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Improved Bounds for Revenue Maximization in Time-Limited Online Dial-a-Ride

Author

Listed:
  • Ananya D. Christman

    (Middlebury College)

  • Christine Chung

    (Connecticut College)

  • Nicholas Jaczko

    (Middlebury College)

  • Tianzhi Li

    (Middlebury College)

  • Scott Westvold

    (Middlebury College)

  • Xinyue Xu

    (Middlebury College)

  • David Yuen

Abstract

In the Online Dial-a-Ride Problem (OLDARP), a server travels to serve requests for rides. We consider a variant where each request specifies a source, destination, release time, and revenue that is earned for serving the request. The goal is to maximize the total revenue earned within a given time limit. We first prove that no non-preemptive deterministic online algorithm can be guaranteed to earn more than half the revenue earned by opt. We then investigate the segmented best path (sbp) algorithm of [1]. The previously established lower and upper bounds for the competitive ratio of sbp are 4 and 6, respectively, under reasonable assumptions about the input instance. We eliminate the gap by proving that the competitive ratio is 5 (under the same assumptions) and also prove that this bound is tight. When revenues are uniform, we prove that sbp has competitive ratio 4. Next we provide a competitive analysis of sbp on complete bipartite graphs. We then consider this problem on the uniform metric and revisit the bp algorithm of [1]; we provide an instance where the algorithm's competitive ratio is unbounded. We conclude with experimental results that suggest that sbp would be effective if applied in practice.

Suggested Citation

  • Ananya D. Christman & Christine Chung & Nicholas Jaczko & Tianzhi Li & Scott Westvold & Xinyue Xu & David Yuen, 2021. "Improved Bounds for Revenue Maximization in Time-Limited Online Dial-a-Ride," SN Operations Research Forum, Springer, vol. 2(3), pages 1-38, September.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:3:d:10.1007_s43069-021-00076-x
    DOI: 10.1007/s43069-021-00076-x
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    References listed on IDEAS

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    1. Yves Molenbruch & Kris Braekers & An Caris, 2017. "Typology and literature review for dial-a-ride problems," Annals of Operations Research, Springer, vol. 259(1), pages 295-325, December.
    2. Ananya Christman & William Forcier & Aayam Poudel, 2018. "From theory to practice: maximizing revenues for on-line dial-a-ride," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 512-529, February.
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