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An integer fuzzy transportation problem. (English) Zbl 0853.90123

Summary: The well-known transportation problem 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. 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.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
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References:

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