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- Title
Technical Note—Pricing in On-Demand and One-Way Vehicle-Sharing Networks.
- Authors
Benjaafar, Saif; Shen, Xiaobing
- Abstract
In this paper, we introduce a new method for evaluating the performance of static pricing in one-way vehicle-sharing systems. Our approach, based on a well-known recursive relationship, leads to a series of increasingly tight bounds on the performance of the static pricing policy. These bounds are valid for systems with multiple locations, nonzero travel times, and an arbitrary number of vehicles. They also apply to systems where the static pricing policy does not lead to a fully connected network. Our method results in a family of asymptotically optimal static pricing policies that improve upon previous results in the literature. The approach applies to the case of a single location and yields a bound that is at least as tight as the best known bound. We consider the dynamic pricing problem that arises in the context of an on-demand vehicle sharing system with one-way trips. Existing results show that a static pricing policy that arises from solving a maximum flow relaxation of the problem guarantees a performance ratio that is bounded by K/(N + K−1) when travel times are negligible and by 1 − O (1 / K ) otherwise, where K is the number of vehicles and N is the number of locations. In this paper, we build on these results by providing an alternative approach to bounding the performance of static pricing policies. Our approach is startlingly simple, producing, upon the application of a well-known recursive relationship that relates system availability in a system with K vehicles to one with K−1 vehicles, a sequence of bounds that are increasingly tight. The worst of these bounds is given by K / (N + K − 1 + Λ / μ) , where Λ is the total demand (sum of all trip requests) rate and 1 / μ is the average trip travel time, implying a convergence rate that is at least of order 1 − O (1 / K) in the number of vehicles for fixed Λ / μ. The same recursive relationship can be used to obtain a bound that is independent of Λ / μ and that is tighter than previous bounds, implying a convergence rate that is at least of order 1 − O (1 / K ) . The approach also yields a parameterized family of static pricing policies that are asymptotically optimal and that generalize static pricing policies previously proposed in the literature. Moreover, the best static pricing policy this approach produces is optimal among those that require a demand balance constraint with a performance that can be significantly higher. Funding: This work was supported by the National Science Foundation [Grant SCC-1831140].
- Subjects
NATIONAL Science Foundation (U.S.); PRICES; TRAVEL time (Traffic engineering); TIME-based pricing; SYSTEMS availability; QUEUEING networks
- Publication
Operations Research, 2023, Vol 71, Issue 5, p1596
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.2023.2446