Model designing and addressing a fixed charge transportation problem considering discount assumptions

Nowadays, one of the most significant aims of supply chain, and also one of the most substantial evaluation criteria of any organization’s performance is making customers' satisfaction. Therefore, delivering products to the right place, at the right time, and with the lowest cost are considered to be important goals in supply chain management. The transportation cost is one of the most important and effective factor for pricing goods and the final price for customers. Also, fixed-charge transportation problem (FCTP) is a primary and important problem which attracts researchers in the last decade. Therefore, focusing on transportation costs in order to reducing the final price of goods is necessary to increase the place of industry among the competitors and the satisfaction of customers. In the problem, when a route in a solution is used, both fixed and variable costs are calculated for opening the rout and also for the amount of the transferred goods in the route. Contrary to the general TP, the FCTP is more difficult to solve because of the fixed costs that result in discontinuities in the objective function and makes it indissoluble by the straight application of the transportation algorithms. In this research, the fixed cost transportation problem with considering the discount limitation is modeled and solved. Due to NP-hardness of the problem, three metaheuristics Simulated Annealing (SA), Genetic Algorithm (GA) and Whale Optimization Algorithm (WOA) are developed. Prufer number encoding is utilized to represent the solution in all algorithms. Because of importance of the parameters calibration, Taguchi method is used for tuning the parameters in algorithm designing. Besides, 28 test problems with different sizes are solved and compared with the results of GAMS.