Optimal order quantity under advance sales and permissible delays in payments

In order to attract more customers, it is a common practice for retailers to provide advance sales, for example, Maximʹs Bakery in Hong Kong, Amazon.com, Movies Unlimited and Toys R Us. Similarly, suppliers often allow their retailers a permissible delay in payment in order to increase sales. Advance sales and trade credit policies provide numerous benefits for companies, including gaining additional discriminative customers and increased profit due to interest earned from payments received from committed customers prior to the start of the regular selling period. This article establishes an inventory model for retailers who simultaneously receive a permissible delay in payments from suppliers while offering advance sales to customers. We first present the model and then provide a simple method of obtaining the optimal order quantity and advance sales discount rate which achieves the maximum total profit per unit of time for the retailer. Finally, several numerical examples are used to illustrate the procedure.