Lot-sizing decisions for deteriorating items with two warehouses under an order-size-dependent trade credit

This study attempts to determine economic order quantity for deteriorating items with two-storage facilities (one is an owned warehouse and the other is a rented warehouse) where trade credit is linked to order quantity. As assumed herein, payment delays depend on the quantity ordered, when the order quantity is less than that at which a payment delay is permitted, the payment for the items must be made immediately. Otherwise, the fixed trade credit period is permitted. Furthermore, if the order quantity exceeds the owned warehouse capacity, it will be necessary to rent a warehouse which results in an additional rental cost. Otherwise, renting a warehouse is unnecessary. The problem discussed in this study involves how retailers decide whether to rent an additional warehouse to hold more items and thus obtain a trade credit period. First, a deterministic inventory model is developed for deteriorating items under the above situation. Second, this study demonstrates that the total cost function per unit time is convex via a rigorous proof. Third, five theorems are developed to optimize the replenishment cycle time and the order lot-size. Finally, numerical examples are used to illustrate these theorems and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out and some important managerial insights are obtained.