Fuzzy total transportation cost measures for fuzzy solid transportation problem

The solid transportation problem considers the supply, the demand, and the conveyance to satisfy the transportation requirement in a cost-effective manner. This paper develops a method that is able to derive the fuzzy objective value of the fuzzy solid transportation problem when the cost coefficients, the supply and demand quantities and conveyance capacities are fuzzy numbers. Based on the extension principle, the fuzzy solid transportation problem is transformed into a pair of mathematical programs that is employed to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level α. From different values of α, the membership function of the objective value is approximated. Since the objective value is fuzzy, the values of the decision variables derived in this paper are fuzzy as well. An example is illustrated for the whole idea.