Joint pricing and delayed empty relocation policies for ride-sourcing systems

113 Pages Posted: 9 Sep 2022 Last revised: 1 Nov 2023

See all articles by Mojtaba Abdolmaleki

Mojtaba Abdolmaleki

University of Michigan, Stephen M. Ross School of Business

Xiuli Chao

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering

Tara Radvand

University of Michigan, Stephen M. Ross School of Business

Yafeng Yin

University of Michigan, Ann Arbor

Date Written: September 6, 2022

Abstract

With the development of shared mobility (e.g., ride-sourcing systems such as Uber and Lyft), there has been a growing interest in pricing and empty vehicle relocation to maximize system performance (e.g., revenue, throughput, social welfare). Although customers exhibit patience during their waiting for available driver, it has been neglected in most studies due to the complexities it introduces. In this paper, we develop a provably near-optimal dynamic pricing and empty vehicle relocation mechanism for a ride-sourcing system with limited customer patience. We model the ride-sourcing system as a network of double-ended queues. To derive a near-optimal control policy, we first establish a fluid limit for the network in a large market regime and show that the fluid-based optimal solution provides an upper bound of the performance of the original ride-sourcing system for all dynamic policies. Then, we develop a simple dynamic policy for the original problem based on the fluid solution and show that its performance almost achieves that upper bound. Among our results, we answer two open questions raised in the literature: (i) the performance of our policy converges to that of the true optimal value exponentially fast in time when the market size is large (Braverman et al., 2019) (ii) the customer loss of our proposed policy decreases to zero exponentially fast when market size increases (Banerjee et al., 2018). Additionally, we show that our simple policy can balance supply utilization and customer waiting times under the Square Root Safety (SRS) staffing rule. Finally, the effectiveness of our proposed policy is demonstrated through extensive numerical experiments using empirical data from DiDi Chuxing.

Keywords: Ride-sourcing, dynamic joint pricing-empty relocation, capacity sizing, queueing, fluid approximation, network of double-ended queues, exponentially fast convergence, exponentially small loss.

Suggested Citation

Abdolmaleki, Mojtaba and Chao, Xiuli and Radvand, Tara and Yin, Yafeng, Joint pricing and delayed empty relocation policies for ride-sourcing systems (September 6, 2022). Available at SSRN: https://ssrn.com/abstract=4210834 or http://dx.doi.org/10.2139/ssrn.4210834

Mojtaba Abdolmaleki (Contact Author)

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
7348815989 (Phone)

Xiuli Chao

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering ( email )

1205 Beal Avenue
Ann Arbor, MI 48109
United States

Tara Radvand

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Yafeng Yin

University of Michigan, Ann Arbor ( email )

2350
Hayward Street
Ann Arbor, MI 48109
United States

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