A model for fixed-cost batch transportation problem under uncertainty

Shipping costs make a significant portion of total cost of goods. The fixed-cost transportation problem is an extension of the general transportation problem. This problem is one of the fundamental and important problems in the field of transportation and has recently received much attention by researchers considering realworld assumptions. The purpose of this research is to develop a mathematical model and an appropriate method to solve the fixed-cost batch transportation problem to reduce variable and fixed costs in a way that supply and demand constraints are met and the optimal transportation decision is made. In this research, it is assumed that products are transported in batches. It is also assumed that the decision variables have fuzzy numbers and the aim is to find the best shipping method with minimum cost. As the extension of transportation problem, which has been proven as an NP-hard problem, four frequently-used metaheuristic algorithms, including Simulated Annealing (SA), Imperialist Competitive Algorithm (ICA), Variable Neighborhood Search (VNS) and hybrid VNS, were used to solve this problem. The Taguchi method was applied to parameter setting. The results of these four algorithms were compared according to the three criteria of optimal value, computational time and dispersion rate. The comparison of the efficiency of the algorithms showed that the hybrid VNS algorithm outperforms the other three algorithms. Finally, the uncertain parameters of the problem were defuzzified by the fuzzy robust method and the dispersion rates of the solutions obtained by the algorithms were compared.