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Optimal search for a moving target with the option to wait

Author

Listed:
  • János Flesch
  • Emin Karagözoǧlu
  • Andrés Perea

Abstract

We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (Pollock, Operat Res 18 (1970) 883–903). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Moreover, when the agent searches the location that contains the object, he finds it with probability 1 (i.e. there is no overlooking). Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber, J Appl Probab 23 (1986) 708–717). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009

Suggested Citation

  • János Flesch & Emin Karagözoǧlu & Andrés Perea, 2009. "Optimal search for a moving target with the option to wait," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 526-539, September.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:6:p:526-539
    DOI: 10.1002/nav.20359
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    References listed on IDEAS

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    1. Y. C. Kan, 1977. "Optimal Search of a Moving Target," Operations Research, INFORMS, vol. 25(5), pages 864-870, October.
    2. Stephen M. Pollock, 1970. "A Simple Model of Search for a Moving Target," Operations Research, INFORMS, vol. 18(5), pages 883-903, October.
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    Cited by:

    1. Benoit Duvocelle & János Flesch & Hui Min Shi & Dries Vermeulen, 2021. "Search for a moving target in a competitive environment," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 547-557, June.
    2. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.

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    More about this item

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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