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. Hsu-Shih Shih and E. Stanley Lee have published almost the first valuable paper on this topic (Fuzzy multi-level minimum cost flow problems,Fuzzy Sets and Systems, Volume 107, Issue 2, 16 October 1999, Pages 159-176). 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). Mehdi Ghatee is another researcher on this topic who is interested in applied fuzzy transportation.

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. Some interesting subjects on fuzzy transportation is gathered which can be seen in (http://math-cs.aut.ac.ir/~ghatee/Publication.htm).

Also, with and without equilibrium consideration, different models can be provided. Vincent Henn is a specialist in fuzzy traffic assignment models. Also Takamasa Akiyama has published various concepts in this category.

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.