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How Much is Location Information Worth? A Competitive Analysis of the Online Traveling Salesman Problem with Two Disclosure Dates

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  • Srour, F.J.
  • Zuidwijk, R.A.

Abstract

In this paper we derive the worst-case ratio of an online algorithm for the Traveling Salesman Problem (TSP) with two disclosure dates. This problem, a variant of the online TSP with release dates, is characterized by the disclosure of a job’s location at one point in time followed by the disclosure of that job’s release date at a later point in time. We present an online algorithm for this problem restricted to the positive real number line. We then derive the worst-case ratio of our algorithm and show that it is best-possible in two contexts – the first, one in which the amount of time between the disclosure events and release time are fixed and equal for all jobs; and a second in which the time between disclosure events varies for each job. We conclude that the value of advanced information can be attributed to the location information alone – yielding an optimal solution in favorable instances.

Suggested Citation

  • Srour, F.J. & Zuidwijk, R.A., 2008. "How Much is Location Information Worth? A Competitive Analysis of the Online Traveling Salesman Problem with Two Disclosure Dates," ERIM Report Series Research in Management ERS-2008-075-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:13837
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    References listed on IDEAS

    as
    1. 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.
    2. Merrill M. Flood, 1956. "The Traveling-Salesman Problem," Operations Research, INFORMS, vol. 4(1), pages 61-75, February.
    3. 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.
    4. 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.
    5. M. Bellmore & G. L. Nemhauser, 1968. "The Traveling Salesman Problem: A Survey," Operations Research, INFORMS, vol. 16(3), pages 538-558, June.
    6. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
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    Cited by:

    1. Rob A. Zuidwijk & Albert W. Veenstra, 2015. "The Value of Information in Container Transport," Transportation Science, INFORMS, vol. 49(3), pages 675-685, August.
    2. F. Jordan Srour & Niels Agatz & Johan Oppen, 2018. "Strategies for Handling Temporal Uncertainty in Pickup and Delivery Problems with Time Windows," Transportation Science, INFORMS, vol. 52(1), pages 3-19, January.
    3. Srour, F.J. & Agatz, N.A.H. & Oppen, J., 2014. "Strategies for Handling Temporal Uncertainty in Pickup and Delivery Problems with Time Windows," ERIM Report Series Research in Management ERS-2014-015-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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    More about this item

    Keywords

    advanced information; competitive ratio; online routing; traveling salesman; worst-case ratio;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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