IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v38y2016i2d10.1007_s00291-015-0423-x.html
   My bibliography  Save this article

Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions

Author

Listed:
  • Margaux Nattaf

    (CNRS, LAAS
    Université de Toulouse, UPS)

  • Christian Artigues

    (CNRS, LAAS
    Université de Toulouse, LAAS)

  • Pierre Lopez

    (CNRS, LAAS
    Université de Toulouse, LAAS)

  • David Rivreau

    (LUNAM Université, Université Catholique de l’Ouest, LISA)

Abstract

This paper addresses a scheduling problem with a continuously divisible, cumulative and renewable resource with limited capacity. During its processing, each task consumes a part of this resource, which lies between a minimum and a maximum requirement. A task is finished when a certain amount of energy is received by it within its time window. This energy is received via the resource and an amount of resource is converted into an amount of energy with a non-decreasing and continuous function. The goal is to find a feasible schedule, which is already NP-complete, and then to minimize the resource consumption. For the case where all functions are linear, we present two new mixed-integer linear programs (MILP), as well as improvements of an existing formulation. We also present a detailed version of the adaptation of the well-known “left-shift/right-shift” satisfiability test for the cumulative constraint and the associated time-window adjustments to our problem. For this test, three ways of computing relevant intervals are described. Finally, a hybrid branch-and-bound using both the satisfiability test and the MILP is presented with a new heuristic for choosing the variable on which the branching is done. Computational experiments on randomly generated instances are reported in order to compare all of these solution methods.

Suggested Citation

  • Margaux Nattaf & Christian Artigues & Pierre Lopez & David Rivreau, 2016. "Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 459-492, March.
    • Handle: RePEc:spr:orspec:v:38:y:2016:i:2:d:10.1007_s00291-015-0423-x
    DOI: 10.1007/s00291-015-0423-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-015-0423-x
    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/s00291-015-0423-x?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. Jacek Błażewicz & Maciej Machowiak & Jan Węglarz & Mikhail Kovalyov & Denis Trystram, 2004. "Scheduling Malleable Tasks on Parallel Processors to Minimize the Makespan," Annals of Operations Research, Springer, vol. 129(1), pages 65-80, July.
    2. Fündeling, C.-U. & Trautmann, N., 2010. "A priority-rule method for project scheduling with work-content constraints," European Journal of Operational Research, Elsevier, vol. 203(3), pages 568-574, June.
    3. Artigues, Christian & Lopez, Pierre & Haït, Alain, 2013. "The energy scheduling problem: Industrial case-study and constraint propagation techniques," International Journal of Production Economics, Elsevier, vol. 143(1), pages 13-23.
    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. Aghelinejad, MohammadMohsen & Ouazene, Yassine & Yalaoui, Alice, 2019. "Complexity analysis of energy-efficient single machine scheduling problems," Operations Research Perspectives, Elsevier, vol. 6(C).
    2. Stefan Bugow & Carolin Kellenbrink, 2023. "The parcel hub scheduling problem with limited conveyor capacity and controllable unloading speeds," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(2), pages 325-357, June.
    3. Rapine, Christophe & Goisque, Guillaume & Akbalik, Ayse, 2018. "Energy-aware lot sizing problem: Complexity analysis and exact algorithms," International Journal of Production Economics, Elsevier, vol. 203(C), pages 254-263.
    4. Rainer Kolisch & Erik Demeulemeester & Rubén Ruiz Garcia & Vincent T’Kindt & Jan Węglarz, 2016. "Editorial “Project Management and Scheduling”," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 279-281, March.
    5. Ali Kordmostafapour & Javad Rezaeian & Iraj Mahdavi & Mahdi Yar Farjad, 2022. "Scheduling unrelated parallel machine problem with multi-mode processing times and batch delivery cost," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1438-1470, December.

    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. Roland Braune, 2022. "Packing-based branch-and-bound for discrete malleable task scheduling," Journal of Scheduling, Springer, vol. 25(6), pages 675-704, December.
    2. Wendi Tian & Erik Demeulemeester, 2014. "Railway scheduling reduces the expected project makespan over roadrunner scheduling in a multi-mode project scheduling environment," Annals of Operations Research, Springer, vol. 213(1), pages 271-291, February.
    3. Hajo Terbrack & Thorsten Claus & Frank Herrmann, 2021. "Energy-Oriented Production Planning in Industry: A Systematic Literature Review and Classification Scheme," Sustainability, MDPI, vol. 13(23), pages 1-32, December.
    4. Beck, Fabian G. & Biel, Konstantin & Glock, Christoph H., 2019. "Integration of energy aspects into the economic lot scheduling problem," International Journal of Production Economics, Elsevier, vol. 209(C), pages 399-410.
    5. Naber, Anulark & Kolisch, Rainer, 2014. "MIP models for resource-constrained project scheduling with flexible resource profiles," European Journal of Operational Research, Elsevier, vol. 239(2), pages 335-348.
    6. J Blazewicz & T C E Cheng & M Machowiak & C Oguz, 2011. "Berth and quay crane allocation: a moldable task scheduling model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1189-1197, July.
    7. Talla Nobibon, Fabrice & Leus, Roel & Nip, Kameng & Wang, Zhenbo, 2015. "Resource loading with time windows," European Journal of Operational Research, Elsevier, vol. 244(2), pages 404-416.
    8. Sven Schulz & Udo Buscher & Liji Shen, 2020. "Multi-objective hybrid flow shop scheduling with variable discrete production speed levels and time-of-use energy prices," Journal of Business Economics, Springer, vol. 90(9), pages 1315-1343, November.
    9. Jeunet, Jully & Bou Orm, Mayassa, 2020. "Optimizing temporary work and overtime in the Time Cost Quality Trade-off Problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 743-761.
    10. Lee, Cheng-Hsiung & Liao, Ching-Jong & Chung, Tsui-Ping, 2014. "Scheduling with multi-attribute setup times on two identical parallel machines," International Journal of Production Economics, Elsevier, vol. 153(C), pages 130-138.
    11. Mick Van Den Eeckhout & Broos Maenhout & Mario Vanhoucke, 2020. "Mode generation rules to define activity flexibility for the integrated project staffing problem with discrete time/resource trade-offs," Annals of Operations Research, Springer, vol. 292(1), pages 133-160, September.
    12. Tritschler, Martin & Naber, Anulark & Kolisch, Rainer, 2017. "A hybrid metaheuristic for resource-constrained project scheduling with flexible resource profiles," European Journal of Operational Research, Elsevier, vol. 262(1), pages 262-273.
    13. Liu, Ying & Dong, Haibo & Lohse, Niels & Petrovic, Sanja, 2016. "A multi-objective genetic algorithm for optimisation of energy consumption and shop floor production performance," International Journal of Production Economics, Elsevier, vol. 179(C), pages 259-272.
    14. Guopeng Song & Tamás Kis & Roel Leus, 2021. "Polyhedral Results and Branch-and-Cut for the Resource Loading Problem," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 105-119, January.
    15. Bahram Alidaee & Haibo Wang & R. Bryan Kethley & Frank Landram, 2019. "A unified view of parallel machine scheduling with interdependent processing rates," Journal of Scheduling, Springer, vol. 22(5), pages 499-515, October.
    16. Emde, Simon & Gendreau, Michel, 2017. "Scheduling in-house transport vehicles to feed parts to automotive assembly lines," European Journal of Operational Research, Elsevier, vol. 260(1), pages 255-267.
    17. Artigues, Christian & Lopez, Pierre & Haït, Alain, 2013. "The energy scheduling problem: Industrial case-study and constraint propagation techniques," International Journal of Production Economics, Elsevier, vol. 143(1), pages 13-23.
    18. Ben Issa, Samer & Patterson, Raymond A. & Tu, Yiliu, 2021. "Solving resource-constrained multi-project environment under different activity assumptions," International Journal of Production Economics, Elsevier, vol. 232(C).
    19. Xiangxin An & Guojin Si & Tangbin Xia & Qinming Liu & Yaping Li & Rui Miao, 2022. "Operation and Maintenance Optimization for Manufacturing Systems with Energy Management," Energies, MDPI, vol. 15(19), pages 1-19, October.
    20. Roland Braune & Karl F. Doerner, 2017. "Real-world flexible resource profile scheduling with multiple criteria: learning scalarization functions for MIP and heuristic approaches," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(8), pages 952-972, August.

    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:orspec:v:38:y:2016:i:2:d:10.1007_s00291-015-0423-x. 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.