Asymptotic Scaling of Optimal Cost and Asymptotic Optimality of Base-Stock Policy in Several Multidimensional Inventory Systems

Abstract

Asymptotic Optimality of Simple Heuristic Policies for Multidimensional Inventory Systems Stochastic inventory systems with multidimensional state spaces, such as lost-sales system with positive lead time and perishable inventory system, are challenging to manage because of the curse of dimensionality, and their optimal control policies are extremely complex. In “Asymptotic Scaling of Optimal Cost and Asymptotic Optimality of Base-Stock Policy in Several Multidimensional Inventory Systems,” Bu, Gong and Chao consider three classes of such systems in the regime of large unit penalty cost, and they establish the asymptotic optimality of (modified) simple base-stock policies as well as an explicit expression for the optimal cost rate in each of these systems. These results justify the applications of such policies in real-world applications, and they are achieved by constructing tight newsvendor upper and lower bounds on the systems’ costs and analyzing the asymptotic scaling of newsvendor costs with large unit penalty cost. This approach is expected to be useful in studying other multidimensional stochastic inventory systems.