Solving a capacitated fixed-charge transportation problem by artificial immune and genetic algorithms with a Prüfer number representation

This paper presents a mathematical model for a capacitated fixed-charge transportation problem in a two-stage supply chain network, in which potential places are candidate to be as distribution centers (DCs) and customers with particular demands. In contrast with the previous studies considered ample capacity for DCs, we consider the capacity for each DC. The presented model minimizes the total cost in such a way that some DCs are selected in order to supply demands of all the customers. To tackle such an NP-hard problem, we propose an artificial immune algorithm (AIA) and a genetic algorithm (GA) based on the spanning tree and Prüfer number representation. We introduce a new method to calculate the affinity value by using an adjustment rate. Furthermore, we apply the Taguchi experimental design method to set the proper values of AIA and GA parameters in order to improve their performances. Finally, we investigate the impact of increasing the problem size on the performance of our proposed algorithms.