Title: Application of multi-objective probabilistic fractional programming problem in production planning

Authors: Berhanu Belay; Srikumar Acharya; Rajashree Mishra

Addresses: Department of Mathematics, KIIT Deemed to be University, Bhubaneswar 751024, India ' Department of Mathematics, KIIT Deemed to be University, Bhubaneswar 751024, India ' Department of Mathematics, KIIT Deemed to be University, Bhubaneswar 751024, India

Abstract: This paper presents the application of multi-objective probabilistic fractional programming problem in production planning. The production planning model for a manufacturing company that produce multiple products with a specified period is formulated by considering some of the parameters in the right hand sides of the constraints as random variables following continuous distribution namely gamma distribution. The formulated mathematical model is a multi-objective probabilistic fractional programming problem. In the solution procedure, the deterministic equivalent of the probabilistic programming problem has not been obtained. The analytical method for multi-objective fractional programming problem has also not been applied to solve the proposed model. A stochastic simulation-based genetic algorithm is applied to solve the proposed model directly. A set of Pareto optimal solutions is obtained for the formulated production planning problem.

Keywords: genetic algorithm; multi-objective programming problem; probabilistic programming problem; stochastic simulation; fractional programming; production planning; gamma distribution; Pareto optimal solution.

DOI: 10.1504/IJOR.2022.121491

International Journal of Operational Research, 2022 Vol.43 No.1/2, pp.150 - 167

Received: 18 Oct 2019
Accepted: 18 May 2020
Published online: 16 Mar 2022 *

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