The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.
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.
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