Capacitated Facility Location Problem With Freight Cost Discount

ABSTRACT:Unit shipment cost, in reality, is a decreasing function in shipment volume because of economics of scale; on the other hand, In view of the applicability of quantity discounts arises commonly in many issues (such as EOQ model), we introduce quantity discount into facility location problem.In this paper, we extend capacitated facility location problem (CFLP) by taking freight cost discount into account, and propose CFLP with freight cost. The model can be formulated as a mixed integer linear problem (MILP), and it does have a conspicuous special property that enables it to be divided into two classes of partial problem separating the continuous from the integer variables, which can be solved efficiently. Therefore a solution technique based on benders decomposition is developed for this problem. Numerical experiments show the impact of freight cost discount on the distribution network, such as, it can lead to lower cost.In development, we consider uncertain demand based on the CFLP with freight cost discount, and proposes capacitated facility location problem with freight cost discount under uncertain demand. In this model, we express uncertain demand based on scenario. A set of examples show the model is robust.Then we extend CFLP with freight cost by considering the capacity of facility as decision variables, and considering the cost of transportation from the first to the second echelon, and obtain two new models. Numerical experiments show effectiveness of two models.The developed models, in this paper, succeed and improve the existing researches on facility location, and extend the applied range of quantity discount, and can be helpful for the practice of facility.