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Solving Resource-Constrained Network Problems by Implicit Enumeration—Nonpreemptive Case

Author

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  • Linus Schrage

    (University of Chicago, Chicago, Illinois)

Abstract

This paper considers a scheduling problem that has both precedence constraints (of a general form as in PERT-CPM problems) and resource constraints (of the form in the general job-shop scheduling problem), and gives an efficient enumerative procedure for generating all active schedules for this problem. Based on this enumerative scheme, the paper describes a branch-and-bound method for implicitly enumerating all schedules and determining the optimum; finally, it gives computational experience for the problem where the objective is minimizing the project makespan.

Suggested Citation

  • Linus Schrage, 1970. "Solving Resource-Constrained Network Problems by Implicit Enumeration—Nonpreemptive Case," Operations Research, INFORMS, vol. 18(2), pages 263-278, April.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:2:p:263-278
    DOI: 10.1287/opre.18.2.263
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    Cited by:

    1. Susana Fernandes & Helena Ramalhinho-Lourenço, 2007. "A simple optimised search heuristic for the job-shop scheduling problem," Economics Working Papers 1050, Department of Economics and Business, Universitat Pompeu Fabra.
    2. V. Jorge Leon & S. David Wu, 1992. "On scheduling with ready‐times, due‐dates and vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(1), pages 53-65, February.
    3. Kolisch, R. & Padman, R., 2001. "An integrated survey of deterministic project scheduling," Omega, Elsevier, vol. 29(3), pages 249-272, June.
    4. Colin E. Bell & Kwangho Park, 1990. "Solving resource‐constrained project scheduling problems by a* search," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(1), pages 61-84, February.
    5. Sprecher, Arno & Kolisch, Rainer & Drexl, Andreas, 1995. "Semi-active, active, and non-delay schedules for the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 94-102, January.
    6. Alexander A. Lazarev & Nikolay Pravdivets & Frank Werner, 2020. "On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
    7. 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.
    8. Abdollah Arasteh, 2020. "Considering Project Management Activities for Engineering Design Groups," SN Operations Research Forum, Springer, vol. 1(4), pages 1-29, December.
    9. Elmaghraby, Salah E., 1995. "Activity nets: A guided tour through some recent developments," European Journal of Operational Research, Elsevier, vol. 82(3), pages 383-408, May.
    10. Sadykov, Ruslan, 2008. "A branch-and-check algorithm for minimizing the weighted number of late jobs on a single machine with release dates," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1284-1304, September.
    11. 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.
    12. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.

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