Setting fulfillment-time guarantees for accepting customer orders in a periodic-review base-stock inventory system

Retailers are increasingly promising a maximum fulfillment time window for fulfilling customer orders. Motivated by such guarantees, we consider an infinite-horizon periodic-review base-stock inventory system that imposes an endogenously determined fulfillment-time limit for accepted orders. The inventory position is reviewed every fixed T periods and an order is placed to bring the system inventory up to R, the target base stock. The replenishment lead time is a constant of L periods. In each period, the realized consumer demand is accepted only if it can be filled within a guaranteed time limit of τ periods. By incorporating a fulfillment-time limit, the model allows both backorders and lost sales. The objective is to find the strategy that minimizes the long-term average cost per unit time by selecting the base stock and guaranteed-delivery time limit. The behavior of the optimal R with respect to the guaranteed service time τ is investigated, and subsequently, the best value of τ is identified. Interestingly, when τ is greater than or equal to L, the best value of τ is independent of the holding cost and the base stock R. Regularity conditions are developed that assure the cost function is unimodal in R, guaranteeing the optimal base-stock solution can be found easily for a broad family of demand distributions. The solution procedure is extended to the case when the mean customer demand depends on the fulfillment time window promised by the retailer. We find greater customer sensitivity to the fulfillment time leads to a decrease in the optimal fulfillment time guarantee.