IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v58y2010i4-part-1p1023-1027.html
   My bibliography  Save this article

Technical Note ---Stochastic Sequential Decision-Making with a Random Number of Jobs

Author

Listed:
  • Alexander G. Nikolaev

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60201)

  • Sheldon H. Jacobson

    (Department of Computer Science, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

Abstract

This paper addresses a class of problems in which available resources need to be optimally allocated to a random number of jobs with stochastic parameters. Optimal policies are presented for variations of the sequential stochastic assignment problem and the dynamic stochastic knapsack problem, in which the number of arriving jobs is unknown until after the final arrival, and the job parameters are assumed to be independent but not identically distributed random variables.

Suggested Citation

  • Alexander G. Nikolaev & Sheldon H. Jacobson, 2010. "Technical Note ---Stochastic Sequential Decision-Making with a Random Number of Jobs," Operations Research, INFORMS, vol. 58(4-part-1), pages 1023-1027, August.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:4-part-1:p:1023-1027
    DOI: 10.1287/opre.1090.0778
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1090.0778
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1090.0778?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
    ---><---

    References listed on IDEAS

    as
    1. L L Lu & S Y Chiu & L A Cox, 1999. "Optimal project selection: Stochastic knapsack with finite time horizon," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(6), pages 645-650, June.
    2. Laura McLay & Sheldon Jacobson & Alexander Nikolaev, 2009. "A sequential stochastic passenger screening problem for aviation security," IISE Transactions, Taylor & Francis Journals, vol. 41(6), pages 575-591.
    3. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    4. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    5. Alexander G. Nikolaev & Sheldon H. Jacobson & Laura A. McLay, 2007. "A Sequential Stochastic Security System Design Problem for Aviation Security," Transportation Science, INFORMS, vol. 41(2), pages 182-194, May.
    6. Richard Van Slyke & Yi Young, 2000. "Finite Horizon Stochastic Knapsacks with Applications to Yield Management," Operations Research, INFORMS, vol. 48(1), pages 155-172, February.
    7. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
    8. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    9. Xuanming Su & Stefanos A. Zenios, 2005. "Patient Choice in Kidney Allocation: A Sequential Stochastic Assignment Model," Operations Research, INFORMS, vol. 53(3), pages 443-455, June.
    10. Toru Nakai, 1986. "A Sequential Stochastic Assignment Problem in a Partially Observable Markov Chain," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 230-240, May.
    11. D. P. Kennedy, 1986. "Optimal Sequential Assignment," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 619-626, November.
    12. Jason D. Papastavrou & Srikanth Rajagopalan & Anton J. Kleywegt, 1996. "The Dynamic and Stochastic Knapsack Problem with Deadlines," Management Science, INFORMS, vol. 42(12), pages 1706-1718, December.
    13. C. Derman & G. J. Lieberman & S. M. Ross, 1975. "A Stochastic Sequential Allocation Model," Operations Research, INFORMS, vol. 23(6), pages 1120-1130, December.
    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. David T. Wu & Sheldon M. Ross, 2015. "A stochastic assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 23-31, February.
    2. Arash Khatibi & Sheldon H. Jacobson, 2016. "Doubly Stochastic Sequential Assignment Problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 124-137, March.
    3. Senay Solak & Armagan Bayram & Mehmet Gumus & Yueran Zhuo, 2019. "Technical Note—Optimizing Foreclosed Housing Acquisitions in Societal Response to Foreclosures," Operations Research, INFORMS, vol. 67(4), pages 950-964, July.
    4. Xuhan Tian & Junmin (Jim) Shi & Xiangtong Qi, 2022. "Stochastic Sequential Allocations for Creative Crowdsourcing," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 697-714, February.
    5. Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    6. 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.
    7. David Bergman & Jason Imbrogno, 2017. "Surviving a National Football League Survivor Pool," Operations Research, INFORMS, vol. 65(5), pages 1343-1354, October.

    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. Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    2. Arash Khatibi & Golshid Baharian & Banafsheh Behzad & Sheldon Jacobson, 2015. "Extensions of the sequential stochastic assignment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 317-340, December.
    3. Meghan Shanks & Ge Yu & Sheldon H. Jacobson, 2023. "Approximation algorithms for stochastic online matching with reusable resources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 43-56, August.
    4. David T. Wu & Sheldon M. Ross, 2015. "A stochastic assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 23-31, February.
    5. Arash Khatibi & Sheldon H. Jacobson, 2016. "Doubly Stochastic Sequential Assignment Problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 124-137, March.
    6. Grace Y. Lin & Yingdong Lu & David D. Yao, 2008. "The Stochastic Knapsack Revisited: Switch-Over Policies and Dynamic Pricing," Operations Research, INFORMS, vol. 56(4), pages 945-957, August.
    7. Adrian Lee & Sheldon Jacobson, 2011. "Sequential stochastic assignment under uncertainty: estimation and convergence," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 21-46, February.
    8. Xuhan Tian & Junmin (Jim) Shi & Xiangtong Qi, 2022. "Stochastic Sequential Allocations for Creative Crowdsourcing," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 697-714, February.
    9. So, Mee Chi & Thomas, Lyn C. & Huang, Bo, 2016. "Lending decisions with limits on capital available: The polygamous marriage problem," European Journal of Operational Research, Elsevier, vol. 249(2), pages 407-416.
    10. , & , & ,, 2011. "Revenue maximization in the dynamic knapsack problem," Theoretical Economics, Econometric Society, vol. 6(2), May.
    11. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    12. Pak, K. & Dekker, R., 2004. "Cargo Revenue Management: Bid-Prices for a 0-1 Multi Knapsack Problem," ERIM Report Series Research in Management ERS-2004-055-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.
    13. Grace Lin & Yingdong Lu & David Yao, 2007. "Stochastic Knapsack Problem Revisited: Switch-Over Policies and Dynamic Pricing," Papers 0708.1146, arXiv.org.
    14. Chen, Kai & Ross, Sheldon M., 2014. "An adaptive stochastic knapsack problem," European Journal of Operational Research, Elsevier, vol. 239(3), pages 625-635.
    15. 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.
    16. David, Israel & Levi, Ofer, 2004. "A new algorithm for the multi-item exponentially discounted optimal selection problem," European Journal of Operational Research, Elsevier, vol. 153(3), pages 782-789, March.
    17. Xuanming Su & Stefanos A. Zenios, 2005. "Patient Choice in Kidney Allocation: A Sequential Stochastic Assignment Model," Operations Research, INFORMS, vol. 53(3), pages 443-455, June.
    18. Feng, Youyi & Xiao, Baichun, 2006. "A continuous-time seat control model for single-leg flights with no-shows and optimal overbooking upper bound," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1298-1316, October.
    19. Baris Ata & Yichuan Ding & Stefanos Zenios, 2021. "An Achievable-Region-Based Approach for Kidney Allocation Policy Design with Endogenous Patient Choice," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 36-54, 1-2.
    20. Golshid Baharian & Sheldon H. Jacobson, 2013. "Limiting behavior of the stochastic sequential assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 321-330, June.

    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:inm:oropre:v:58:y:2010:i:4-part-1:p:1023-1027. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.