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Optimal Search On Spatial Paths With Recall: Theoretical Foundations

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  • Mitchell Harwitz
  • Barry Lentnek
  • Peter Rogerson
  • T.E. Smith

Abstract

ABSTRACT This is the first of two articles which analyzes the problem of organizing an optimal sequential search among sites located in space. Here it is assumed that the payoffs or costs at sites are independent random variables with known distributions, and that recall of previously inspected sites is possible. Optimal sequential search is then taken to include optimization with respect to both stopping rules and search paths. In this article, it is shown that such optima always exist, and that under mild regularity conditions, optimal stopping rules on search paths always exhibit the classical reservation price property. In a companion article, a computational procedure for the optimization problem with continuous distributions is developed. It is illustrated for small examples, and optimal search paths are also computed for examples with discrete contributions.

Suggested Citation

  • Mitchell Harwitz & Barry Lentnek & Peter Rogerson & T.E. Smith, 1998. "Optimal Search On Spatial Paths With Recall: Theoretical Foundations," Papers in Regional Science, Wiley Blackwell, vol. 77(3), pages 301-327, July.
    • Handle: RePEc:bla:presci:v:77:y:1998:i:3:p:301-327
    DOI: 10.1111/j.1435-5597.1998.tb00719.x
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    Cited by:

    1. Gunther Maier, 2009. "Spatial prices, search behavior and location," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 43(1), pages 27-48, March.
    2. Ralph Braid, 2014. "The socially optimal and equilibrium locations of two stores or libraries with consumer search," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 123-136, August.

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