Fuzzy transportation

The aim of fuzzy transportation is to find the least transportation cost of some commodities through a capacitated network when the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers. This problem is a new branch in combinatorial optimization and network flow problems. Combinatorial algorithms can be provided to solve fuzzy transportation problem to find the fuzzy optimal flow(s). Such methods are capable of handling the decision maker's risk taking. Some application of such standpoint were presented in industries. Liu and Kao pursued this attempt to find better solution for this problem (Network flow problems with fuzzy arc lengths, IEEE Transactions on Systems, Man and Cybernetics Part B: Cybernetics, 34 (2004) 765-769).

It is interesting to check that which methods in traditional fuzzy optimization problem can be extended to combinatorial optimization problems e.g., transformation that they maintain the nice structure of problem. Then, valuable algorithms can be proposed for fuzzy combinatorial optimization to take the uncertainty of real problems into account.

By using fuzzy transportation, it is a reasonable attempt to find special solutions for hazardous material transportation because of the possibility of implementing the optimistic and pessimistic concepts into account.

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