Improving DVD-by-Mail Operations for In-Circulation Items with Accurate Forecasts

In this paper we study forecast and inventory control problems for DVD-by-mail operations. Specifically, we focus on inventory management for in-circulation items after the new release rental peak. For such items, the demand volume is usually low and unpredictable. Leveraging on the unique operational feature of DVD-by-mail services, we propose effective forecast models for item-level returns and demands. Based on the forecast models, we formulate a service-constrained multi-item inventory control problem. Unlike previous studies in the literature, which rely on approximated service levels, we develop an algorithm for computing the exact service level. The resulting inventory optimization problem is a nonlinear integer program. To tackle the computational challenge, we propose an effective solution based on a dynamic program. Our benchmark study shows that the dynamic program solution is superior to the heuristics used for similar problems in the literature, and it achieves the minimum cost in all numerical scenarios. To evaluate the performance of our forecast and inventory control methods, we conduct an extensive simulation study. Our simulation results suggest that our forecast models play a crucial role in improving the cost performance. In addition, we find that the combined value of our forecast and inventory control methods increases with service level requirements, but is relatively insensitive to customers’ return speed; these features are all desirable for practical implementations.