A New Method to Solve Multi-Objective Linear Fractional Problems

Abstract

Background: In the literature, there exists several approaches to address the multi-objective linear fractional programming problem (MOLFPP). However, there is a drawback to these methods.

Aim: This paper presents an efficient method treating the MOLFPP.

Methodology: To construct our approach,the membership functions of the objectives, suitable non-linear variable transformations, and max-min technique are used.

Results: In our proposed method, the MOLFPP is finally changed into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an efficient solution for the MOLFPP.

Conclusion: Numerical examples are solved, and the results demonstrate that our method with less computational expenses and cost reach the efficient solutions.

KEYWORDS:

• Efficient solution
• membership function
• max–min technique
• linear programming
• fractional programming

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by Universiti Kebangsaan Malaysia [Grant Number ST-2019-016].

Notes on contributors

Mojtaba Borza

Mojtaba Borza is Ph.D. of applied mathematics doing research in optimization and operations research under the supervision of Dr. Azmin Sham Rambely.

Azmin Sham Rambely

Dr. Azmin Sham Rambely is associate professor of department of mathematics, University Kebangsaan Malaysia. Her research interest is optimization and bio-mechanic.