Inventory Repositioning in On-Demand Product Rental Networks
Thursday, December 6, 2018 - 10:30am - 11:30am
We consider a product rental network with a fixed number of rental units distributed across multiple locations. The units are accessed by customers without prior reservation and on an on-demand basis. Customers are provided with the flexibility to decide on how long to keep a unit and where to return it. Because of the randomness in demand and in the length of the rental periods and in unit returns, there is a need to periodically reposition inventory away from some locations and into others. In deciding on how much inventory to reposition and where the system manager balances potential lost sales with repositioning costs. Although the problem is increasingly common in applications involving on-demand rental services, little is known about the nature of the optimal policy or about effective approaches to solving the problem for systems with a general network structure. In this paper, we offer a characterization of the optimal policy. We show that the optimal policy in each period can be described in terms of a well-specified region over the state space. Within this region, it is optimal not to reposition any inventory, while, outside the region, it is optimal to reposition but only such that the system moves to a new state that is on the boundary of the no-repositioning region. We provide a simple check for when a state is in the no-repositioning region. Finally, we propose a new cutting-plane-based, infinite-horizon approximate dynamic programming algorithm that leverages the structural properties of the value function and optimal policy. We then give a novel convergence analysis showing that the value function approximations generated by our method are optimal in the limit and accompany the theoretical analysis with numerical experiments.