vdocuments.mx_supplier-selection-fuzzy-ahp.ppt

Rtf

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

2. Outline
•Aim
•Supplier selection problem
•Analytical Hierarchy Process
•Illustrative example
•Results

3. 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)?

4. 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 VALUEof
manufacturer.
•Reducing the product supply RISK.
•Maximizing the customer SATISFACTIONlevel.

5. 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% ofcost of goods corresponds to raw
materials.
•Enhanced QUALITYof products and services.

6. 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.

7. 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.

8. 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

9. The Analytic Hierarchy Process
Objective
Criterion 2Criterion 1 Criterion K
Level 2
Subcriterion 1Subcriterion 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
…
…
…
.
.
.
9

10. The Analytic Hierarchy Process
Decision maker
Identification of
SCNPerformance evaluation
Identification of
Optimal transshipment
and vehicle routing
Level 2
Resource UL,
Response time,
Product variety
Capacity, Demand
location
Travel time
Total cost of shipment
Travel comfort
Alternative 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

11. 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

12. AHP-Steps
•Step 1: Determination of pair wise matrix
A B C D
B 1
C e
211
D e
31e
321
e
12e
13
e
23
Degree of
preference of rows
over the column
Inverse of entities
given below the
diagonal

13. Step2: Determination of Normalized value
AHP-Steps…
e
33
/Ce
32
/Be
31
/A
e
23
/Ce
22
/B
e
21
/A
e
13
/Ce
12
/Be
11
/A
This matrix is
known as the
Normalized matrix
Divide j column
elements with
summation of column
A=e
11+e
21+e
31
B=e
12+e
22+e
32
C=e
13+e
23+e
33
M=

14. AHP-Steps…
C
1
C
2
C
3
Represents the
relative importance
for i
th
alternative
selection criteria
=C=
k
1=e
11/A+ e
12/B +e
13/C
k
2=e
21/A+ e
22/B +e
23/C
k
3=e
31/A+ e
32/B +e
33/C
K
1/3
K
2/3
K
3/3
Step3: Determination of principal vector or
Eigen Vector

15. Consistency Ratio
The purpose is to make sure that the original
preference ratings were consistent.
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).
There are 3 steps to arrive at the consistency
ratio:

16. 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 λ
max
which is maximum Eigen value of the pairwise
comparison matrix.

17. Consistency ratio…1
max


m
m
3. The approximate CI is
CI-theconsistencyindex
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.

18. 18
RANDOM INDEX (RI)
2 0.00
3 0.58
4 0.90
5 1.12
6 1.24
7 1.32
8 1.41
9 1.45
10 1.51
m
Random Index (RI)
the CI of a randomly-generated pairwise comparison matrix

19. Limitations
Nomorethanabout7elementsshouldbecompared
atonetimebecausetheinconsistencywillbelarge
anddeterminingwhichvaluetochangewillbe
difficult
Iftherearegreaterthan7elements,theelements
shouldbegroupedintoclustersofseven

20. 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.

21. 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

22. 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.

23. 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 1/61 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

24. Step 1
Performance evaluation
A B C
A 1 3 2
+ + +
B 1/31 1/5
+ + +
C 1/2 5 1
= 11/6 9 16/5
First sum (add up) all
the values in each
column.

25. Step 2
A B C
A 1+11/6= 6/11 3+9= 3/92+16/5= 5/8
+ + +
B 1/3+11/6= 2/111+9= 1/ 9 1/5+16/51/16
+ + +
C 1/2+11/6= 3/115+9= 5/91+16/5= 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.

26. 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.

27. Step 4
Apply Step 1-3 on each criteria that results in the average for all
the criteria.
performance Identification Identification
evaluationSCN Transshipment
A .5012 .2819 .1790
B .1185 .0598 .6850
C .3803 .6583 .1360

28. 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 transshipment1/3 1/9 1

29. 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

30. Row average= preference
vector for the criteria
CRITERIA
Price .18033
Distance .74813
Quality .07154

31. 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
SupplierA score = .18033(.0512) + .74813(.2819) + .07154(.1790) = .2328
SupplierB score = .18033(.1185) + .74813(.0598) + .07154(.6850) = .19639
Supplier C score = .18033(.3803) + .74813(.6583) + .07154(.1360) = .5708

32. 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

33. 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.