An entropy based solid transportation problem in uncertain environment

The uncertain solid transportation problem considers material dispatching with uncertain elements like demands. Now, it plays an increasingly important role in logistics managements. Traditionally, the transportation cost is used as the optimization objective, while the dispersals of trips between origins and destinations are usually neglected. In order to minimize the transportation penalties and ensure uniform distribution of goods between origins and destinations, this paper employs entropy function of dispersals of trips between origins and destinations as a second objective function. Within the framework of uncertainty theory, the uncertain entropy based solid transportation model is transformed into its deterministic equivalent, which can be solved by general optimization methods. Finally, a numerical example is given for illustrating purpose.