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Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios

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  • Patrick Jaillet

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

  • Michael R. Wagner

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We consider online versions of the traveling salesman problem (TSP) and traveling repairman problem (TRP) where instances are not known in advance. Cities (points) to be visited are revealed over time, while the server is en route serving previously released requests. These problems are known in the literature as the online TSP (TRP, respectively). The corresponding offline problems are the TSP (TRP) with release dates, problems where each point has to be visited at or after a given release date. In the current literature, the assumption is that a request becomes known at the time of its release date. In this paper we introduce the notion of a request’s disclosure date , the time when a city’s location and release date are revealed to the server. In a variety of disclosure date scenarios and metric spaces, we give new online algorithms and quantify the value of this advanced information in the form of improved competitive ratios. We also provide a general result on polynomial-time online algorithms for the online TSP.

Suggested Citation

  • Patrick Jaillet & Michael R. Wagner, 2006. "Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios," Transportation Science, INFORMS, vol. 40(2), pages 200-210, May.
    • Handle: RePEc:inm:ortrsc:v:40:y:2006:i:2:p:200-210
    DOI: 10.1287/trsc.1060.0147
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    References listed on IDEAS

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    1. Michiel Blom & Sven O. Krumke & Willem E. de Paepe & Leen Stougie, 2001. "The Online TSP Against Fair Adversaries," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 138-148, May.
    2. Harilaos N. Psaraftis & Marius M. Solomon & Thomas L. Magnanti & Tai-Up Kim, 1990. "Routing and Scheduling on a Shoreline with Release Times," Management Science, INFORMS, vol. 36(2), pages 212-223, February.
    3. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
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