Tradeoff Information in Interactive Multiobjective Linear Programming Methods

Kok, M. (1984). Tradeoff Information in Interactive Multiobjective Linear Programming Methods. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-84-035

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Abstract

All of the various methods developed to handle models with multiple objectives require preference information from a decision maker in order to obtain a satisfactory solution. The ability of most decision makers to give a priori information about their preference structure is generally weak, but it is assumed that inspection of trial solutions generated during a computer session will help them to formulate their preferences.

In this paper we consider the information that interactive methods can supply to a decision maker. For example, they could provide tradeoff values that could be useful in assessing the interdependence of the objective functions once a trial solution has been obtained. Because there is no unique approach to the multiobjective linear programming (MOLP) problem, several approaches (and scalarization methods) are considered. The relations between the tradeoffs and the dual variables in each of these formulations of the MOLP problem are discussed. These theoretical notions are illustrated by examining the information that is given to a decision maker by some commonly used interactive methods. We show that these methods supply only a part of the available (tradeoff) information. Two existing interactive methods are then extended using the dual variables and duality properties of the problem.

In the next few years we plan to carry out some experiments with decision makers (opinion leaders) in public energy planning to see whether the ideas developed here are actually useful in practice.

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