An integer fuzzy transportation problem

The well-known transportation problem [1] is often represented by a bipartite network that consists of two node-sets, i.e., sets of supply (or plant) and demand (or warehouse) nodes. The problem is to determine a flow such that the total transportation cost is minimized. However, in some situations, the values of supplies and demands may not be determined rigidly. Accordingly, we considered a fuzzy version of the transportation problem by introducing two kinds of membership functions which characterize fuzzy supplies and fuzzy demands [2]. The objective is to determine an optimal flow that maximizes the smallest value of all membership functions under the constraint that the total transportation cost must not exceed a certain upper limit. In this paper, we generalize the fuzzy transportation problem. That is, an integral constraint of flow is added to the problem. We call it IFTP: Integer Fuzzy Transportation Problem, in which it is assumed that every value of supply and demand is integer and that the values of commodities to be transported are all integers.