Emergency orders in the periodic-review inventory system with fixed ordering costs and compound Poisson demand

Emergency orders have shorter lead times but incur extra costs compared to normal orders. We present a discrete-time Markov decision model where normal orders are issued according to a reorder point policy with a fixed order quantity, whereas emergency orders are controlled by a state-dependent reorder point policy with a target stock level. A rapid policy iteration algorithm is used to find and evaluate the policy that minimizes the long-run average cost per review period. In addition to fixed and variable costs for normal and emergency orders our model includes linear holding and backorder costs. The review period is of any given length. Neither the normal order nor the emergency order lead time are required to be integer multiples of the review period.