IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v27y2024i6d10.1007_s10951-024-00822-z.html
   My bibliography  Save this article

Resource leveling: complexity of a unit execution time two-processor scheduling variant and related problems

Author

Listed:
  • Pascale Bendotti

    (EDF R&D
    Sorbonne Université, CNRS)

  • Luca Brunod Indrigo

    (EDF R&D
    Sorbonne Université, CNRS)

  • Philippe Chrétienne

    (Sorbonne Université, CNRS)

  • Bruno Escoffier

    (Sorbonne Université, CNRS
    Institut Universitaire de France)

Abstract

This paper mainly focuses on a resource leveling variant of a two-processor scheduling problem. The latter problem is to schedule a set of dependent UET jobs on two identical processors with minimum makespan. It is known to be polynomial-time solvable. In the variant we consider, the resource constraint on processors is relaxed and the objective is no longer to minimize makespan. Instead, a deadline is imposed on the makespan and the objective is to minimize the total resource use exceeding a threshold resource level of two. This resource leveling criterion is known as the total overload cost. Sophisticated matching arguments allow us to provide a polynomial algorithm computing the optimal solution as a function of the makespan deadline. It extends a solving method from the literature for the two-processor scheduling problem. Moreover, the complexity of related resource leveling problems sharing the same objective is studied. These results lead to polynomial or pseudo-polynomial algorithms or NP-hardness proofs, allowing for an interesting comparison with classical machine scheduling problems.

Suggested Citation

  • Pascale Bendotti & Luca Brunod Indrigo & Philippe Chrétienne & Bruno Escoffier, 2024. "Resource leveling: complexity of a unit execution time two-processor scheduling variant and related problems," Journal of Scheduling, Springer, vol. 27(6), pages 587-606, December.
    • Handle: RePEc:spr:jsched:v:27:y:2024:i:6:d:10.1007_s10951-024-00822-z
    DOI: 10.1007/s10951-024-00822-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-024-00822-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/s10951-024-00822-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. Erik Demeulemeester, 1995. "Minimizing Resource Availability Costs in Time-Limited Project Networks," Management Science, INFORMS, vol. 41(10), pages 1590-1598, October.
    2. Malgorzata Sterna & Kateryna Czerniachowska, 2017. "Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 927-944, September.
    3. Neumann, K. & Zimmermann, J., 1999. "Resource levelling for projects with schedule-dependent time windows," European Journal of Operational Research, Elsevier, vol. 117(3), pages 591-605, September.
    4. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    5. Zhu, Xia & Ruiz, Rubén & Li, Shiyu & Li, Xiaoping, 2017. "An effective heuristic for project scheduling with resource availability cost," European Journal of Operational Research, Elsevier, vol. 257(3), pages 746-762.
    6. Xin Chen & Malgorzata Sterna & Xin Han & Jacek Blazewicz, 2016. "Scheduling on parallel identical machines with late work criterion: Offline and online cases," Journal of Scheduling, Springer, vol. 19(6), pages 729-736, December.
    7. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    8. Lucio Bianco & Massimiliano Caramia & Stefano Giordani, 2016. "Resource levelling in project scheduling with generalized precedence relationships and variable execution intensities," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 405-425, March.
    9. Hartmann, Sönke & Briskorn, Dirk, 2022. "An updated survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 1-14.
    10. Györgyi, Péter & Kis, Tamás, 2020. "A common approximation framework for early work, late work, and resource leveling problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 129-137.
    11. Drótos, Márton & Kis, Tamás, 2011. "Resource leveling in a machine environment," European Journal of Operational Research, Elsevier, vol. 212(1), pages 12-21, July.
    12. Atan, Tankut & Eren, Elif, 2018. "Optimal project duration for resource leveling," European Journal of Operational Research, Elsevier, vol. 266(2), pages 508-520.
    13. Rieck, Julia & Zimmermann, Jürgen & Gather, Thorsten, 2012. "Mixed-integer linear programming for resource leveling problems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 27-37.
    14. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    15. Hongbo Li & Li Xiong & Yinbin Liu & Haitao Li, 2018. "An effective genetic algorithm for the resource levelling problem with generalised precedence relations," International Journal of Production Research, Taylor & Francis Journals, vol. 56(5), pages 2054-2075, March.
    16. Cédric Verbeeck & Vincent Peteghem & Mario Vanhoucke & Pieter Vansteenwegen & El-Houssaine Aghezzaf, 2017. "A metaheuristic solution approach for the time-constrained project scheduling problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 353-371, March.
    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. Györgyi, Péter & Kis, Tamás, 2020. "A common approximation framework for early work, late work, and resource leveling problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 129-137.
    2. Hartmann, Sönke & Briskorn, Dirk, 2022. "An updated survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 1-14.
    3. Chen, Xin & Miao, Qian & Lin, Bertrand M.T. & Sterna, Malgorzata & Blazewicz, Jacek, 2022. "Two-machine flow shop scheduling with a common due date to maximize total early work," European Journal of Operational Research, Elsevier, vol. 300(2), pages 504-511.
    4. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    5. Lena Sophie Wohlert & Jürgen Zimmermann, 2024. "Resource overload problems with tardiness penalty: structural properties and solution approaches," Annals of Operations Research, Springer, vol. 338(1), pages 151-172, July.
    6. Jiang, Yiwei & Wu, Mengjing & Chen, Xin & Dong, Jianming & Cheng, T.C.E. & Blazewicz, Jacek & Ji, Min, 2024. "Online early work scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 315(3), pages 855-862.
    7. Cédric Verbeeck & Vincent Peteghem & Mario Vanhoucke & Pieter Vansteenwegen & El-Houssaine Aghezzaf, 2017. "A metaheuristic solution approach for the time-constrained project scheduling problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 353-371, March.
    8. Patrick Gerhards, 2020. "The multi-mode resource investment problem: a benchmark library and a computational study of lower and upper bounds," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(4), pages 901-933, December.
    9. Marinos Aristotelous & Andreas C. Nearchou, 2025. "h-NSDE—A Solution Algorithm for the Multi-objective Resource Leveling Problem," SN Operations Research Forum, Springer, vol. 6(1), pages 1-22, March.
    10. Hongbo Li & Linwen Zheng & Hanyu Zhu, 2023. "Resource leveling in projects with flexible structures," Annals of Operations Research, Springer, vol. 321(1), pages 311-342, February.
    11. Kreter, Stefan & Schutt, Andreas & Stuckey, Peter J. & Zimmermann, Jürgen, 2018. "Mixed-integer linear programming and constraint programming formulations for solving resource availability cost problems," European Journal of Operational Research, Elsevier, vol. 266(2), pages 472-486.
    12. Xiaofei Liu & Yajie Li & Weidong Li & Jinhua Yang, 2023. "Combinatorial approximation algorithms for the maximum bounded connected bipartition problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.
    13. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    14. Ilia Tarasov & Alain Haït & Alexander Lazarev & Olga Battaïa, 2024. "Metric estimation approach for managing uncertainty in resource leveling problem," Annals of Operations Research, Springer, vol. 338(1), pages 645-673, July.
    15. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    16. Gahm, Christian & Dünnwald, Bastian & Sahamie, Ramin, 2014. "A multi-criteria master production scheduling approach for special purpose machinery," International Journal of Production Economics, Elsevier, vol. 149(C), pages 89-101.
    17. Yunhong Min & Byung-Cheon Choi & Myoung-Ju Park & Kyung Min Kim, 2023. "A parallel-machine scheduling problem with an antithetical property to maximize total weighted early work," 4OR, Springer, vol. 21(3), pages 421-437, September.
    18. Malgorzata Sterna & Kateryna Czerniachowska, 2017. "Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 927-944, September.
    19. Xin Chen & Sergey Kovalev & Małgorzata Sterna & Jacek Błażewicz, 2021. "Mirror scheduling problems with early work and late work criteria," Journal of Scheduling, Springer, vol. 24(5), pages 483-487, October.
    20. Christian Billing & Florian Jaehn & Thomas Wensing, 2020. "Fair task allocation problem," Annals of Operations Research, Springer, vol. 284(1), pages 131-146, January.

    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:jsched:v:27:y:2024:i:6:d:10.1007_s10951-024-00822-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.