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2016•Pure and Applied Mathematics JournalOpen access

The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems

Geleta Tadele Mohammed

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Abstract

Most of real world decision making problems have multiple objectives, which cannot be optimized simultaneously due to the conflicting nature of the objectives. Such problems can be solved by various methods to obtain the best-compromise solutions. Modified Sequential Linear Goal Programming (MSLGP) method can be used to solve Multiple Objective Linear programming Problems. In this paper, the use of existing single objective Linear Programming (LP) techniques is there, and the information required for MSLGP in each iteration are taken from the previous iteration. In this study, there is a great Revised Multi-phase Simplex Algorithm, which is used to solve MSLGP Accordingly within small number of computations as much as possible. This method is illustrated by some numerical examples, and provides ‘best compromise’ solution.

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What this paper is about

Most of real world decision making problems have multiple objectives, which cannot be optimized simultaneously due to the conflicting nature of the objectives. Such problems can be solved by various methods to obtain the best-compromise solutions. Modified Sequential Linear Goal Programming (MSLGP) method can be used to solve Multiple Objective Linear programming Problems. In this paper, the use of existing single objective Linear Programming (LP) techniques is there, and the information required for MSLGP in each iteration are taken from the previous iteration. In this study, there is a great Revised Multi-phase Simplex Algorithm, which is used to solve MSLGP Accordingly within small number of computations as much as possible. This method is illustrated by some numerical examples, and provides ‘best compromise’ solution.

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Available abstract

Most of real world decision making problems have multiple objectives, which cannot be optimized simultaneously due to the conflicting nature of the objectives. Such problems can be solved by various methods to obtain the best-compromise solutions. Modified Sequential Linear Goal Programming (MSLGP) method can be used to solve Multiple Objective Linear programming Problems. In this paper, the use of existing single objective Linear Programming (LP) techniques is there, and the information required for MSLGP in each iteration are taken from the previous iteration. In this study, there is a great Revised Multi-phase Simplex Algorithm, which is used to solve MSLGP Accordingly within small number of computations as much as possible. This method is illustrated by some numerical examples, and provides ‘best compromise’ solution.

Key concepts: Linear programming, Simplex algorithm, Mathematical optimization, Mathematics, Linear-fractional programming, Goal programming, Revised simplex method, Criss-cross algorithm

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