A Transportation Problem with Uncertain Costs and Random Supplies

Transportation problem is an optimization problem. In general, it was studied under random or uncertain condition. Considering the recent complexity, it is not enough to make should be a perfect transportation plan only based on. Usually, there is not only uncertainty but also randomness in many systems. In this paper, the aim is to investigate a transportation problem under uncertain and random environment. As a result, a conceptual uncertain random model is proposed for the problem, where the supplies are considered as random variables, and the costs and the demands are uncertain variables. By minimizing the expected value of uncertain objective function and taking confidence levels on constraints, transforming the model into a crisp mathematical form is the main conclusion. By minimizing the expected value of uncertain objective function and taking confidence levels on constraints, the above model can be turned to a mathematical form. Then transforming the model into a typical mathematical programming model is the main conclusion by using uncertainty theory and probability theory. At the end, a numerical example is given to show the feasibility of the model.