Multicriteria Transportation Problems with Fuzzy Parameters

In the classical transportation problem, it is assumed that the transportation costs are known constants. In practice, however, transport costs depend on weather, road and technical conditions. The concept of fuzzy numbers is one approach to modeling the uncertainty associated with such factors. There have been a large number of papers in which models of transportation problems with fuzzy parameters have been presented. Just as in classical models, these models are constructed under the assumption that the total transportation costs are minimized. This article proposes two models of a transportation problem where decisions are based on two criteria. According to the first model, the unit transportation costs are fuzzy numbers. Decisions are based on minimizing both the possibilistic expected value and the possibilistic variance of the transportation costs. According to the second model, all of the parameters of the transportation problem are assumed to be fuzzy. The optimization criteria are the minimization of the possibilistic expected values of the total transportation costs and minimization of the total costs related to shortages (in supply or demand). In addition, the article defines the concept of a truncated fuzzy number, together with its possibilistic expected value. Such truncated numbers are used to define how large shortages are. Some illustrative examples are given.