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Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses

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  • Patrick Jaillet

    (Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Michael R. Wagner

    (Department of Management, California State University East Bay, Hayward, California 94542)

Abstract

We consider online routing optimization problems where the objective is to minimize the time needed to visit a set of locations under various constraints; the problems are online because the set of locations are revealed incrementally over time. We consider two main problems: (1) the online traveling salesman problem (TSP) with precedence and capacity constraints, and (2) the online TSP with m salesmen. For both problems we propose online algorithms, each with a competitive ratio of 2; for the m -salesmen problem, we show that our result is best-possible. We also consider polynomial-time online algorithms.We then consider resource augmentation, where we give the online servers additional resources to offset the powerful offline adversary advantage. In this way, we address a main criticism of competitive analysis. We consider the cases where the online algorithm has access to faster servers, servers with larger capacities, additional servers, and/or advanced information. We derive improved competitive ratios. We also give lower bounds on the competitive ratios under resource augmentation, which in many cases are tight and lead to best-possible results.Finally, we study online algorithms from an asymptotic point of view. We show that, under general stochastic structures for the problem data, unknown and unused by the online player, the online algorithms are almost surely asymptotically optimal. Furthermore, we provide computational results that show that the convergence can be very fast.

Suggested Citation

  • Patrick Jaillet & Michael R. Wagner, 2008. "Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses," Operations Research, INFORMS, vol. 56(3), pages 745-757, June.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:3:p:745-757
    DOI: 10.1287/opre.1070.0450
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    Cited by:

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    2. Xingang Wen & Yinfeng Xu & Huili Zhang, 2015. "Online traveling salesman problem with deadlines and service flexibility," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 545-562, October.
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    5. Devansh Jalota & Dario Paccagnan & Maximilian Schiffer & Marco Pavone, 2023. "Online Routing Over Parallel Networks: Deterministic Limits and Data-driven Enhancements," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 560-577, May.
    6. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    7. Pillac, Victor & Gendreau, Michel & Guéret, Christelle & Medaglia, Andrés L., 2013. "A review of dynamic vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 225(1), pages 1-11.
    8. Zhang, Huili & Tong, Weitian & Xu, Yinfeng & Lin, Guohui, 2015. "The Steiner Traveling Salesman Problem with online edge blockages," European Journal of Operational Research, Elsevier, vol. 243(1), pages 30-40.
    9. Sabine Büttner & Sven O. Krumke, 2016. "The Canadian Tour Operator Problem on paths: tight bounds and resource augmentation," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 842-854, October.
    10. Wen, Jian & Nassir, Neema & Zhao, Jinhua, 2019. "Value of demand information in autonomous mobility-on-demand systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 121(C), pages 346-359.
    11. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    12. Davood Shiri & Vahid Akbari & F. Sibel Salman, 2024. "Online algorithms for ambulance routing in disaster response with time-varying victim conditions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 785-819, September.
    13. 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.
    14. Cong Chen & Huili Zhang & Yinfeng Xu, 2022. "Online machine minimization with lookahead," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1149-1172, July.
    15. Zhang, Huili & Tong, Weitian & Lin, Guohui & Xu, Yinfeng, 2019. "Online minimum latency problem with edge uncertainty," European Journal of Operational Research, Elsevier, vol. 273(2), pages 418-429.
    16. Davood Shiri & Hakan Tozan, 2022. "Online routing and searching on graphs with blocked edges," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1039-1059, September.
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