A continuous cost evaluation approach for periodic review inventory systems with threshold rationing policy

This study analyzes an inventory problem with two stochastic demand classes in a periodic review inventory setting, in which a firm reviews its inventory position periodically and fulfills two Poisson demand classes continuously during periods. This study simultaneously assumes positive lead time and full backorders. An inventory policy consisting of order-up-to policy and threshold rationing policy is adopted, in which the firm places an order to raise its inventory position to order-up-to level in a fixed length of review interval and the inventory is rationed with a threshold level. Specifically, the total demand is served on a first-come first-served basis (FCFS) if its available inventory is above the threshold level. Otherwise, only the high-priority demand class is served. With such an inventory policy, this study provides a novel approach to evaluate the exact long-run expected inventory costs by assuming a threshold backorder clearing mechanism. This evaluation approach can easily incorporate FCFS policy. Furthermore, a method is provided to find the optimal policy parameters. Numerical experiments show that, relative to the FCFS policy and separate policy, the rationing policy can generate significant cost savings.