Supplier Selection Fuzzy Ahp

Global supplier selection: An AHP based approach Lecture by: Prof M. K. Tiwari Department of Industrial Engineering and Management Indian Institute of Technology, Kharagpur

Outline • • • • •

Aim Supplier selection problem Analytical Hierarchy Process Illustrative example Results

Aim • How to develop a methodology which facilitates selection of best supplier from a bunch of suppliers? – The methodology considers various selection criteria for this purpose.

• How to handle the vague and unclear selection criteria? – The solution is Fuzzy Set Theory.

• How to apply the Analytical Hierarchy Process (AHP)?

What is supplier selection?

• A process to select a number of suppliers from a group of suppliers.

• In order to • • • •

Improve the QUALITY of goods and services. Maximize the OVERALL VALUE of manufacturer. Reducing the product supply RISK. Maximizing the customer SATISFACTION level.

Why supplier selection? • To establish a LONG-TERM EFFECTIVE COLLABORATION with the efficient organizations. • An efficient one is capable to handle the COMPLEXITY of the current business scenario. • Reduced cost of OUTSOURCING. • About 70% of cost of goods corresponds to raw materials. • Enhanced QUALITY of products and services.

Analytic Hierarchy Process (AHP) • A multi-criteria decision making (MCDM) process since used to select alternatives based on many criteria. • A simple, useful, and systematic approach. • Encompasses matrix theory. • Utilizes Eigen value and Eigen vector to select alternatives.

AHP… • In this approach – Hierarchy is developed from a general criterion to particular. – Or from the uncertain or uncontrollable to the more certain or controllable one. • This hierarchy is subjected to a pair wise comparison. • Traditionally, this comparison is done using a nine point (1-9) scale. • This converts the human preferences between available alternatives as equally, moderately, strongly, very strongly or extremely preferred.

Standard Preference Table PREFERENCE LEVEL

NUMERICAL VALUE

Equally preferred

1

Equally to moderately preferred

2

Moderately preferred

3

Moderately to strongly preferred

4

Strongly preferred

5

Strongly to very strongly preferred

6

Very strongly preferred

7

Very strongly to extremely preferred

8

Extremely preferred

9

The Analytic Hierarchy Process Step 1. Decompose the problem into a hierarchy of interrelated decision criteria and alternatives Objective

Level 1 Level 2 Level 3 . . .

Level P

Criterion 1

Criterion 2

Subcriterion 1

Subcriterion 2

Alternative 1

Alternative 2

…

Criterion K

…

…

Subcriterion L Alternative N

Hierarchy with P Levels 9

The Analytic Hierarchy Process Step 1. Decompose the problem into a hierarchy of interrelated

Level 1 Level 2

decision criteria and alternatives Decision maker Identification of Performance evaluation SCN

Level 3

Resource UL, Response time, Product variety

Level P

Alternative 1

Capacity, Demand location

Identification of Optimal transshipment and vehicle routing Travel time Total cost of shipment Travel comfort

Alternative 2 Alternative 3

Hierarchy with P Levels 9

The basic procedure is as follows: Develop the ratings for each decision alternative for each criterion by • developing a pairwise comparison matrix for each criterion • normalizing the resulting matrix • averaging the values in each row to get the corresponding rating • calculating and checking the consistency ratio

AHP-Steps • Step 1: Determination of pair wise matrix A

B

C

B

1

C

e21

1

D

e31

e32

e12

Degree of preference of rows over the column

D e13 e23 1

Inverse of entities given below the diagonal

AHP-Steps… Step2: Determination of Normalized value

M=

e11/A

e12/B

e13/C

e21/A

e22/B

e23/C

e31/A

e32/B

e33/C

Divide j column elements with summation of column

A=e11+e21+e31 B=e12+e22+e32 C=e13+e23+e33

This matrix is known as the Normalized matrix

AHP-Steps… Step3: Determination of principal vector or Eigen Vector

K1/3

C1

C=

C2 C3

=

Represents the relative importance for ith alternative selection criteria

K2/3 K3/3

k1=e11/A+ e12/B +e13/C k2=e21/A+ e22/B +e23/C k3=e31/A+ e32/B +e33/C

Consistency Ratio The purpose is to make sure that the original preference ratings were consistent. There are 3 steps to arrive at the consistency ratio: 1. Calculate the consistency measure for each criterion. 2. Calculate the consistency index (CI). 3. Calculate the consistency ratio (CI/RI where RI is a random index).

Approximation of the Consistency Index

•

Multiply each column of the pairwise comparison matrix by the corresponding weight.

2.

Compute the average of the values, denote it by λmax which is maximum Eigen value of the pairwise comparison matrix.

Consistency ratio… 3. The approximate CI is

λmax − m m −1 

CI - the consistency index

If this ratio (CI/RI) is very large (Saaty suggests > 0.10), then we are not consistent enough and the best thing to do is go back and revise the comparisons.

m

RANDOM INDEX (RI)

2 3 4 5 6 7 8 9 10

0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.51

Random Index (RI) the CI of a randomly-generated pairwise comparison matrix 18

Limitations 

No more than about 7 elements should be compared

at

one

time

because

the

inconsistency will be large and determining which value to change will be difficult 

If there are greater than 7 elements, the elements should be grouped into clusters of seven

Which one you choose?? If – There are two products A & B. – Two criteria are COST and PERFORMANCE. – The cost for A= $75 and the performance is above average. – The cost for B=$20 and the performance is right at average. – Price of B is very strongly preferred to A and A is only moderately preferred to B.

How to create preference matrix? •

The matrices of these preferences COST A

B

A

1

7

B

1/7

1

Since price B is very strongly preferred to the price of A. The score of B to A is 7 and A to B is the reciprocal or inverse of 1/7 QUALITY

Degree of preference of B over A

A

B

A

1

1/3

B

3

1

Example An organization is trying to select the best supplier from a set of three suppliers. The company want to use AHP to help it decide which one to select. The organization has four criteria they will base their decision that are as following: 1. Property price 2. Distance 3. Quality 4. Cost of labor.

Matrices given criteria and preferences Performance evaluation A

B

C

A

1

3

2

B

1/3

1

1/5

C

1/2

5

1

Identification of SCN A

B

Identification of transshipment

C

A

B

C

A

1

1/3

1

A

1

6

1/3

B

3

1

7

B

1/6

1

1/9

C

1

1/7

1

C

3

9

1

Step 1 Performance evaluation

A

A

B

C

1

3

2

+ B

+ 1/3

+ C

+ 1

+ 1/2

= 11/6

1/5 +

5 9

1 16/5

First sum (add up) all the values in each column.

Step 2 A A

111/6

B

= 6/11

39

+ B

1/311/6

= 2/11

1/211/6

= 3/11 = 1

216/5

= 5/8

+ 19

+ C

= 3/9

C

+

= 1/ 9

1/516/5

+ 59

= 5/9 1

1/16 +

116/5

Next the values in each column are divided by the corresponding column sums.

= 5/16 1

NOTICE: the values in each column sum to 1.

Step 3 Next convert fractions to decimals and find the average of each row. Performance evaluation A

B

C

Row Average

A

6/11 ~.5455 +

3/9~.3333

+

5/8~ .6250 = 1.5038 3 = .0512

B

2/11~.1818

+

1/9~.1111

+

1/16~.0625 = .3544 3 = .1185

C

3/11~.2727 +

5/9~.5556

+

5/16~.3803 = 1.2086 3 = .3803 1.000

Step 4 Apply Step 1-3 on each criteria that results in the average for all the criteria.

performance

Identification

Identification

evaluation

SCN

Transshipment

A

.5012

.2819

.1790

B

.1185

.0598

.6850

C

.3803

.6583

.1360

Step 5 Rank the criteria in order of importance. Criteria

Performance evaluation

Identification of SCM

Identification of transshipment

Performance evaluation

1

1/5

5

1

3

Identification of SCN

9

Identification of transshipment

1/3

1/9

1

STEP 6-9 Criteria

Price

Distance

Quality

Row Average

Price

.1578

. 1525

.2307

.18033

Distance

.7894

. 7627

.6923

.74813

Quality

.0526

. 0847

.07704

.07154

1.000

Row average= preference vector for the criteria CRITERIA Price

.18033

Distance

.74813

Quality

.07154

FINAL CALCULATIONS Supplier

Price

Distance

QUALITY

A

.5012

.2819

.1790

B

.1185

.0598

.6850

C

.3803

.6583

.1360

CRITERIA

X

Price

.18033

Distance

.74813

QUALITY

.07154

Supplier A score = .18033(.0512) + .74813(.2819) + .07154(.1790) = .2328 Supplier B score = .18033(.1185) + .74813(.0598) + .07154(.6850) = .19639 Supplier C score = .18033(.3803) + .74813(.6583) + .07154(.1360) = .5708

And the results are . . . LOCATION

Score

A

.3091

B

.1595

C

.5314

This is the best supplier

1.0000 Based on the scored supplier C should be chosen.

Limitations • Uses only scaled numbers for judgments and for their resulting priorities. • Inadequate to handle the inherent uncertainty and imprecision associated with the mapping of the decision-maker’s perception to exact numbers.