Optimal inventory polices with order-size dependent trade credit under delayed payment and cash discount

In todayʹs competitive business environment, it is very common that suppliers are always willing to provide the purchaser with certain incentives. As a result, suppliers frequently offer two distinct alternatives to increase possible volume of procurement. One is that if the order quantity is greater than or equal to a predetermined quantity, the purchaser obtains a longer permissible delay in payments. The other is that if the order quantity is greater than or equal to a predetermined quantity, the purchaser gets a cash discount with a shorter permissible delay in payments. Viewed from above perspective, this study develops an inventory model with order-size dependent trade credit, in which the supplier provides not only a permissible delay but also a cash discount to the customers. Moreover, an efficient algorithm is provided to obtain the optimal solution, and then an empirical case is investigated to illustrate the theoretical results from both the supplier and customer viewpoints.