Optimal ordering policies in response to a disposable coupon

This study investigates a retailer's ordering strategy under the framework of the economic order quantity (EOQ) model. A supplier offers a retailer a disposable coupon and allows it to place a special order at any time in a promotion period. The promotion period is not necessary short and shortages are allowed throughout the time horizon. In addition to the special order time and the special order quantity, the retailer needs to decide whether to place some regular orders in the promotion period before placing the special order for the purpose of making better use of this coupon. We show that the coupon should be used to the retailer's first order in the promotion period regardless of the duration of the promotion period. Moreover, the retailer's maximum inventory level is higher than that in the classical EOQ model. We find that a longer promotion period can benefit the retailer by endowing it with more flexibility in its decision-making. Therefore, the supplier can improve the cash flow and reduce the overstock by integrating a disposable coupon with a longer promotion period. Numerous managerial insights are obtained from sensitivity analysis and numerical experiments.