Quantity-Based Emergency Shipment Policies

Either structurally or in an ad hoc manner, emergency shipments are widely utilized for preventing the potentially negative impacts of stock-outs. In addition to having policies for their regular orders, companies need to decide when and for how many units to place emergency orders. In this paper, we consider the periodic-review problem of a retailer who uses a quantity-based emergency shipment policy. Under this policy an emergency order is triggered if the inventory level within the review period falls below a certain level. We consider the base-stock policy for the regular replenishment orders. The goal is to determine the optimal base-stock level, the optimal period length as well as the optimal size and threshold value of emergency orders such that the total expected cost rate is minimized. We use renewal reward theory to derive the expressions of operating characteristics. The expected cost rate's properties are analyzed to develop an optimization algorithm for finding the optimal policy parameters. We compare our policy with the time-based and hybrid emergency shipment policies and conclude that the quantity-based policy can bring substantial benefits compared to other policies.