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. We then extend the model to a setting with multiple buyers, whereby the supplier announces a discount that is available for all buyers, and we reexamine the optimal decisions by approximating and aggregating the demand from the buyers. Our analysis provides insight into the two parties' benefits from the auto-delivery business model and the behavior of their optimal decisions. Buyers benefit from the auto-delivery discount, the supplier benefits from the demand-expansion effect and the inventory-reduction effect, and the supply chain benefits from reducing the bullwhip effect. Moreover, in the one-supplier-one-buyer setting, we show that channel coordination requires the supplier to pass the inventory-related savings to the buyer through the auto-delivery discount, which in turn is influenced by the ratio of the two parties’ holding cost rates. Furthermore, in a one-supplier-multiple-buyer setting, we show that the supplier's optimal auto-delivery discount under exponential demand can be determined based on the aggregate-level demand information from the buyers, and the discount rate is decreasing in the supplier's market share and increasing in the supplier's holding cost rate