A Linearization to the Sum of Linear Ratios Programming Problem

Mojtaba Borza and Azmin Sham Rambely
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Mojtaba Borza: Department of Mathematical Sciences, Faculty of Science & Technology, UKM Bangi, Selangor 43600, Malaysia
Azmin Sham Rambely: Department of Mathematical Sciences, Faculty of Science & Technology, UKM Bangi, Selangor 43600, Malaysia

Mathematics, 2021, vol. 9, issue 9, 1-10

Abstract: Optimizing the sum of linear fractional functions over a set of linear inequalities (S-LFP) has been considered by many researchers due to the fact that there are a number of real-world problems which are modelled mathematically as S-LFP problems. Solving the S-LFP is not easy in practice since the problem may have several local optimal solutions which makes the structure complex. To our knowledge, existing methods dealing with S-LFP are iterative algorithms that are based on branch and bound algorithms. Using these methods requires high computational cost and time. In this paper, we present a non-iterative and straightforward method with less computational expenses to deal with S-LFP. In the method, a new S-LFP is constructed based on the membership functions of the objectives multiplied by suitable weights. This new problem is then changed into a linear programming problem (LPP) using variable transformations. It was proven that the optimal solution of the LPP becomes the global optimal solution for the S-LFP. Numerical examples are given to illustrate the method.

Keywords: global optimization problem; local optimal solution; global optimal solution; membership function; linear programming; linear fractional programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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