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Selection of distribution centers with the time value of money and the loyal customer effect

This paper addresses a distribution center selection problem in a three-echelon supply chain including suppliers, distribution centers (DCs) and retailers. There is a set of DCs, in which some of them should be selected in each period. Due to the imperative role of the time value of money (TVM), we consider this decisive factor in the problem. Besides it is assumed that the setup cost of each DC can be decreased in period t based on its number of the previous periods that it has been selected. This phenomenon, which shows the loyalty of a customer, is named as loyal customer (LC) effect. The aim of the problem is to minimize the total costs, including transportation and setup costs. A non-linear mathematical model is developed for the mentioned problem and it has been solved by the GAMS optimization software to obtain the optimum set of DCs.