Multiple criteria subset selection under interdependence of actions

Abstract

Multiple Criteria Decision Making (MCDM) is a problem that has been studied extensively. Most pitfalls are by now well-known, and many proven algorithms permit choices to be made efficiently. But, when the problem is a multiple criteria subset selection, new difficulties appear, and most algorithms of MCDM are either inapplicable or impractical.

Even when actions are independent, so their cumulative effects are additive, multiple criteria subset selection is a challenging problem. Moreover, applicable multiple criteria subset selection approaches suffer from large computational requirements. To deal with these difficulties, techniques are introduced for screening individual actions when a subset of a large discrete set of independent actions is to be selected, both when the number of actions to be selected is given a priori, and when the subset to be selected must satisfy several constraints.

When actions are interdependent the subset selection problem becomes even harder. A novel definition and characterization of the interdependence of actions in the context of multiple criteria subset selection problems are presented. Most of the interdependence discussion can be generalized to sets of actions rather than individual actions. Exploration of the main relationships of set-independence and action-independence produces several different methods for evaluating a set of inter-dependent actions. A general approach to evaluate a combination of interdependent actions is proposed and applied to the multiple criteria structure. The effects of interdependence of actions on the modeling and resolution of a subset choice problem are illustrated, and the importance of taking interdependence of actions into account is demonstrated.

The subset selection problem under interdependence of actions is formulated as a multiple criteria integer program and two solution methodologies are proposed. The advantages of these approaches in comparison to others are discussed. These methodologies and associated analytical techniques are applied to an on-going water supply planning problem in the Regional Municipality of Waterloo. The results indicate both the importance of interdependence of actions and the effectiveness of the proposed methodologies.