On Solving Multi-Commodity Multi-Choice Transportation Problem in Fuzzy Random Hybrid Uncertainty Environment

Transportation problem or moving goods from one place to another is one of the most important problems in the economy of a country. The displacement of millions of goods per day poses the role of transportation programming as a science. In the meantime, Multi-Commodity Transportation Problem (MCTP) is particularly important. In this paper, due to increasing competition in the business world, which makes decision makers dealing with multiple options/ information for optimal decisions on a single task, we will look at multi-choice programming in hybrid fuzzy random environment. By using polynomials interpolation for each multichoice parameter, the model is transformed into a fuzzy random programming problem. Then, to convert this model to its deterministic form, we use the concept of the mean value of fuzzy random variables. Finally, to validate the proposed mathematical operations, we solve a multi-commodity transportation problem with fuzzy random multi-choice parameters.

Keywords:

Multi-choice programming , fuzzy random variable , Er-expected value , multi-commodity transportation problem.