1. Fundamentals of Multi-criteria Decision Making (MCDM) Problems

2. Decision making is an important part of our life.
People have continuously devised means and ways to enlarge their abilities to cope with the growing complexity of their decision making problems.
Decision making problems:
-- Deterministic
-- Probabilistic

3. Decision making problems:
-- Number of decision makers
-- Single decision maker
-- A group of decision makers
-- Number of criteria
-- Single criterion
-- Multiple criteria

4. Job Selection Criteria
Salary
Job security
Working environment
Advancement opportunity
Location
Reputation

5. Car Selection Problem:
Alternatives: BMW, Ford, Honda, Mercedes, Nissan, Proton, Toyota, Volvo etc.
Criteria: Price, MPG, Style, Riding comfort etc.

6. Classification of MCDM Problems

7. Maximise z = 2x1 + 3 x2
subject to: x1 + 5 x2  50
3 x1 + 4 x2  85
x1, x2  0
Maximise z1 = 2x1 + 3 x2
Minimise z2 = 3 x1 + x2

8. One MODM Example

9. Maximise z1 = 3x1 + 5 x2
Minimise z2 = 0.5 x x2
subject to x x2 = 80,000
x1, x2  0

10. General form of MOLP Maximise z1 = c11x1+c12 x2 + …… + c1n xn
  
Maximise zk = ck1x1 + ck2 x2 + … . + ckn xn
subject to a11 x1 + a12 x2 + ….. + a1n xn  b1
a21 x1 + a22 x2 + …… + a2n xn  b2
: : :
am1 x1 + am2 x2 + … + amn xn  bm
x1, x2 , ……… xn  0

11. MODM problems arises in design, modelling, and planning of many complex resource allocation systems in the area of:
Industrial production
Urban transportation
Health
Layout and landscaping of new cities
Energy production and distribution
Wild life management
Operations and controls of firms
Agriculture, etc, etc.

12. MODM Problems Methods Goal Programming Fuzzy Programming
Utility Function Method
Global Criterion Method
Lexicographic Method

13. An Example of A Multi-Attribute Decision Making (MADM) Problem

14. General formulation of a MADM problem

15. Methods to solve MADM Problems
ELECTRE (1968)
Simple Additive Weighting Method(1969)
Elimination by Aspects (1971)
LINMAP (1973)
Permutation Method (1976)
Multi Attribute Utility Theory (1976)
Linear Assignment Method ((1977)
Analytic Hierarchy Process (1977)
TOPSIS (1980)

16. Determining criteria weights
Methods:
Ranking
Rating
Pairwise Comparison
The weights are normalized:

17. Ranking Method: where n = total number of criteria
where n = total number of criteria
ri = rank of the ith criterion
Ranking Method:

18. Ranking Method Criteria Straight Rank Weight (n-ri+1) Normalized
Cost of land 3
3/15 = 0.20
Proximity to population 1 5
0.33
Earthquake proneness 4 2
0.13
Transportation
0.27
Proximity to water
0.067
Total = 15

19. Rating Method : Point Allocation
Criteria
Points
Weights
Cost 17
0.17
Proximity to population 28
0.28
Earthquake 20
0.20
Transportation 14
0.14
Proximity to water 21
0.21

20. 20 Rating Method: Ratio estimation Criteria Rank Ratio scale Weight
Normalized weight
Cost of land 3 60
60/20 = 3
0.2020
Proximity to population 1
100 5
0.3367
Earthquake 4 45
2.25
0.1515
Transportation 2 72
3.6
0.2424
Proximity to water 20
0.0673
14.85

21. Self Test : Each year, “CEO of the Year is selected” on the basis of a comprehensive set of criteria which are considered in a stringent selection process.
What should be the selection criteria from your point of view? Consider only six and determine their weights by
Ranking Method.

22. Thank you
for your attention