Dynamic Pricing of Relocating Resources in Large Networks

Abstract

Motivated by applications in shared vehicle systems, we study dynamic pricing of resources that relocate over a network of locations. Customers with private willingness-to-pay sequentially request to relocate a resource from one location to another, and a revenue-maximizing service provider sets a price for each request. This problem can be formulated as an infinite horizon stochastic dynamic program, but is quite difficult to solve, as optimal pricing policies may depend on the locations of all resources in the network. We first focus on networks with a hub-and-spoke structure, and 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 supply-constrained large network regime in which the number of spokes (n) and the number of resources grow at the same rate. We show that the Lagrangian policy loses no more than O(\sqrt{\ln n/n}) in performance compared to an optimal policy, thus implying asymptotic optimality as n grows large. We also show that no static policy is asymptotically optimal in the large network regime. Finally, we extend the Lagrangian relaxation to provide upper bounds and policies to general networks with multiple, interconnected hubs and spoke-to-spoke connections, and to incorporate relocation times.
We also examine the performance of the Lagrangian policy and the Lagrangian relaxation bound on some numerical examples, including examples based on data from RideAustin.

Keywords: Dynamic Pricing, Resource Relocation, Hub-and-Spoke Networks, Lagrangian Relaxations, Asymptotic Optimality