Uncertain Solid Transportation Problem with Product Blending

In order to satisfy the required quality of demand points in a practical transportation system of chemical products such as petroleum and gasoline, blending of products should be considered. In this paper, we have considered a solid transportation problem with product blending in an uncertain environment, in which the fixed charges of vehicles and the unit transportation costs of products are assumed to be uncertain variables. Using different criteria to rank uncertain variables, we have constructed uncertain models for this problem, namely expected cost minimization model (ECMM) and chance-constrained uncertain model (CCUM). Within the framework of uncertainty theory, we prove that both of ECMM and CCUM can be transformed into the corresponding deterministic forms. Numerical examples are presented to illustrate the models, and the results are obtained by using the standard optimization solver Gurobi.