Dynamic Relocations in Car-Sharing Networks

47 Pages Posted: 18 Feb 2021 Last revised: 31 Mar 2021

See all articles by Mahsa Hosseini

Mahsa Hosseini

Rotman School of Management

Joseph Milner

affiliation not provided to SSRN

Gonzalo Romero

University of Toronto - Rotman School of Management

Date Written: January 27, 2021

Abstract

We propose a novel dynamic car relocation policy for a car-sharing network with centralized control and uncertain, unbalanced demand. The policy is derived from a reformulation of the linear programming fluid model approximation of the dynamic problem. We project the full-dimensional fluid approximation onto the lower-dimensional space of relocation decisions only. This projection results in a characterization of the problem as n+1 linear programs, where n is the number of nodes in the network. The reformulation uncovers structural properties that are interpretable using absorbing Markov chain concepts and allows us to write the gradient with respect to the relocation decisions in closed form. Our policy exploits these gradients to make dynamic car relocation decisions. We provide extensive numerical results where our dynamic car relocation policy consistently outperforms the standard static policy in realistic instances from the literature. In fact, it reduces the static policy's optimality gap by more than 13% in all of these instances and up to 35% in some.

Keywords: car-sharing, fluid limit, closed queuing network, car relocation

Suggested Citation

Hosseini, Mahsa and Milner, Joseph and Romero, Gonzalo, Dynamic Relocations in Car-Sharing Networks (January 27, 2021). Rotman School of Management Working Paper No. 3774324, Available at SSRN: https://ssrn.com/abstract=3774324 or http://dx.doi.org/10.2139/ssrn.3774324

Mahsa Hosseini

Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

Joseph Milner

affiliation not provided to SSRN

Gonzalo Romero (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

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