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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. Aghelinejad, MohammadMohsen & Ouazene, Yassine & Yalaoui, Alice, 2019. "Complexity analysis of energy-efficient single machine scheduling problems," Operations Research Perspectives, Elsevier, vol. 6(C).
    4. 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.
    5. 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.

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