This article was downloaded by: [78.183.135.108] On: 20 November 2020, At: 04:16 Publisher: Institute for Operations Research and the Management Sciences (INFORMS) INFORMS is located in Maryland, USA Stochastic Systems Publication details, including instructions for authors and subscription information: http://pubsonline.informs.org Dynamic Matching for Real-Time Ride Sharing Erhun Özkan, Amy R. Ward To cite this article: Erhun Özkan, Amy R. Ward (2020) Dynamic Matching for Real-Time Ride Sharing. Stochastic Systems 10(1):29-70. https:// doi.org/10.1287/stsy.2019.0037 Full terms and conditions of use: https://pubsonline.informs.org/Publications/Librarians-Portal/PubsOnLine-Terms-and- Conditions This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. 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For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org STOCHASTIC SYSTEMS Vol. 10, No. 1, March 2020, pp. 29–70 http://pubsonline.informs.org/journal/stsy ISSN 1946-5238 (online) Dynamic Matching for Real-Time Ride Sharing Erhun Özkan,a Amy R. Wardb a College of Administrative Sciences and Economics, Koç University, 34450 Istanbul, Turkey; b Booth School of Business, University of Chicago, Chicago, Illinois 60637 Contact: [email protected], http://orcid.org/0000-0001-6870-9495 (EÖ); [email protected], http://orcid.org/0000-0003-2744-2960 (ARW) Received: July 26, 2018 Abstract. In a ride-sharing system, arriving customers must be matched with available Revised: February 2, 2019 drivers. These decisions affect the overall number of customers matched, because they Accepted: May 10, 2019 impact whether future available drivers will be close to the locations of arriving customers. Published Online in Articles in Advance: A common policy used in practice is the closest driver policy, which offers an arriving February 25, 2020 customer the closest driver. This is an attractive policy because it is simple and easy to implement. However, we expect that parameter-based policies can achieve better per- MSC2010 Subject Classification: 90B22, 60F99, 90C99 formance. We propose matching policies based on a continuous linear program (CLP) that accounts for (i) the differing arrival rates of customers and drivers in different areas of the https://doi.org/10.1287/stsy.2019.0037 city, (ii) how long customers are willing to wait for driver pickup, (iii) how long drivers are willing to wait for a customer, and (iv) the time-varying nature of all the aforementioned Copyright: © 2020 The Author(s) parameters. We prove asymptotic optimality of a forward-looking CLP-based policy in a large market regime and of a myopic linear program–based matching policy when drivers are fully utilized. When pricing affects customer and driver arrival rates and parameters are time homogeneous, we show that asymptotically optimal joint pricing and matching decisions lead to fully utilized drivers under mild conditions. History: Former designation of this paper was SSY-2018-022. Open Access Statement: This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to copy, distribute, transmit and adapt this work, but you must attribute this work as “Stochastic Systems. Copyright © 2020 The Author(s). https://doi.org/10.1287/stsy.2019.0037,used under a Creative Commons Attribution License: https://creativecommons.org/licenses/by/4.0/.” Keywords: ride sharing • dynamic matching • fluid model • asymptotic optimality 1. Introduction We consider the control of a two-sided matching system with multiple item types on both sides arriving randomly to the system with potentially time-varying rates; see Figure 1. The items arriving to the circles must be matched at the time of their arrival, and there is a time-varying probability that the match is acceptable. The items arriving to the queues will wait to be matched, but are impatient, and may leave their queue if left waiting for too long. The goal of the system controller is to maximize the cumulative number of (weighted) matchings in a finite time horizon. Our main motivation for studying the system in Figure 1 is the customer–driver matching in ride-sharing platforms. The N queue locations in Figure 1 represent different areas in the city; the items arriving to the circles are customers, and those arriving to the queues are drivers. Customer types are categorized by factors such as their origin and destination areas and their priority status. Driver types are categorized by their current areas. Customers arrive in the system to request a ride. If the system controller, who is the corresponding ride-sharing company, offers a driver to a customer, then the customer accepts to be matched with the driver with respect to a specific probability that depends on the pickup time of the driver. If a customer must wait too long for pickup, then she may refuse the ride and use another transportation option. If a driver is not matched with a customer for a long time, he can either leave the system or travel to another region (i.e., another queue) to look for customers. Because customers do not want to wait for driver pickup for a long time, the ride-sharing company would like to ensure there is always a nearby driver to offer to an arriving customer. However, maintaining adequate driver supply is difficult. Not only do customers choose when to request a ride, but also drivers choose when to begin work, how long to work, and where to go to search for customers. The result can be dramatic changes in customer demand and driver supply across different locations and over the course of a day, which sometimes results in significant driver shortages (see Hall et al. 2016, figures 1–3). One common operational strategy is to match customers with the closest driver (CD) and to use pricing to incentivize drivers to move to undersupplied locations. However, surges in price can lead to negative 29 Özkan and Ward: Dynamic Matching for Real-Time Ride Sharing 30 Stochastic Systems, 2020, vol. 10, no. 1, pp. 29–70, © 2020 The Author(s) Figure 1. A Two-Sided Matching System with Multiple Item Types on Both Sides publicity (see The Economist 2016, Michallon 2016,White2016). This leads to the question of whether better matching decisions could reduce the need for price surges. An ideal is to solve a joint pricing and matching problem that accounts for the impact of differing customer and driver locations. We do this in a static environment, but that joint problem is very difficult in a time-varying environment. As a first step to making progress in a time-varying environment, we assume customer and driver arrival rates are given and focus on optimizing the matching decisions. The aforementioned time-varying arrival rates could be thought of as the result of a pricing policy as well as other underlying incentives that may be given to drivers or customers, such as demand information sharing or discount coupons, but we do not explicitly model that. The CD policy is a greedy policy, and, therefore, a forward-looking policy is likely to perform better than the CD policy does. The following example illustrates this point. Figure 2 represents a region of a city partitioned into 10 disjoint hexagonal areas (for motivation that ride-sharing companies find such a representation useful see Chen and Sheldon 2015, figure 3). Suppose a customer arrives at area 1 and requests a ride. There are three drivers idle in area 4, and there is a single idle driver in area 3. Moreover, a concert recently ended in area 8, which implies a high potential customer arrival rate in that area. If the destination of the current area 1 customer is far away, the driver assigned to that customer will not return to area 1 for a long time. Then, the system controller has two options: he can offer either one of the drivers in area 4 or the driver in area 3 to the customer in area 1. Under the CD policy, the system controller offers an area 4 driver. However, offering the driver in area 3 saves all drivers in area 4 to match with the potential customers departing the concert in area 8. This prevents the potential future need to offer an area 8 customer a faraway area 3 driver, whom the customer will likely refuse, ending in no match being made. We conclude there is a nontrivial trade-off between offering the closest driver in accordance with the CD policy and offering a farther driver in order to maximize the future number of customers matched. 1.1. Contributions of this Paper We analyze the two-sided matching system depicted in Figure 1 that is motivated by ride-sharing systems. The objective is to maximize the cumulative number of matchings in a finite time horizon.