The role of weights and scales in the application of multiobjective decision making

Abstract

The application of multiobjective solution techniques requires, at some point in the analysis, the specification of the preference structure of the decision maker over the set of objectives. In practice, this step must often take the form of determining a set of weights that attempts to quantify the relative importance of the various competing objectives. This paper looks at how some of the well known techniques make use of these weights in attempting to achieve the best compromise solution. The definition of the weights (i.e., what meaning they carry into the analysis) is also explored. It is found that one must be very careful about applying weights when using these techniques. A different set of weights for the same objectives may apply when implementing two different techniques. In addition, a related factor, the specification of scales or ranges over which the objectives are to be evaluated, is explored. Again, it is found that different techniques use these scales in ways that change the manner in which they should be defined. The techniques reviewed are compromise programming, multiattribute utility theory, ELECTRE and cooperative game theory. Concepts are illustrated through the use of a water resources example problem.