IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v81y2015i3p317-336.html
   My bibliography  Save this article

Optimal discrete search with technological choice

Author

Listed:
  • Joseph Kadane

Abstract

Consider a search problem in which a stationary object is in one of $$L \epsilon \mathcal {N}$$ L ϵ N locations. Each location can be searched using one of $$T \epsilon \mathcal {N}$$ T ϵ N technologies, and each location-technology pair has a known associated cost and overlook probability. These quantities may depend on the number of times that the technology is applied to the location. This paper finds a search policy that maximizes the probability of finding the object given a constraint on the available budget. It also finds the policy that maximizes the probability of correctly stating at the end of a search where the object is. Additionally it exhibits another policy that minimizes the expected cost required to find the object and the optimal policy for stopping. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Joseph Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    • Handle: RePEc:spr:mathme:v:81:y:2015:i:3:p:317-336
    DOI: 10.1007/s00186-015-0499-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-015-0499-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-015-0499-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    2. Moshe Kress & Kyle Lin & Roberto Szechtman, 2008. "Optimal discrete search with imperfect specificity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 539-549, December.
    3. Nah-Oak Song & Demosthenis Teneketzis, 2004. "Discrete search with multiple sensors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(1), pages 1-13, September.
    4. Scott Shorey Brown, 1980. "Optimal Search for a Moving Target in Discrete Time and Space," Operations Research, INFORMS, vol. 28(6), pages 1275-1289, December.
    5. Bernard O. Koopman, 1957. "The Theory of Search," Operations Research, INFORMS, vol. 5(5), pages 613-626, October.
    6. Joseph B. Kadane, 1971. "Optimal Whereabouts Search," Operations Research, INFORMS, vol. 19(4), pages 894-904, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joseph B. Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    2. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    3. Michael Atkinson & Moshe Kress & Rutger-Jan Lange, 2016. "When Is Information Sufficient for Action? Search with Unreliable yet Informative Intelligence," Operations Research, INFORMS, vol. 64(2), pages 315-328, April.
    4. Hohzaki, Ryusuke & Iida, Koji, 2001. "Optimal ambushing search for a moving target," European Journal of Operational Research, Elsevier, vol. 133(1), pages 120-129, August.
    5. Jake Clarkson & Kevin D. Glazebrook & Kyle Y. Lin, 2020. "Fast or Slow: Search in Discrete Locations with Two Search Modes," Operations Research, INFORMS, vol. 68(2), pages 552-571, March.
    6. Wilson, Kurt E. & Szechtman, Roberto & Atkinson, Michael P., 2011. "A sequential perspective on searching for static targets," European Journal of Operational Research, Elsevier, vol. 215(1), pages 218-226, November.
    7. Baycik, N. Orkun & Sharkey, Thomas C. & Rainwater, Chase E., 2020. "A Markov Decision Process approach for balancing intelligence and interdiction operations in city-level drug trafficking enforcement," Socio-Economic Planning Sciences, Elsevier, vol. 69(C).
    8. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    9. Voelkel, Michael A. & Sachs, Anna-Lena & Thonemann, Ulrich W., 2020. "An aggregation-based approximate dynamic programming approach for the periodic review model with random yield," European Journal of Operational Research, Elsevier, vol. 281(2), pages 286-298.
    10. Tan, Madeleine Sui-Lay, 2016. "Policy coordination among the ASEAN-5: A global VAR analysis," Journal of Asian Economics, Elsevier, vol. 44(C), pages 20-40.
    11. D. W. K. Yeung, 2008. "Dynamically Consistent Solution For A Pollution Management Game In Collaborative Abatement With Uncertain Future Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 517-538.
    12. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    13. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    14. Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economics Research Papers 2015-005, Friedrich-Schiller-University Jena.
    15. Changming Ji & Chuangang Li & Boquan Wang & Minghao Liu & Liping Wang, 2017. "Multi-Stage Dynamic Programming Method for Short-Term Cascade Reservoirs Optimal Operation with Flow Attenuation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(14), pages 4571-4586, November.
    16. Ghassan, Hassan B. & Al-Jefri, Essam H., 2015. "الحساب الجاري في المدى البعيد عبر نموذج داخلي الزمن [The Current Account in the Long Run through the Intertemporal Model]," MPRA Paper 66527, University Library of Munich, Germany.
    17. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    18. Mercedes Esteban-Bravo & Jose M. Vidal-Sanz & Gökhan Yildirim, 2014. "Valuing Customer Portfolios with Endogenous Mass and Direct Marketing Interventions Using a Stochastic Dynamic Programming Decomposition," Marketing Science, INFORMS, vol. 33(5), pages 621-640, September.
    19. Ohno, Katsuhisa & Boh, Toshitaka & Nakade, Koichi & Tamura, Takayoshi, 2016. "New approximate dynamic programming algorithms for large-scale undiscounted Markov decision processes and their application to optimize a production and distribution system," European Journal of Operational Research, Elsevier, vol. 249(1), pages 22-31.
    20. Oleg Malafeyev & Achal Awasthi, 2015. "A Dynamic Model of Functioning of a Bank," Papers 1511.01529, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:81:y:2015:i:3:p:317-336. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.