Trade-off analysis using parametric optimization techniques

Abstract

In multi-objective programming problems, one of the most difficult tasks is ‘balancing among multiple objectives’, i.e. ‘trade-off’. This difficulty originates from the value judgment of decision makers. During the past decade, several methods have been developed to overcome this difficulty in multiobjective programming problems. Among them, from a practical viewpoint, the aspiration level approach is very attractive, since it does not require any consistency of the decision maker's judgement, and it makes the trade-off (in other words, balancing) among the objectives very easy. On the other hand, some of the practical problems have very many objective functions, say, about one hundred. For this kind of problem, decision makers tend to be tired with answering their aspiration levels for all objective functions. It is very important, therefore, to decrease the burden of the decision makers in their trade-off. In this paper, a method for trade-off using parametric optimization techniques will be suggested. In linear and quadratic problems, the method can show the exact trade-off information very rapidly even in cases with very many objective functions. Therefore, it can be expected to help decision makers' judgement in their trade-offs effectively in many practical problems.