SOLVING LINEAR GOAL PROGRAMMING PROBLEM USING LEXICOGRAPHIC AND DUAL SIMPLEX METHODS

Abstract

Goal programming is an important class of multi-criteria decision models widely used to solve problems involving conflicting objectives. Primarily to find a compromised solution which will simultaneously satisfy a number of goals. This note proposes a solution algorithm for linear goal programming problems. In solving goal programming problems, the solution methods reduce the multiple goal programming problems into a single objective of minimizing a weighted sum of deviations from goals. In this paper, we propose the goal programming problem as a multi- objective optimization problem of minimizing deviations from individual goals. This procedure eliminates the need of having extra constraints needed with classical formulations and also eliminates the need of any user-defined weight factor for each goal. The main objective of this study was to solve linear goal programming problem by using Lexicographic and Dual Simplex Method.. An optimal solution is attained when all the goals are reached as close as possible to their aspiration level, while satisfying a set of constraints. Finally, some illustrative examples are presented to show the applicability and effectiveness of the solution method.