A heuristic approach for fuzzy fixed charge transportation problem
Ali Mahmoodirad, Sadegh Niroomand
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 transforms into the classical fuzzy transportation problem. Next, we obtain the best approximation of the optimal value of the fuzzy fixed-charge transportation problem. This method obtains a lower and upper bound on the fuzzy optimal value of the fuzzy fixed-charge transportation problem, which can be easily obtained by using the approximation solution. To conclude, we propose a new method as the best approximation method, with representation of both the transportation cost and the fixed cost, to find a fuzzy approximation solution close to the optimal solution for the fuzzy fixed charge transportation problem.