A Linearization to the Multi-objective Linear Plus Linear Fractional Program

Mojtaba Borza (), Azmin Sham Rambely and Seyed Ahmad Edalatpanah
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Mojtaba Borza: Faculty of Science & Technology, UKM
Azmin Sham Rambely: Faculty of Science & Technology, UKM
Seyed Ahmad Edalatpanah: Ayandegan Institute of Higher Education

SN Operations Research Forum, 2023, vol. 4, issue 4, 1-22

Abstract: Abstract The structure of the sum of linear plus linear ratio program is complex and 𝒩𝒫-completeness. In management science, game theory, and industry, there are problems such that their mathematical models can be represented as a multi-objective linear plus linear fractional programming problem (MOLLFPP). The aim of this study is to introduce a method to address the MOLLFPP. The approach is designed in 2 phases. In phase 1, a method is created to reach the global optimal solution of the linear plus linear fractional programming problem (LLFPP) using suitable variable transformations. In fact, in this phase, the LLFPP is changed into a linear programming problem (LPP). In phase 2, taking into account the information of phase 1, the MOLLFPP is transformed into LPPs by applying the weighted sum and max–min techniques. Two examples are solved to illustrate the method and comparisons are made to show the accuracy.

Keywords: Membership function; Weighted sum method; Max–min technique; Genetic algorithm (GA); Pareto front; Pareto optimal solution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s43069-023-00256-x

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