IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v296y2022i2p440-452.html
   My bibliography  Save this article

Time-critical testing and search problems

Author

Listed:
  • Agnetis, Alessandro
  • Hermans, Ben
  • Leus, Roel
  • Rostami, Salim

Abstract

This paper introduces a problem in which the state of a system needs to be determined through costly tests of its components by a limited number of testing units and before a given deadline. We also consider a closely related search problem in which there are multiple searchers to find a target before a given deadline. These natural generalizations of the classical sequential testing problem and search problem are applicable in a wide range of time-critical operations such as machine maintenance, diagnosing a patient, and new product development. We show that both problems are NP-hard, develop a pseudo-polynomial dynamic program for the special case of two time slots, and describe a partial-order-based as well as an assignment-based mixed integer program for the general case. Based on extensive computational experiments, we find that the assignment-based formulation performs better than the partial-order-based formulation for the testing variant, but that this is the other way round for the search variant. Finally, we propose a pairwise-interchange-based local search procedure and show that, empirically, it performs very well in finding near-optimal solutions.

Suggested Citation

  • Agnetis, Alessandro & Hermans, Ben & Leus, Roel & Rostami, Salim, 2022. "Time-critical testing and search problems," European Journal of Operational Research, Elsevier, vol. 296(2), pages 440-452.
    • Handle: RePEc:eee:ejores:v:296:y:2022:i:2:p:440-452
    DOI: 10.1016/j.ejor.2021.03.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721002642
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.03.038?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. Martijn van Ee, 2020. "On efficient algorithms for finding efficient salvo policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(2), pages 147-158, March.
    2. Clyde L. Monma & Jeffrey B. Sidney, 1979. "Sequencing with Series-Parallel Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 215-224, August.
    3. Jerren Gould, 1984. "On efficient salvo policies," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(1), pages 159-162, March.
    4. Rebi Daldal & Iftah Gamzu & Danny Segev & Tonguç Ünlüyurt, 2016. "Approximation algorithms for sequential batch‐testing of series systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(4), pages 275-286, June.
    5. Brian Gluss, 1959. "An Optimum Policy for Detecting a Fault in a Complex System," Operations Research, INFORMS, vol. 7(4), pages 468-477, August.
    6. Jeffrey B. Sidney, 1975. "Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs," Operations Research, INFORMS, vol. 23(2), pages 283-298, April.
    7. Rebi Daldal & Özgür Özlük & Barış Selçuk & Zahed Shahmoradi & Tonguç Ünlüyurt, 2017. "Sequential testing in batches," Annals of Operations Research, Springer, vol. 253(1), pages 97-116, June.
    8. J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "Complexity of Scheduling under Precedence Constraints," Operations Research, INFORMS, vol. 26(1), pages 22-35, February.
    9. Rostami, Salim & Creemers, Stefan & Wei, Wenchao & Leus, Roel, 2019. "Sequential testing of n-out-of-n systems: Precedence theorems and exact methods," European Journal of Operational Research, Elsevier, vol. 274(3), pages 876-885.
    10. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    11. Lidbetter, Thomas, 2020. "Search and rescue in the face of uncertain threats," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1153-1160.
    12. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    13. Salim Rostami & Stefan Creemers & Wenchao Wei & Roel Leus, 2019. "Sequential testing of n-out-of-n systems: Precedence theorems and exact methods," Post-Print hal-02114147, HAL.
    14. F. P. Kelly, 1982. "A Remark on Search and Sequencing Problems," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 154-157, February.
    15. Ben Hermans & Herbert Hamers & Roel Leus & Roy Lindelauf, 2019. "Timely exposure of a secret project: Which activities to monitor?," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 451-468, September.
    16. Kevin Glazebrook & Alan Washburn, 2004. "Shoot-Look-Shoot: A Review and Extension," Operations Research, INFORMS, vol. 52(3), pages 454-463, June.
    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. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    2. Ben Hermans & Roel Leus & Jannik Matuschke, 2022. "Exact and Approximation Algorithms for the Expanding Search Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 281-296, January.
    3. Rostami, Salim & Creemers, Stefan & Wei, Wenchao & Leus, Roel, 2019. "Sequential testing of n-out-of-n systems: Precedence theorems and exact methods," European Journal of Operational Research, Elsevier, vol. 274(3), pages 876-885.
    4. Lidbetter, Thomas, 2020. "Search and rescue in the face of uncertain threats," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1153-1160.
    5. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    6. D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.
    7. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Other publications TiSEM 17013f33-1d65-4294-802c-b, Tilburg University, School of Economics and Management.
    8. Christoph Ambühl & Monaldo Mastrolilli & Nikolaus Mutsanas & Ola Svensson, 2011. "On the Approximability of Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 653-669, November.
    9. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    10. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    11. Murali Agastya & Oleksii Birulin, 2023. "Optimal Task Scheduling under Adverse Selection and Hidden Actions," American Economic Journal: Microeconomics, American Economic Association, vol. 15(2), pages 660-698, May.
    12. 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.
    13. van Beek, Andries, 2023. "Solutions in multi-actor projects with collaboration and strategic incentives," Other publications TiSEM 3739c498-5edb-442f-87d8-c, Tilburg University, School of Economics and Management.
    14. Felix Happach & Lisa Hellerstein & Thomas Lidbetter, 2022. "A General Framework for Approximating Min Sum Ordering Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1437-1452, May.
    15. Andreas S. Schulz & Nelson A. Uhan, 2011. "Near-Optimal Solutions and Large Integrality Gaps for Almost All Instances of Single-Machine Precedence-Constrained Scheduling," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 14-23, February.
    16. Lisa Hellerstein & Thomas Lidbetter & Daniel Pirutinsky, 2019. "Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games," Operations Research, INFORMS, vol. 67(3), pages 731-743, May.
    17. Mordechai I. Henig & David Simchi‐Levi, 1990. "Scheduling tasks with failure probabilities to minimize expected cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(1), pages 99-109, February.
    18. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Discussion Paper 2023-009, Tilburg University, Center for Economic Research.
    19. Marieke Quant & Marc Meertens & Hans Reijnierse, 2008. "Processing games with shared interest," Annals of Operations Research, Springer, vol. 158(1), pages 219-228, February.
    20. Lili Liu & Guochun Tang & Baoqiang Fan & Xingpeng Wang, 2015. "Two-person cooperative games on scheduling problems in outpatient pharmacy dispensing process," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 938-948, November.

    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:eee:ejores:v:296:y:2022:i:2:p:440-452. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.