Optimal and Approximate Policies for Inventory Systems with Order Crossover

A common assumption in inventory analysis is that replenishment orders arrive in the same sequence in which they were placed. In practice, however, a variety of factors may cause orders to arrive out of sequence, a phenomenon known as order crossover. This paper analyzes a periodic review inventory system for a single item with discrete variable demand and discrete variable and long lead-times (relative to the review period). Under such a scenario, multiple orders are simultaneously outstanding, and orders may arrive in a different sequence than placed. If such order crossover occurs, traditional inventory analysis overstates expected shortages and standard inventory control policies are no longer optimal. This paper discusses why orders may cross over in practice and investigates the implications of order crossover to inventory management policies. We investigate the cost performance of optimal policies under order crossover and also suggest approximate policies which are easier to compute and implement. Both the optimal and approximate policies take advantage of detailed real-time information about the status of pending orders and goods in transit, and hence in a majority of cases perform better than commonly used policies which do not incorporate such information.