Water Resources Systems Planning and Management: Advanced Topics – Multi-criteria Decision Making D Nagesh Kumar, IISc, Bangalore 1 M9L3 MODULE - 9 LECTURE NOTES – 3 MULTI-CRITERIA DECISION MAKING INTRODUCTION Multicriterion decision making (MCDM) is a process of evaluating real world situations, based on various qualitative / quantitative criteria in certain / uncertain / risky environments to suggest a course of action / choice/ strategy / policy among the available options. In this lecture we will discuss about the structured decision making and various MCDM methods. STRUCTURED DECISION MAKING The evaluation of multicriterion situations using conventional approaches may be difficult. A structured decision making (SDM) is necessary to visualize the decision making. It also helps in replicating the same steps if the given decision is proved to be right. The steps in SDM are shown in figure 1. These steps are to be followed to arrive at an effective decision. Fig. 1 Steps in SDM Purpose and necessity of decision making Identification of decision makers Identification of criteria that will influence decision making Assume suitable priority to each criterion Formulate various strategies on which criteria can be evaluated Estimate each strategy using SDM Determine the suitable strategy Implement the strategy Evaluate the outcome of the decision Document the lessons that have been learnt in this process for further improvement of decision making skills
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Water Resources Systems Planning and Management: Advanced Topics – Multi-criteria Decision Making
D Nagesh Kumar, IISc, Bangalore
1
M9L3
MODULE - 9 LECTURE NOTES – 3
MULTI-CRITERIA DECISION MAKING
INTRODUCTION
Multicriterion decision making (MCDM) is a process of evaluating real world situations,
based on various qualitative / quantitative criteria in certain / uncertain / risky environments
to suggest a course of action / choice/ strategy / policy among the available options. In this
lecture we will discuss about the structured decision making and various MCDM methods.
STRUCTURED DECISION MAKING
The evaluation of multicriterion situations using conventional approaches may be difficult. A
structured decision making (SDM) is necessary to visualize the decision making. It also helps
in replicating the same steps if the given decision is proved to be right. The steps in SDM are
shown in figure 1. These steps are to be followed to arrive at an effective decision.
Fig. 1 Steps in SDM
Purpose and necessity of decision making
Identification of decision makers
Identification of criteria that will influence decision making
Assume suitable priority to each criterion
Formulate various strategies on which criteria can be evaluated
Estimate each strategy using SDM
Determine the suitable strategy
Implement the strategy
Evaluate the outcome of the decision
Document the lessons that have been learnt in this process for
further improvement of decision making skills
Water Resources Systems Planning and Management: Advanced Topics – Multi-criteria Decision Making
D Nagesh Kumar, IISc, Bangalore
2
M9L3
STEPS IN MCDM METHODOLOGY
The steps for the selection of best alternative from a set of available alternatives are
(Duckstein et al., 1989):
Defining the problem and fixing the criteria
Data collection
Establishment of feasible alternatives
Formulation of payoff matrix i.e., matrix comprising evaluation of alternatives with
reference to criteria
Selection of appropriate method
Incorporation of decision maker’s preferences
Choosing one or more best alternatives for further analysis
MCDM METHODS
MCDM methods can be classified into four groups:
1. Distance
(a) Compromise Programming (CP)
(b) Cooperative Game Theory (CGT)
(c) Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS)
(d) Composite Programming (COP)
2. Outranking
(a) Preference Ranking Organisation METHod of Enrichment Evaluation
(PROMETHEE)
(b) ELimination Et Choix Traduisant la REalite (ELECTRE)
3. Priority / Utility and
(a) Weighted Average Method
(b) Multi Attribute Utility Theory
(c) Analytic Hierarchy Process
4. Mixed category
(a) Multicriterion Q- Analysis -2
(b) EXPROM-2
(c) STOPROM-2
In this lecture we will discuss about compromise programming, PROMETHEE and weighted
average method.
Water Resources Systems Planning and Management: Advanced Topics – Multi-criteria Decision Making
D Nagesh Kumar, IISc, Bangalore
3
M9L3
COMPROMISE PROGRAMMING (CP)
The objective in CP is to obtain a solution that is as ‘close’ as possible to some ‘ideal’
solution in terms of distance. The distance measure used in Compromise Programming is the
family of Lp - metrics and expressed as
pJ
j
p
jj
p
jp affwaL
1
1
)()( * (1)
Normalizing between the range [0, 1], eqn. (1) becomes,
pJ
j
p
jj
jjp
jpmM
affwaL
1
1
)()(
*
(2)
where )(aLp = pL - metric for alternative a, )(af j = Value of criterion j for alternative a,
jM = Maximum value of criterion j in set N , jm = Minimum value of criterion j in set N ,
*
jf = Ideal value of criterion j, jw = Weight assigned to the criterion j, p =
Parameter/balancing factor reflecting the attitude of the decision maker with respect to
compensation between deviations. For p = 1, all deviations from *
jf are taken into account in
direct proportion to their magnitudes. For p , the largest deviation is the only one taken
into account corresponding to zero compensation between deviations. The flow chart of CP
methodology is given in figure 2.
Fig. 2 Flow chart of Compromise Programming methodology
Enter the number of alternatives, criteria, payoff matrix, and weight
of each criterion
Specify the parameter p ; Compute pL - metric value
Print results
Start
Stop
Rank alternatives based on minimum pL - metric value
Water Resources Systems Planning and Management: Advanced Topics – Multi-criteria Decision Making
D Nagesh Kumar, IISc, Bangalore
4
M9L3
Example
Compute pL - metric values of alternatives and corresponding ranking pattern for the payoff
matrix presented in Table 1 [Brans et al. (1986)] using Compromise Programming method
for p = 1, 2, . Assume equal weights for each criterion. Alternatives A1 to A6 in payoff
matrix represent hydropower projects and criteria C1 to C6 correspond to man power,
Hydropower (MW), construction cost (109 $), maintenance cost (10
6 $), number of villages
to be evacuated and security level respectively.
Table 1. Payoff Matrix
Crit.
Alt.
C1 C2 C3 C4 C5 C6
A1 80 90 6 5.4 8.0 5
A2 65 58 2 9.7 1.0 1
A3 83 60 4 7.2 4.0 7
A4 40 80 10 7.5 7.0 10
A5 52 72 6 2.0 3.0 8
A6 94 96 7 3.6 5.0 6
Max/Min Min Max Min Min Min Max
Solution:
Negative sign is assigned to the criterion of minimization in nature to enable to analyze the
problem uniformly in maximization perspective i.e., (-min) = max. Table 2 presents payoff
matrix after this transformation, where all criteria are made to be of maximization in nature.
Table 2. Transformed payoff matrix
Crit.
Alt.
C1 C2 C3 C4 C5 C6
A1 -80 90 -6 -5.4 -8.0 5
A2 -65 58 -2 -9.7 -1.0 1
A3 -83 60 -4 -7.2 -4.0 7
A4 -40 80 -10 -7.5 -7.0 10
A5 -52 72 -6 -2.0 -3.0 8
A6 -94 96 -7 -3.6 -5.0 6
Water Resources Systems Planning and Management: Advanced Topics – Multi-criteria Decision Making
D Nagesh Kumar, IISc, Bangalore
5
M9L3
pL - metric value can be computed as follows:
pJ
j
p
jj
jjp
jpmM
affwaL
1
1
)()(
*
Parameters that are required for the computation of pL - metric value are: maximum,
minimum and ideal value for each criterion, weight of each criterion and parameter p. These
parameters are presented in Table 3.
Table 3. Parameters required for computation of pL - metric value