Dynamic Pricing of Relocating Resources in Large Networks

Abstract

We study dynamic pricing of resources that are distributed over a network of locations (e.g., shared vehicle systems and logistics networks). Customers with private willingness-to-pay sequentially request to relocate a resource from one location to another. We focus on networks with a hub-and-spoke structure. We develop a dynamic pricing policy and a performance bound based on a Lagrangian relaxation. This relaxation decomposes the problem over spokes and is thus far easier to solve than the original problem. We analyze the performance of the Lagrangian-based policy and focus on a large network regime in which the number of spokes (n) and number of resources grow at the same rate. We show that our policy loses no more than O (p lnn/n) in performance compared to an optimal policy, thus implying asymptotic optimality as n grows large. We provide examples that show that upper bounds and static policies based on fluid relaxations fail to work well in this asymptotic regime. Finally, we discuss how our approach extends to more general networks involving multiple, interconnected hubs.