Retailer's optimal ordering policy for deteriorating items under order-size dependent trade credit and complete backlogging

The retail inventory management literature generally assumes that suppliers seek to stimulate demand by offering retailers a delay in payment. In practice, however, suppliers tend to offer retailers a partial delay in payment. To accommodate this possibility, this paper establishes an economic order quantity inventory model for deteriorating items, with allowable shortages and permissible partial delay in payment based on the order quantity. This paper presents theoretical results to determine the optimal replenishment time and the length of time for the stock to draw down completely, and with these time values the optimal ordering and backlogging policies are calculated for the retailer in order to minimize the total inventory cost per unit time. The optimal solutions are obtained analytically. The inventory model is validated numerically. A sensitivity analysis of the optimal solution with respect to the parameters of the inventory system and managerial insights are given. The proposed inventory model reduces to some existing inventory models.