Stochastic Transportation Problem with Multichoice Random Parameter

Abstract

This paper deals with the situation of multiple random choices along with multiple objective functions of the transportation problem. Due to the uncertainty in the environment, the choices of the cost coefficients are considered multichoice random parameters. The other parameters (supply and demand) are replaced by random variables with Gaussian distributions, and each multichoice parameter alternative is treated as a random variable. In this paper, the Newton divided difference interpolation technique is used to convert the multichoice parameter into a single choice in the objective function. Then, the chance-constrained method is applied to transform the probabilistic constraints into deterministic constraints. Due to the consideration of multichoices in the objective function, the expectation minimization model is used to get the deterministic form. Moreover, the fuzzy programming approach with the membership function is utilized to convert the multiobjective function into a single-objective function. A case study is also illustrated for a better understanding of the methodology.