Fundamentals of Multi-criteria Decision Making (MCDM) Problems

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

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

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

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

Classification of MCDM Problems

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

One MODM Example

Maximise z1 = 3x1 + 5 x2 Minimise z2 = 0.5 x1 + 0.25x2 subject to 25 x1 + 50 x2 = 80,000 x1, x2  0

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

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.

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

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

General formulation of a MADM problem

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)

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

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

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

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 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

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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