A heuristic approach for fuzzy fixed charge transportation problem

Abstract

The fixed charge transportation problem is a nonlinear programming problem in which a fixed charge is incurred if a distribution variable assumes a nonzero value. Its structure is almost identical to that of a linear programming problem, and indeed it can be written as a mixed-integer linear program. In this paper, we consider the fixed charge transportation problem under uncertainty, particularly when the direct and fixed costs are the generalized trapezoidal fuzzy numbers. The first step it transforms into the classical fuzzy transportation problem. The next we obtain the best approximation fuzzy on the optimal value of the fuzzy fixed-charge transportation problem. This method obtains a lower and upper bound both on the fuzzy optimal value of the fuzzy fixed-charge transportation problem which can be easily obtained by using the approximation solution. Conclusion: we propose a new method as the best approximation method, with representation both of the transportation cost and the fixed cost, to find a fuzzy approximation solution close to the optimal solution for fuzzy fixed charge transportation problem.