Fuzzy Transportation Problem with Random Transportation Costs

We consider the following transportation problem with both random and fuzzy factors. There exist m supply points and n demand points. For each route between supply point and demand point, unit transportation cost is a random variable according to a normal distribution and existence possibility denoting the preference choosing this route is attached. The probability that the total transportation cost is not greater than the budget F should be not less than the fixed probability level. Under the above setting, we seek transportation pattern minimizing F and maximizing the minimal preference among the routes used in a transportation. Since usually there is no transportation pattern optimizing two objectives at a time, we propose a solution algorithm to find some non-dominated transportation patterns after defining non-domination. Finally we discuss the further research problems.