A periodic review inventory system with emergency replenishments

This paper proposes and analyzes a periodic review inventory system with two replenishment modes. Regular orders are placed periodically following a base stock policy on inventory position, and arrive at the stocking location after a deterministic lead time. The location also has the option of placing emergency orders, characterized by a shorter lead time but higher acquisition cost, in case of imminent stockouts. Thus, at some appropriate time in the replenishment cycle, the necessity and size of an emergency order is determined according to a base stock policy on net stock. The timing of the emergency order is such that this order arrives and can be used to satisfy the demand in the time period just before the arrival of a regular order, when the likelihood of a stockout is highest. An approximate cost model is developed which can easily be optimized with respect to the order-up-to parameters. This model is used as the basis for a heuristic algorithm, which leads to solutions that are very close to the exact optimal solutions determined through simulation. It is shown that the proposed system offers substantial cost savings relative to a system without the emergency replenishment option.