Genetic and differential evolution algorithms for the allocation of customers to potential distribution centers in a fuzzy environment

Abstract

In order to serve the customers' demands in a supply chain, one of the important decisions is to select some candidate places as distribution centers (DCs) in the network. For opening a potential DC and also shipping from the DC to the customers, there are two types of costs named fixed and variable costs, respectively. Contrary to previous work, we consider fuzzy costs and utilize differential evolution (DE) algorithm for the first time for the given problem. In addition, some new crossover and mutation operators are proposed in DE. We also address the problem with genetic algorithm (GA) and compare the results with the presented DE algorithm. In the both presented algorithms, Prufer number representation is employed. Besides, the Taguchi experimental design method is employed to study the behavior of the parameters dealing with the problem. To evaluate the performance of proposed algorithms, various problem sizes are considered and the computational results are analyzed. Finally, the impact of the rise in the problem size on the performance of the algorithms is investigated. The DE depicts a superior performance over GA in all problem sizes.