Fundamentals of Multicriteria Decision Making
(MCDM) Problems
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University Malaysia
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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
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Decision making problems:
-- Number of decision makers
-- Single decision maker
-- A group of decision makers
-- Number of criteria
-- Single criterion
-- Multiple criteria
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Job Selection Criteria
• Salary
• Job security
• Working environment
• Advancement opportunity
• Location
• Reputation
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Car Selection Problem:
Alternatives: BMW, Ford, Honda, Mercedes, Nissan, Proton,
Toyota, Volvo etc.
Criteria: Price, MPG, Style, Riding comfort etc.
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Classification of MCDM
Problems
Multi-Criteria Decision Making
(MCDM)
Multi-Objective Decision Making Multi-Attribute Decision Making
(MODM)
(MADM)
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University Malaysia
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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
subject to:
x1 + 5 x2  50
3 x1 + 4 x2  85
x1, x2  0
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University Malaysia
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One MODM Example
Stock Price/share Estimated
Annual
return/share
ELB RM 25
RM 3
Risk
index/
share
0.5
ECB RM 50
0.25
RM 5
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University Malaysia
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Maximise z1 = 3x1 + 5 x2
Minimise z2 = 0.5 x1 + 0.25x2
subject to
25 x1 + 50 x2 = 80,000
x1, x2  0
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University Malaysia
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General form of MOLP
Maximise z1 = c11x1+c12 x2 + …… + c1n xn
Maximise z2 = c21x1 + c22 x2 + … + c2n 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
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University Malaysia
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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.
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University Malaysia
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MODM Problems Methods
•
•
•
•
•
Goal Programming
Fuzzy Programming
Utility Function Method
Global Criterion Method
Lexicographic Method
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University Malaysia
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An Example of A Multi-Attribute
Decision Making (MADM) Problem
Salary Location
Working
Environment
Not
Satisfactory
Very good
Job # 1 7,000
good
Job # 2 6,000
bad
Job # 3 5,000
Very good Average
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University Malaysia
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General formulation of a MADM problem
C1
C2
 Cn
A1 x11
x12
 x1m
A2 x21
x22
 x2m



xn2
 xnm

An xn1
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University Malaysia

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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)
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Determining criteria weights
Methods:
1. Ranking
2. Rating
3. Pairwise Comparison
n
The weights are normalized:
 wi 1.
i 1
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Ranking Method:
wi 
n  ri  1
 n  ri 1
i
where n = total number of criteria
ri = rank of the ith criterion
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Ranking Method
Criteria
Straight
Rank
Weight
(n-ri+1)
Normalized
Weight
Cost of land
3
3
3/15 = 0.20
Proximity to
1
population
Earthquake
4
proneness
Transportation 2
5
0.33
2
0.13
4
0.27
Proximity to
water
1
0.067
5
Total = 15
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Rating Method : Point Allocation
Criteria
Points
Weights
Cost
17
0.17
Proximity to
population
Earthquake
28
0.28
20
0.20
Transportation
14
0.14
Proximity to
water
21
0.21
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Rating Method: Ratio estimation
Criteria
Rank Ratio
scale
3
60
Weight
1
100
5
0.3367
4
45
2.25
0.1515
Transportation 2
72
3.6
0.2424
Proximity to
water
20
1
0.0673
Cost of land
Proximity to
population
Earthquake
5
Normalized
weight
60/20 = 3 0.2020
14.85
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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.
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University Malaysia
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