Abstract
In this paper, we have proposed a new technique to find an efficient solution to fractional programming problems (FPP). The multi-objective fractional programming problem (MOFPP) is converted into multi-objective linear programming (MOLPP) utilizing the point-slopes formula for a plane, which has equivalent weights to the MOFPP. The MOLPP is diminished to a single objective linear programming problem (SOLPP) through using two new techniques for the values of the objective function and suggesting an algorithm for its solution. Finally, we obtained the optimal solution for MOFPP by solving the consequent linear programming problem (LPP). The proposed practicability is confirmed with the existing approaches, with some numerical examples and we indicated comparison with other techniques.
Highlights
In the past five decades, the fractional programming problem (FPP), which has been utilized as a significant designing tool, has been exercised in various disciplines, for instance, business, manufacturing planning, economic and corporate organization, health care, and hospital planning, etc
We suggested a new mean deviation and advanced mean deviation techniques be used to tackle the MOLPP reduced into linear programming problem (LPP); this LPP is solved by the classical simplex method
We presented a new technique to solve the multi-objective fractional programming problems (MOFPP)
Summary
In the past five decades, the fractional programming problem (FPP), which has been utilized as a significant designing tool, has been exercised in various disciplines, for instance, business, manufacturing planning, economic and corporate organization, health care, and hospital planning, etc. To resolve or suggest new methodology issues, we will be able to provide some previous facts and concepts. Some of them compact with theory, (Borza & Rambely, 2021; Hejazi & Nobakhtian, 2020) or some of them methods of solution with applications(Akhtar et al, 2017; Pramy & Islam, 2017; Suleiman & Nawkhass, 2013) and many researchers have studied how to convert MOFPP into LPP, using several methods and techniques, such as Chakraborty and Gupta’s approach(Chakraborty & Gupta, 2002), Dinkelbach’s methodology(Dinkelbach, 1967), and Nayak, & Ojha (Nayak & Ojha, 2019) etc. A new model has been suggested for solving MOFPP always yields an efficient solution and reduces the complexity of solving the MOFPP.
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