1 of 10

MULTICRITERIA

Class Notes

Pere Riera

2 of 10

Lección 4

DCMA

3 of 10

Multicriteria (or Multiple-Criteria) Decision Analysis (MCDA)

Sometimes it is referred to as Multicriteria Decision Making (MCDM)
Or simply Multicriteria Analysis

It is typically used to rank a set of mutually exclusive options (called alternatives)

DCMA lecture notes

4 of 10

MCDA does not inform on the desirability of each alternative (except in some variants, like in goal programing, under some conditions)

One could be ranking negative welfare alternatives

It only informs on the relative desirability among alternatives

DCMA lecture notes

5 of 10

There are many variants of MCDA

The two main families are

The one that uses weights (“Anglo-Saxon tradition”)
The one that uses algorithms without weights (“French tradition”)

The most popular is the first one (weighted)

DCMA lecture notes

6 of 10

A simple weighted MCDA application can typically be performed with the following steps

1. Decide the alternatives to be ranked

Often restricted to 2, 3, 4…

2. Decide the relevant criteria to be used

Often restricted to 3, 4, 5…

DCMA lecture notes

7 of 10

3. Decide the weight values for each criterion

By your own decision, literature review, a survey, Delphi process, or any other procedure

A mixed procedure is the complete ranking one where the order of importance is first (a priory) decided, and then an expression of the type

is applied, with β_j = relative weight, r = rank order according to a priori importance, and j = the criteria, from 1 to n

DCMA lecture notes

8 of 10

4. Value the “impacts” v_ij (each criterion i for each alternative j) in their own units, quantitatively or qualitatively

5. “Normalize” the values to express them in common units. There are different ways, e.g.

Normalized value a_ij = v_ij / Sum of values of criterion j

It yields values normalized between 0 and 1

Normalized value a_ij = v_ij / Maximum value of criterion j

It yields values normalized between 0 and 1

DCMA lecture notes

9 of 10

6. Aggregate the values from each criterion within an alternative, to obtain a Preference Index (PI_i) or aggregated value, as in

and for each alternative, from j = 1 to m

7. Perform sensitivity analyses

8. Rank alternatives according to PI values

DCMA lecture notes

10 of 10

PRACTICAL EXAMPLE FROM CLASS

Exercise

Using a standard weighted multicriteria analysis, find the desirability ranking of the three following locations for an incineration plant. The first criterion for location A is estimated in 1000 unit of air pollution, 150 units for location B, and 140 for C. The value for the second criterion for location A is of 10000 units of cost, 5000 units for location B, and 15000 for C. The third criterion for A is of 0.2 units of soil pollution, 0.3 for B and 0.2 for C.

Most desirable location: ______ , score: ______
Second most desirable location: ______ , score: ______
Least desirable location: ______ , score: ______

DCMA lecture notes