Network Inventory Management : Approximate Optimality in Large-Scale Systems

We consider a discrete time network inventory management problem on a hub-and-spoke network. Each period begins with an initial inventory at each of the nodes in the network, after which the customers (demand) materialize at the nodes. Each customer picks up a unit at the origin node and drops it off at a randomly sampled destination node given by an origin-specific probability distribution. An important task in inventory management of such systems is the periodic physical repositioning of the inventory to avoid stockouts or excess inventory at nodes with unbalanced flows. In our work, we model the above network inventory management problem as an infinite horizon discrete-time discounted Markov Decision Process, and prove the asymptotic optimality of a novel mean-field approximation to the original MDP as the number of spokes becomes large. To compute an approximately optimal policy for the mean-field dynamics, we provide an algorithm whose running time is logarithmic in the desired optimality gap. Lastly, we compare the performance of our mean-field based policy to other policies via synthetic numerical experiments