Article

Mathematical Programming

, Volume 17, Issue 1, pp 16-31

First online:

Goal programming sensitivity analysis using interval penalty weights

  • Ralph E. SteuerAffiliated withPrinceton University

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Abstract

This paper presents an application of the vector-maximum research [4–8] to the sensitivity analysis of goal programming problems as several of the criterion function penalty weights are simultaneously and independently varied. A generalized goal programming capability is presented and a six-stage analytic procedure is described. The problem is generalized in the sense that the regular goal programming penalty weights can be expanded to intervals if desired. The solution procedure is new in that it depends upon an algorithm for the vector-maximum problem, “criterion cone” contraction procedures, and “filtering” techniques. Together they are able to generate and process all extreme points on the portion of the surface of the goal programming “augmented” feasible region corresponding to the interval penalty weights specified. In effect, the procedure and adapted algorithm of this paper delivers to goal programming an operational power of sensitivity analysis not previously available to users. A numerical example is provided in order to illustrate the computerized application of the total goal programming procedure outlined.

Key words

Goal Programming Sensitivity Analysis Vector-Maximum Algorithms Multiple Objective Linear Programming Multiple Criteria Decision Making