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New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues (Short Paper)

Authors Barbara M. Anthony , Christine Chung , Ananya Das , David Yuen

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OASIcs.ATMOS.2024.8.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • Applied computing → Transportation
Keywords
  • Dial-a-Ride problems
  • Lower bounds
  • Vehicle routing

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Abstract

We revisit the Segmented Best Path (sbp) algorithm for online DARP in an offline setting with revenues and a time limit. The goal is to find a subset of the inputted ride requests that can be served within the time limit while maximizing the total revenue earned. sbp divides the time into segments and greedily chooses the highest-revenue path of requests to serve within each time segment. We show that sbp’s performance has an upper bound of 5. Further, while sbp is a tight 4-approximation in the uniform-revenue case, we find that with non-uniform revenues, the approximation ratio of sbp has a lower bound strictly greater than 4; in particular, we provide a lower bound of (√e + 1)/(√e - 1) ≈ 4.08299, which we show can be generalized to instances with ratio greater than 4.278.

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Barbara M. Anthony, Christine Chung, Ananya Das, and David Yuen. New Bounds on the Performance of SBP for the Dial-a-Ride Problem with Revenues (Short Paper). In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 8:1-8:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/OASIcs.ATMOS.2024.8

Author Details

Barbara M. Anthony
  • Southwestern University, Georgetown, TX, USA
Christine Chung
  • Connecticut College, New London, CT, USA
Ananya Das
  • Middlebury College, VT, USA
David Yuen
  • Independent Researcher, Kapolei, HI, USA

References

  1. Barbara M. Anthony, Ananya D. Christman, Christine Chung, and David Yuen. Serving Rides of Equal Importance for Time-Limited Dial-a-Ride. In Panos Pardalos, Michael Khachay, and Alexander Kazakov, editors, Mathematical Optimization Theory and Operations Research, pages 35-50. Springer International Publishing, 2021. URL: https://doi.org/10.1007/978-3-030-77876-7_3.
  2. Egon Balas. The prize collecting traveling salesman problem. Networks, 19(6):621-636, 1989. URL: https://doi.org/10.1002/net.3230190602.
  3. Daniel Bienstock, Michel X. Goemans, David Simchi-Levi, and David Williamson. A note on the prize collecting traveling salesman problem. Mathematical programming, 59(1-3):413-420, 1993. URL: https://doi.org/10.1007/BF01581256.
  4. Jannis Blauth and Martin Nägele. An improved approximation guarantee for prize-collecting TSP. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, STOC 2023, pages 1848-1861, New York, NY, USA, 2023. URL: https://doi.org/10.1145/3564246.3585159.
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  6. Ananya Christman, Christine Chung, Nicholas Jaczko, Marina Milan, Anna Vasilchenko, and Scott Westvold. Revenue Maximization in Online Dial-A-Ride. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017), volume 59, pages 1:1-1:15, Dagstuhl, Germany, 2017. URL: https://doi.org/10.4230/OASIcs.ATMOS.2017.1.
  7. Ananya D. Christman, Christine Chung, Nicholas Jaczko, Tianzhi Li, Scott Westvold, Xinyue Xu, and David Yuen. Improved Bounds for Revenue Maximization in Time-Limited Online Dial-a-Ride. SN Operations Research Forum, 2(3):1-38, September 2021. URL: https://doi.org/10.1007/S43069-021-00076-X.
  8. Sin C. Ho, W.Y. Szeto, Yong-Hong Kuo, Janny M.Y. Leung, Matthew Petering, and Terence W.H. Tou. A survey of dial-a-ride problems: Literature review and recent developments. Transportation Research Part B: Methodological, 111:395-421, 2018. Google Scholar
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