Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

This manuscript presents a technique for solving a multiple-objective probabilistic fractional programming problem with discrete random variables. A multiple-objective probabilistic mathematical model is constructed with fractional objectives. In the model, some parameters of coefficients and right hand side parameters of restrictions are assumed as random variables having Pascal and Hyper geometric distributions. The feasibility of probabilistic constraints is checked by means of stochastic simulation. Genetic algorithm approach method is used to obtain the Pareto optimal solution of the proposed model without finding the deterministic model. Genetic algorithm parameters are fixed in all generation. The proposed method is coded by C++ programming language. To illustrate the method, a numerical example and practical example on the case of supply chain management are presented. The result shows that the values of the objective functions are conflicting each other.