Optimizing a two-warehouse system under shortage backordering, trade credit, and decreasing rental conditions

This study develops an inventory model for the optimization of a two-echelon system with deteriorating loss and shortage backordering, which consists of one supplier and one distributor with a two-warehouse environment, where the storage price of the rented warehouse decreases over time. Some warehouse owners may decrease their storage prices after a certain period as an incentive to distributors. In addition, offering a credit period stimulates suppliers’ sales and reduces on-hand stock levels, and distributors can use this credit period to reduce costs and increase profits. This study determines the optimal production lot size of both players, as well as the number of shipments, in order to minimize the net present value (NPV) of the total joint cost over the planning horizon. In addition, it demonstrates that an optimal solution exists and is unique. A numerical example and sensitivity analyses are provided to illustrate the proposed model. The results of this study provide managerial insights for enterprises that use a rented warehouse to minimize costs by coordinating lot sizes.