Multi-choice goal programming approach to solve multi-objective probabilistic programming problem

Abstract

Stochastic Programming is an art of modeling optimization problems in an environment, where randomness occurs. In this manuscript, we present a multi-objective probabilistic programming problem, where the random parameter follow logistic distribution. We transform the probabilistic programming model to an equivalent deterministic mathematical model by using chance constrained technique. Multiple number of aspiration levels are allocated to the objective function by Decision maker, the main aim is to obtain such a decision. After allocating several aspiration levels to the objective function, which will provide minimum deviation from objective function and aspiration level. Such minimization of deviation is possible by using multi-choice goal programming technique. Multi-choice parameters are handled by three different techniques viz; binary variable approach, Vandermonde's interpolating polynomial approach and linear least square approximation approach. To illustrate the methodology, a numerical example is presented.