An integrated inventory model with capacity constraint under order-size dependent trade credit, all-unit discount and partial backordering

Abstract

In today’s competitive business situation, the supplier frequently offers his or her retailers a permissible delay period (i.e., trade credit) to stimulate sales. In addition, the capacity of any warehouse is limited in practice, thus the retailer needs an additional rented warehouse (RW) to store the excess units when the order quantity exceeds the capacity of the own warehouse (OW). Furthermore, with the globalization of the marketing policy, the supplier may provide the retailer with a discounted price if the quantity of purchase is large enough. Considering all of the factors mentioned above, in this paper we study an integrated inventory model with capacity constraint under order-size dependent trade credit and all-units discount. Shortages are allowed and partially backordered. In addition, the unit production cost, which is a function of the production rate, is considered. An algorithm is developed to determine the optimal production and replenishment policies for both the supplier and the retailer. Finally, numerical examples are presented to illustrate theoretical results. Sensitivity analysis of the major parameters are performed and some insights are obtained.