Multiple Objective Linear Programming with Interval Criterion Weights

Abstract

The purpose of this research is to develop a computer applicable methodology for analyzing multiple objective linear programming problems when interval, rather than fixed, weights are assigned to each of the objectives. Rather than obtaining a single efficient extreme point as one would normally expect with fixed weights, a cluster of efficient extreme points is typically generated when interval weights are specified. Then, from the subset of solutions generated, it is contemplated, that the decision-maker will be able to qualitatively identify his efficient extreme point of greatest utility (which should either be the decision-maker's optimal point or be close enough to it to terminate the decision process). The procedure presented in this paper involves converting the multiple objective linear programming problem with interval criterion weights into an equivalent vector-maximum problem. Once in such form, an algorithm for the vector-maximum problem can then be used to determine the subset of “efficient extreme” points corresponding to the interval weights specified. General computational experience regarding the operation of the equivalent vector-maximum problem is reported. Also, a numerical example is provided to illustrate the total procedure described.