Modelling and optimization of multi-item solid transportation problems with uncertain variables and uncertain entropy function

Abstract

This paper concentrates on modeling of the uncertain entropy multi item solid transportation problem, in which the supply capacities, demands, conveyances and transportation capacities are thought to be uncertain variables due to the obvious uncertainty of information. In general, the transportation cost in the transportation problem is employed by the optimization aim, while the dispersals of trips among sources, destinations, and conveyances are often ignored. In order to minimize both transportation penalties and maximize entropy value which guarantees uniform transportation of products from sources to destinations via conveyances, this paper holds entropy function of dispersals of trips among sources, destinations, and conveyances as a second objective function. Inside the construction of uncertainty theory, the uncertain entropy function for transportation models is first proposed here. Thus the model is turned into its crisp equivalent by using uncertainty theory, which can be solved by applying minimizing distance optimization method. Finally, a numerical experiment is given to illustrate the models.