Download - 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
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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.