IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v288y2020i1d10.1007_s10479-019-03472-z.html
   My bibliography  Save this article

Dynamic search models with multiple items

Author

Listed:
  • Rebecca Dizon-Ross

    (University of Chicago Booth School of Business)

  • Sheldon M. Ross

    (University of Southern California)

Abstract

We generalize the classic dynamic single-item search model to a setting with multiple items and vector offers for subsets of items. We first show a computationally feasible way to solve the dynamic optimization problem, and then prove structural results. Although assignment is not generally monotonically increasing in offer value, we show that, in a special case “additive” model, monotonicity holds if costs are submodular. We examine how the thresholds for assignment change with the remaining items, and whether there are gains to grouping searches. Finally, we consider a stopping rule version of the problem with no subsets for sale, showing the optimal policy is myopic.

Suggested Citation

  • Rebecca Dizon-Ross & Sheldon M. Ross, 2020. "Dynamic search models with multiple items," Annals of Operations Research, Springer, vol. 288(1), pages 223-245, May.
    • Handle: RePEc:spr:annopr:v:288:y:2020:i:1:d:10.1007_s10479-019-03472-z
    DOI: 10.1007/s10479-019-03472-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-019-03472-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-019-03472-z?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. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    3. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    4. Dirk Bergemann & Juuso V‰lim‰ki, 2010. "The Dynamic Pivot Mechanism," Econometrica, Econometric Society, vol. 78(2), pages 771-789, March.
    5. David, Israel & Levi, Ofer, 2001. "Asset-selling problems with holding costs," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 317-321, May.
    6. Stigler, George J., 2011. "Economics of Information," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 5, pages 35-49.
    7. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey," Economic Inquiry, Western Economic Association International, vol. 14(3), pages 347-368, September.
    8. C. Derman & J. Sacks, 1960. "Replacement of periodically inspected equipment. (An optimal optional stopping rule)," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(4), pages 597-607, December.
    9. Alex Gershkov & Benny Moldovanu, 2009. "Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 168-198, August.
    10. George J. Stigler, 1962. "Information in the Labor Market," NBER Chapters, in: Investment in Human Beings, pages 94-105, National Bureau of Economic Research, Inc.
    11. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey: Part I," Economic Inquiry, Western Economic Association International, vol. 14(2), pages 155-189, June.
    12. Jérémie Gallien, 2006. "Dynamic Mechanism Design for Online Commerce," Operations Research, INFORMS, vol. 54(2), pages 291-310, April.
    13. J. MacQueen & R. G. Miller, 1960. "Optimal Persistence Policies," Operations Research, INFORMS, vol. 8(3), pages 362-380, June.
    14. Sofronov, Georgy, 2013. "An optimal sequential procedure for a multiple selling problem with independent observations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 332-336.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sheldon M. Ross & Gideon Weiss & Zhengyu Zhang, 2021. "Technical Note—A Stochastic Assignment Problem with Unknown Eligibility Probabilities," Operations Research, INFORMS, vol. 69(1), pages 266-272, January.

    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. Georgy Sofronov, 2020. "An Optimal Decision Rule for a Multiple Selling Problem with a Variable Rate of Offers," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    2. Georgy Yu. Sofronov, 2020. "An Optimal Double Stopping Rule for a Buying-Selling Problem," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 1-12, March.
    3. Churlzu Lim & J. Neil Bearden & J. Cole Smith, 2006. "Sequential Search with Multiattribute Options," Decision Analysis, INFORMS, vol. 3(1), pages 3-15, March.
    4. Maarten van Ham & Clara H. Mulder & Pieter Hooimeijer, 2001. "Local Underemployment and the Discouraged Worker Effect," Urban Studies, Urban Studies Journal Limited, vol. 38(10), pages 1733-1751, September.
    5. Henneberger, Fred & Sousa-Poza, Alfonso, 2002. "Beweggründe und Determinanten zwischenbetrieblicher Mobilität: Die Schweiz in einer internationalen Perspektive (Motives and determinants of job-to-job mobility : Switzerland in an international persp," Mitteilungen aus der Arbeitsmarkt- und Berufsforschung, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 35(2), pages 205-231.
    6. German Blanco, 2017. "Who benefits from job placement services? A two-sided analysis," Journal of Productivity Analysis, Springer, vol. 47(1), pages 33-47, February.
    7. Chi Zhou & Wansheng Tang & Ruiqing Zhao, 2017. "An uncertain search model for recruitment problem with enterprise performance," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 695-704, March.
    8. Wolfgang Stadje, 1997. "An optimal stopping problem with two levels of incomplete information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 119-131, February.
    9. Sofronov, Georgy, 2013. "An optimal sequential procedure for a multiple selling problem with independent observations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 332-336.
    10. Henneberger, Fred & Sousa-Poza, Alfonso, 2002. "Beweggründe und Determinanten zwischenbetrieblicher Mobilität: Die Schweiz in einer internationalen Perspektive (Motives and determinants of job-to-job mobility : Switzerland in an international persp," Mitteilungen aus der Arbeitsmarkt- und Berufsforschung, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 35(2), pages 205-231.
    11. Kruse, Thomas & Strack, Philipp, 2015. "Optimal stopping with private information," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 702-727.
    12. Tan Wang & Tony S. Wirjanto, 2016. "Risk Aversion, Uncertainty, Unemployment Insurance Benefit and Duration of "Wait" Unemployment," Annals of Economics and Finance, Society for AEF, vol. 17(1), pages 1-34, May.
    13. Pantelis P. Analytis & Amit Kothiyal & Konstantinos Katsikopoulos, 2014. "Multi-attribute utility models as cognitive search engines," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 9(5), pages 403-419, September.
    14. Schunk, Daniel & Winter, Joachim, 2009. "The relationship between risk attitudes and heuristics in search tasks: A laboratory experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 347-360, August.
    15. Simon P. Anderson & Régis Renault & Claude Jessua, 1996. "Produits différenciés et information imparfaite des consommateurs," Revue Économique, Programme National Persée, vol. 47(3), pages 425-435.
    16. Christelle Garrouste & Cyrille Piatecki & Yvan Stroppa, 2021. "Matching dynamics and optima in a multi-agents labor market setting, 2015," Working Papers hal-03245585, HAL.
    17. repec:cup:judgdm:v:9:y:2014:i:5:p:403-419 is not listed on IDEAS
    18. Adam, Klaus, 2001. "Learning While Searching for the Best Alternative," Journal of Economic Theory, Elsevier, vol. 101(1), pages 252-280, November.
    19. Maarten Janssen & Alexei Parakhonyak, 2014. "Consumer search markets with costly revisits," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 481-514, February.
    20. , & , & ,, 2011. "Revenue maximization in the dynamic knapsack problem," Theoretical Economics, Econometric Society, vol. 6(2), May.
    21. Timothy N. Cason & Shakun D. Mago, 2010. "Costly Buyer Search In Laboratory Markets With Seller Advertising," Journal of Industrial Economics, Wiley Blackwell, vol. 58(2), pages 424-449, June.

    More about this item

    Keywords

    Dynamic programming; Job search; Multiple applicants; Optimal stopping; Stochastic assignment problem;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    Statistics

    Access and download statistics

    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:annopr:v:288:y:2020:i:1:d:10.1007_s10479-019-03472-z. 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.