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

Abstract

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.The numerical study shows that the mixed policy found from our Markov decision model generally outperforms the best pure replenishment policy using either only normal or only emergency orders. Our model provides results that are similar to or slightly better than the results obtained with earlier models in the literature. Moreover, because our model accommodates compound Poisson demand, we are able to demonstrate that considerable cost reductions can then be obtained with the mixed policy when compared to the best pure replenishment policy. Finally, using sensitivity analysis we observe that a result on when a mixed policy is most beneficial, which has been found to hold for the simpler model without fixed ordering costs, seems to hold also for the more complex model that we investigate.