IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v64y2017i5p373-387.html
   My bibliography  Save this article

Exact algorithms and bounds for the dynamic assignment interdiction problem

Author

Listed:
  • Jorge A. Sefair
  • J. Cole Smith

Abstract

We study a multi‐stage dynamic assignment interdiction (DAI) game in which two agents, a user and an attacker, compete in the underlying bipartite assignment graph. The user wishes to assign a set of tasks at the minimum cost, and the attacker seeks to interdict a subset of arcs to maximize the user's objective. The user assigns exactly one task per stage, and the assignment costs and interdiction impacts vary across stages. Before any stage commences in the game, the attacker can interdict arcs subject to a cardinality constraint. An interdicted arc can still be used by the user, but at an increased assignment cost. The goal is to find an optimal sequence of assignments, coupled with the attacker's optimal interdiction strategy. We prove that this problem is strongly NP‐hard, even when the attacker can interdict only one arc. We propose an exact exponential‐state dynamic‐programming algorithm for this problem as well as lower and upper bounds on the optimal objective function value. Our bounds are based on classical interdiction and robust optimization models, and on variations of the DAI game. We examine the efficiency of our algorithms and the quality of our bounds on a set of randomly generated instances. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 373–387, 2017

Suggested Citation

  • Jorge A. Sefair & J. Cole Smith, 2017. "Exact algorithms and bounds for the dynamic assignment interdiction problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 373-387, August.
    • Handle: RePEc:wly:navres:v:64:y:2017:i:5:p:373-387
    DOI: 10.1002/nav.21753
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21753
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21753?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. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    2. Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2016. "Sequential Shortest Path Interdiction with Incomplete Information," Decision Analysis, INFORMS, vol. 13(1), pages 68-98, March.
    3. Zhi-Long Chen & Guruprasad Pundoor, 2006. "Order Assignment and Scheduling in a Supply Chain," Operations Research, INFORMS, vol. 54(3), pages 555-572, June.
    4. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.
    5. Arash Khatibi & Golshid Baharian & Estelle R. Kone & Sheldon H. Jacobson, 2014. "The sequential stochastic assignment problem with random success rates," IISE Transactions, Taylor & Francis Journals, vol. 46(11), pages 1169-1180, November.
    6. 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.
    7. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    8. Vladimir Stozhkov & Vladimir Boginski & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2017. "A simple greedy heuristic for linear assignment interdiction," Annals of Operations Research, Springer, vol. 249(1), pages 39-53, February.
    9. Behdad Beheshti & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2016. "Exact solution approaches for bilevel assignment problems," Computational Optimization and Applications, Springer, vol. 64(1), pages 215-242, May.
    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. Smith, J. Cole & Song, Yongjia, 2020. "A survey of network interdiction models and algorithms," European Journal of Operational Research, Elsevier, vol. 283(3), pages 797-811.
    2. Claudio Contardo & Jorge A. Sefair, 2022. "A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 890-908, March.
    3. Tayyebi, Javad & Mitra, Ankan & Sefair, Jorge A., 2023. "The continuous maximum capacity path interdiction problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 38-52.

    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. 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.
    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. Agatz, Niels & Erera, Alan & Savelsbergh, Martin & Wang, Xing, 2012. "Optimization for dynamic ride-sharing: A review," European Journal of Operational Research, Elsevier, vol. 223(2), pages 295-303.
    4. Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.
    5. 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.
    6. 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.
    7. David Bergman & Jason Imbrogno, 2017. "Surviving a National Football League Survivor Pool," Operations Research, INFORMS, vol. 65(5), pages 1343-1354, October.
    8. 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.
    9. Amit Kumar & Anila Gupta, 2013. "Mehar’s methods for fuzzy assignment problems with restrictions," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 27-44, March.
    10. Pritibhushan Sinha, 2009. "Assignment problems with changeover cost," Annals of Operations Research, Springer, vol. 172(1), pages 447-457, November.
    11. 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.
    12. Ullrich, Christian A., 2013. "Integrated machine scheduling and vehicle routing with time windows," European Journal of Operational Research, Elsevier, vol. 227(1), pages 152-165.
    13. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    14. 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.
    15. Azeddine Cheref & Alessandro Agnetis & Christian Artigues & Jean-Charles Billaut, 2017. "Complexity results for an integrated single machine scheduling and outbound delivery problem with fixed sequence," Journal of Scheduling, Springer, vol. 20(6), pages 681-693, December.
    16. Xi, Haoning & Aussel, Didier & Liu, Wei & Waller, S.Travis. & Rey, David, 2024. "Single-leader multi-follower games for the regulation of two-sided mobility-as-a-service markets," European Journal of Operational Research, Elsevier, vol. 317(3), pages 718-736.
    17. Ágoston, Kolos Csaba & Biró, Péter & Kováts, Endre & Jankó, Zsuzsanna, 2022. "College admissions with ties and common quotas: Integer programming approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 722-734.
    18. 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.
    19. Hugo P. Simão & Jeff Day & Abraham P. George & Ted Gifford & John Nienow & Warren B. Powell, 2009. "An Approximate Dynamic Programming Algorithm for Large-Scale Fleet Management: A Case Application," Transportation Science, INFORMS, vol. 43(2), pages 178-197, May.
    20. Qingzhu Yao & Xiaoyan Zhu & Way Kuo, 2014. "A Birnbaum-importance based genetic local search algorithm for component assignment problems," Annals of Operations Research, Springer, vol. 212(1), pages 185-200, January.

    More about this item

    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:wly:navres:v:64:y:2017:i:5:p:373-387. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.