Solving Multi-Objective Probabilistic Factional Programming Problem

This paper presents the solution methodology of a multiobjective probabilistic fractional programming problem. In the proposed model the parameters in the constraints coefficient and the right-hand sides of the constraints follow continuous random variables having known distribution. Since the programming problem consists of random variables, multi-objective function and fractional objective function, it is lengthy, time-consuming and clumsy to solve the proposed programming problem using analytical methods. Stochastic simulation-based genetic algorithm approach is directly applied to solve multi-objective probabilistic non-linear fractional programming problem involving beta distribution and chi-square distribution. In the proposed method, it is not necessary to find the deterministic equivalent of a probabilistic programming problem and applying any traditional methods of fractional programming problem. The stochastic simulation-based genetic algorithm is coded by Code block C++ 16.01 compiler. A set of Pareto optimal solutions are generated for a multi objective probabilistic non-linear fractional programming problem. A numerical example and case study on inventory problem are presented to validate the proposed method.