supplier selection fuzzy ahp

Global supplier Global supplier selection: An AHP based selection: An AHP based

approach approach

Global supplier Global supplier selection: An AHP based selection: An AHP based

approach 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

NUMERICAL VALUE

1

2

3

4

5

6

7

8

9

PREFERENCE LEVEL

Equally preferred

Equally to moderately preferred

Moderately preferred

Moderately to strongly preferred

Strongly preferred

Strongly to very strongly preferred

Very strongly preferred

Very strongly to extremely preferred

Extremely preferred

The Analytic Hierarchy Process

Objective

Criterion 2Criterion 1 Criterion KLevel 2

Subcriterion 1 Subcriterion 2 Subcriterion L

Alternative 1 Alternative 2 Alternative N

Level 3

Level P

Hierarchy with P Levels

Level 1

Step 1. Decompose the problem into a hierarchy of interrelated decision criteria and alternatives

…

…

…

.

.

.

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The Analytic Hierarchy Process

Decision maker

Identification ofSCNPerformance evaluation

Identification ofOptimal transshipment

and vehicle routingLevel 2

Resource UL,Response time,Product variety

Capacity, Demand location

Travel timeTotal cost of shipment

Travel comfortAlternative 1 Alternative 2

Alternative 3

Level 3

Level P

Hierarchy with P Levels

Level 1

Step 1. Decompose the problem into a hierarchy of interrelated decision criteria and alternatives

9

The basic procedure is as follows:The basic procedure is as follows:

Develop the ratings for each decision alternative for Develop the ratings for each decision alternative for each criterion byeach criterion by

• developing a pairwise comparison matrix for developing a pairwise comparison matrix for each criterioneach criterion

• normalizing the resulting matrixnormalizing the resulting matrix

• averaging the values in each row to get the averaging the values in each row to get the corresponding ratingcorresponding rating

• calculating and checking the consistency calculating and checking the consistency ratioratio

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

A B C D

B 1

C e21 1

D e31 e32 1

e12 e13

e23

Degree of preference of rows over the column

Inverse of entities given below the

diagonal

Step2: Determination of Normalized value

AHP-Steps…

e33/Ce32/Be31/A

e23/Ce22/Be21/A

e13/Ce12/Be11/A

This matrix is known as the Normalized

matrix

Divide j column elements with summation of

column

A=e11+e21+e31

B=e12+e22+e32

C=e13+e23+e33

M=

AHP-Steps…

C1

C2

C3

Represents the

relative importance for ith alternative selection criteria

=C=

k1=e11/A+ e12/B +e13/Ck2=e21/A+ e22/B +e23/Ck3=e31/A+ e32/B +e33/C

K1/3

K2/3

K3/3

Step3: Determination of principal vector or Eigen Vector

Consistency Ratio

The purpose is to make sure that the original The purpose is to make sure that the original preference ratings were consistent.preference ratings were consistent.

1.1. Calculate the consistency measure for Calculate the consistency measure for each criterion. each criterion.

2.2. Calculate the consistency index (CI).Calculate the consistency index (CI).3.3. Calculate the consistency ratio (CI/RI Calculate the consistency ratio (CI/RI

where RI is a random index).where RI is a random index).

There are 3 steps to arrive at the consistency There are 3 steps to arrive at the consistency ratio:ratio:

Approximation of the Consistency Index

1. 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…

1max

m

m3. The approximate CI is

CI - the consistency index

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

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RANDOM INDEX (RI)RANDOM INDEX (RI)

22 0.000.00 33 0.580.58 44 0.900.90 55 1.121.12 66 1.241.24 77 1.321.32 88 1.411.41 99 1.451.451010 1.511.51

mm

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

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

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

COST

A B

A 1 7

B 1/7 1

QUALITY

A B

A 1 1/3

B 3 1

Degree of preference of

B over A

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 transshipment

A B C

A 1 6 1/3

B 1/6 1 1/9

C 3 9 1

Identification of SCN

A B C

A 1 1/3 1

B 3 1 7

C 1 1/7 1

Step 1Performance evaluation

A B C

A 1 3 2

+ + +

B 1/3 1 1/5

+ + +

C 1/2 5 1

= 11/6 9 16/5

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

Step 2

A B C

A 111/6 = 6/11 39 = 3/9 216/5 = 5/8

+ + +

B 1/311/6 = 2/11 19 = 1/ 9 1/516/5 1/16

+ + +

C 1/211/6 = 3/11 59 = 5/9 116/5 = 5/16

= 1 1 1

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

NOTICE: the values in each column sum to 1.

Step 3

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

Next convert fractions to decimals and find the average of each row.

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 Identification Identification

evaluation of SCM of transshipment

Performance

evaluation 1 1/5 3

Identification

of SCN 5 1 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

Price .18033

Distance .74813

QUALITY .07154

X

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

1.0000

Based on the scored supplier C should be chosen.

This is the best

supplier

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.