/metre.

Mathematical Formulation of LPP for the Company The profit maximization objective of the company is mathematically expressed as: Zmax = 2x1 + x2 + 2x3 + 1.5x4 Decision variables are mathematical symbols that represent levels of activity. Let, x1 = the meters of saree material manufactured per day x2 = the meters of polyester dress material manufactured per day x3 = the meters of cotton dress material manufactured per day x4 = the meters of shirt material manufactured per day The model constraints are also linear relationships of the decision variables; they represent the restrictions placed on the firm by the operating environment. (III) The constraints relate to the number of hours of machine time available on five processes (bleaching, dyeing, printing, Stentering and packing); and demand also restricts the number of tons of the items that can be manufactured as presented below:

Number of hours of machine time on five processes and the demand of items Products

Saree material

bleaching 0.00051

Polyester dress 0.00051 material Cotton dress 0.00051 material Shirt material 0.00051 24

Machine Hours per metre per day dyeing 0.00063

Produced/day (in meters)

Profit /meter(in rupees)

print 0.0006

stenter 0.00068

packing 0.00045

35000

2

0.00057

0.00057

0.00063

0.00034

28000

1

0.00057

0.00057

0.00063

0.00034

22000

2

0.00051

0.00057

0.00057

0.00022

21000

1.50

24

24

24

24

Available resource

The constraints of the company are expressed as follows: Maximize Zmax = 2x1 + x2 + 2x3 + 1.50x4 Subject to: 0.00051x1 + 0.00051x2+ 0.00051x3+ 0.00051x4 ≤24 hrs. (machine hrs. on Bleaching), 0.00063x1 + 0.00057x2+ 0.00057x3+ 0.00051x4 ≤24 hrs. (machine hrs. on Dyeing), 0.0006x1+ 0.00057x2+ 0.00057x3+ 0.00057x4 ≤24 hrs. (machine hrs. on Printing), 0.00068x1+ 0.00063x2+ 0.00063x3+ 0.00057x4 ≤24 hrs. (machine hrs. on Stenter), 0.00045x1+ 0.00034x2+ 0.00034x3+ 0.00022x4 ≤24 hrs. (machine hrs. on Packaging) x1≤35000 meters (production for saree material per day), x2≤28000 meters (production for polyester dress material per day), x3≤22000 meters (production for cotton dress material per day), x4≤21000 meters(production for shirting material per day)

x1, x2, x3,x4≥0 (non-negativity).

Solution of the LPP Using MS-Excel Solver

To apply the MS-Excel Solver, first we translate the linear programming model into its standard form. Thus, the above model, written in the standard form, becomes:

Zmax = 2x1 + x2 + 2x3 + 1.50x4 + 0s1 + 0s2 + 0s3 + 0s4 + 0s5 + 0s6 + 0s7 + 0s8 + 0s9 Subject to: 0.00051x1 + 0.00051x2+ 0.00051x3+ 0.00051x4 + s1 = 24 hrs. 0.00063x1 + 0.00057x2+ 0.00057x3+ 0.00051x4 + s2 = 24 hrs. 0.0006x1+ 0.00057x2+ 0.00057x3+ 0.00057x4 + s3 = 24 hrs. 0.00068x1+ 0.00063x2+ 0.00063x3+ 0.00057x4 + s4= 24 hrs. 0.00045x1+ 0.00034x2+ 0.00034x3+ 0.00022x4 + s5 =24 hrs. x1 + s6 = 35000 meters x2 + s7 = 28000 meters x3 + s8 = 22000 meters x4 + s9 = 21000 meters x1, x2, x3,x4, s1,…..s9 ≥0 (non-negativity).

Microsoft Excel 15.0 Sensitivity Report Worksheet: [or.xlsx]Sheet1 Report Created: 10/5/2018 9:42:04 AM

Variable Cells Final

Reduced

Objective

Allowable

Allowable

Name

Value

Cost

Coefficient

Increase

Decrease

$B$4

Values X1

14911.76471

0

2

0.158730159

0.210526316

$C$4

Values X2

0

-0.852941176

1

0.852941176

1E+30

$D$4

Values X3

22000

0

2

1E+30

0.147058824

$E$4

Values X4

0

-0.176470588

1.5

0.176470588

1E+30

$F$4

Values s1

5.175

0

0

3921.568627

2139.037433

$G$4

Values s2

2.065588235

0

0

3174.603175

10752.68817

$H$4

Values s3

2.512941176

0

0

3333.333333

2631.578947

$I$4

Values s4

0

-2941.176471

0

2941.176471

1E+30

$J$4

Values s5

9.809705882

0

0

1122.544434

1912.045889

$K$4

Values s6

20088.23529

0

0

0.210526316

0.158730159

$L$4

Values s7

28000

0

0

1E+30

0.852941176

$M$4

Values s8

0

-0.147058824

0

0.147058824

1E+30

$N$4

Values s9

21000

0

0

1E+30

0.176470588

Cell

Constraints

Cell

Name

Final

Shadow

Constraint

Allowable

Allowable

Value

Price

R.H. Side

Increase

Decrease

$O$10 c4

24

2941.176471

24

2.22952381

10.14

$O$11 c5

24

0

24

1E+30

9.809705882

$O$12 c6

35000

0

35000

1E+30

20088.23529

$O$13 c7

28000

0

28000

1E+30

28000

$O$14 c8

22000

0.147058824

22000

16095.2381

21682.53968

$O$15 c9

21000

0

21000

1E+30

21000

$O$7

c1

24

0

24

1E+30

5.175

$O$8

c2

24

0

24

1E+30

2.065588235

$O$9

c3

24

0

24

1E+30

2.512941176

Result Analysis Company produces 14911.765 meters of Saree material per day (14911.765 x 330 working days = 4920882.45 meters/annum) and 22000 meters of cotton dress material per day (22000 x 330 days = 7260000 meters/annum) in order to get a maximum daily profit of Rs. 73823.529 per day. In this way the company is left with an ideal bleaching, dyeing , print and packaging times of 5.17 hours, 2.06 hours, 2.51 hours and 9.80 hours respectively. The unutilized demand for Saree material is 20088.235 meters, 28000 meters for dress material polyester and 21000 meters for shirting material.

Conclusion 1) Linear programming model is applied for profit optimization of ‘imperial dyeing ltd’ and the maximum profit of Rs. 73823.53 per day was found. 2) The company is left with an ideal bleaching, dyeing, print and packaging times of 5.17 hours, 2.06 hours, 2.51 hours and 9.80 hours respectively. 3) The production value for polyester dress material and shirt material is nil. So it is advised to the firm that the production for these materials should be stopped after they break even. 4) The unutilized demand for Saree material is 20088.235 meters, 28000 meters for dress material polyester and 21000 meters for shirting material.

References Çağatay Teke, C. O. (2017, April). Determining the Production Amounts in Textile Industry with Fuzzy Linear Programming. INTERNATIONAL JOURNAL OF ENGINEERING AND TECHNOLOGY RESEARCH. Eshetie Kassegn, D. A. (2016, April 6). Case Study on Profit Planning of Textile Industry Using Linear Programming Approach. REST Journal on Emerging trends in Modelling and Manufacturing. Foundation, I. B. (n.d.). Textile Industry & Market Growth in India. Retrieved from www.ibef.org: https://www.ibef.org/archives/detail/b3ZlcnZpZXcmMzc3NDEmMTEy Gera Workie, A. B. (2016, August 10). Application of Linear Programming Techniques to Determine the Type and Quantity of Textile Dyed Fabrics. Research Journal aof Science and IT Management. III, B. W. (n.d.). Introduction to management science . In B. W. III, Linear Programming : Model Formulation and Graphical Solution. Vishwa Nath Maurya, R. B. (2015, September ). Profit Optimization Using Linear Programming Model: A Case Study of Ethiopian Chemical Company. American Journal of Biological and Environmental Statistics, 1(2), 51-57. Woubante, G. W. (2017, June). The Optimization Problem of Product Mix and Linear Programming Applications: Case Study in the Apparel Industry. Open Science Journal.