Inventory and supply chain management with auto‐delivery subscription

Auto‐delivery is a subscription model widely employed in supply chains, whereby a supplier delivers products to a buyer (or multiple buyers) according to the buyer's choice of a constant shipping quantity to be delivered at prescheduled dates. The buyer enjoys a discount for the auto‐delivery orders and other benefits, including free subscription and cancellation. Because these benefits seem to all accrue to the buyer at the supplier's expense, the rationale for the supplier's decision to offer auto‐delivery and its impact on the profitability of both parties is an intriguing concern. We first develop a model that consists of a supplier and a single buyer, whereby the supplier offers a discount for the auto‐delivery orders and the buyer chooses the auto‐delivery quantity with the flexibility of cancelling the subscription. We derive the two parties' operating characteristics of their inventory systems and examine their optimal decisions. Our analysis shows that buyers benefit from the auto‐delivery discount; the supplier benefits from the demand‐expansion effect and the inventory‐reduction effect, a potential discount on the cost of the auto‐delivery units; and the supply chain benefits from reducing the bullwhip effect. We also find that channel coordination requires the supplier to pass the inventory‐related savings to the buyer through the auto‐delivery discount, which depends on the ratio of the two parties' holding cost rates. Moreover, we examine a model extension whereby the supplier announces a discount that is available for multiple buyers, we show that the supplier's optimal auto‐delivery discount under exponential demand can be determined based on the aggregate‐level demand information from all buyers. Finally, we discuss another model extension whereby the lead time of the supplier's recurring orders for auto‐delivery is longer than that of the regular orders and present a full analysis of the case when the lead time differential is one time period.