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Satisfiability tests and time‐bound adjustmentsfor cumulative scheduling problems

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  • Ph. Baptiste
  • C. Le Pape
  • W. Nuijten

Abstract

This paper presents a set of satisfiability tests and time‐bound adjustmentalgorithms that can be applied to cumulative scheduling problems. An instance of thecumulative scheduling problem (CuSP) consists of (1) one resource witha given capacity, and (2) a set of activities, each having a release date, adeadline, a processing time and a resource capacityrequirement. The problem is to decide whether there exists a start time assignment to allactivities such that at no point in time the capacity of the resource is exceeded and alltiming constraints are satisfied. The cumulative scheduling problem can be seen as a relaxationof the decision variant of the resource‐constrained project scheduling problem.We present three necessary conditions for the existence of a feasible schedule. Two ofthem are obtained by polynomial relaxations of the CuSP. The third is based on energeticreasoning. We show that the second condition is closely related to the subset bound, awell‐known lower bound of the m‐machine problem. We also present three algorithms,based on the previously mentioned necessary conditions, to adjust release dates anddeadlines of activities. These algorithms extend the time‐bound adjustment techniquesdeveloped for the one‐machine problem. They have been incorporated in a branch andbound procedure to solve the resource‐constrained project scheduling problem.Computational results are reported. Copyright Kluwer Academic Publishers 1999

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  • Ph. Baptiste & C. Le Pape & W. Nuijten, 1999. "Satisfiability tests and time‐bound adjustmentsfor cumulative scheduling problems," Annals of Operations Research, Springer, vol. 92(0), pages 305-333, January.
    • Handle: RePEc:spr:annopr:v:92:y:1999:i:0:p:305-333:10.1023/a:1018995000688
    DOI: 10.1023/A:1018995000688
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    Cited by:

    1. Xiangtong Qi & Jonathan F. Bard & Gang Yu, 2004. "Class Scheduling for Pilot Training," Operations Research, INFORMS, vol. 52(1), pages 148-162, February.
    2. Carlier, Jacques & Neron, Emmanuel, 2007. "Computing redundant resources for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1452-1463, February.
    3. Guyon, O. & Lemaire, P. & Pinson, É. & Rivreau, D., 2010. "Cut generation for an integrated employee timetabling and production scheduling problem," European Journal of Operational Research, Elsevier, vol. 201(2), pages 557-567, March.
    4. Néron, Emmanuel & Baptiste, Philippe & Gupta, Jatinder N. D., 2001. "Solving hybrid flow shop problem using energetic reasoning and global operations," Omega, Elsevier, vol. 29(6), pages 501-511, December.
    5. Roland Braune, 2022. "Packing-based branch-and-bound for discrete malleable task scheduling," Journal of Scheduling, Springer, vol. 25(6), pages 675-704, December.
    6. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.
    7. Arkhipov, Dmitry & Battaïa, Olga & Lazarev, Alexander, 2019. "An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 35-44.
    8. Thierry Petit & Emmanuel Poder, 2011. "Global propagation of side constraints for solving over-constrained problems," Annals of Operations Research, Springer, vol. 184(1), pages 295-314, April.
    9. Carlier, J. & Neron, E., 2003. "On linear lower bounds for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 149(2), pages 314-324, September.
    10. Carlier, J. & Pinson, E. & Sahli, A. & Jouglet, A., 2020. "An O(n2) algorithm for time-bound adjustments for the cumulative scheduling problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 468-476.
    11. Carlier, Jacques & Neron, Emmanuel, 2000. "A new LP-based lower bound for the cumulative scheduling problem," European Journal of Operational Research, Elsevier, vol. 127(2), pages 363-382, December.
    12. Nolz, Pamela C. & Absi, Nabil & Feillet, Dominique & Seragiotto, Clóvis, 2022. "The consistent electric-Vehicle routing problem with backhauls and charging management," European Journal of Operational Research, Elsevier, vol. 302(2), pages 700-716.

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