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Some Properties of Schedules for Large Projects with Limited Resources

Author

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  • Jerome D. Wiest

    (Graduate School of Business Administration, University of California, Los Angeles)

Abstract

The Critical Path Method, PERT, and related techniques that make use of arrow diagrams for scheduling large projects implicitly assume that unlimited resources are available for assignment to project activities. When resources are limited, however, the usual concepts of “critical path” and “job slack” basic to these methods lose their normal meaning. Jobs may be delayed by the unavailability of resources as well as by technological orderings. A scheme for analyzing project schedules in the limited resource case is developed in this paper, with the intent of preserving for the project scheduler the operational utility of the slack concept. A new procedure for calculating slack values leads to the identification of a “critical sequence” of jobs in a certain class of project schedules—a notion analogous to that of a critical path in the unlimited resource case. Some properties of project schedules when resources are limited are explored and suggestions are made for utilizing the revised concept of slack in scheduling large projects.

Suggested Citation

  • Jerome D. Wiest, 1964. "Some Properties of Schedules for Large Projects with Limited Resources," Operations Research, INFORMS, vol. 12(3), pages 395-418, June.
    • Handle: RePEc:inm:oropre:v:12:y:1964:i:3:p:395-418
    DOI: 10.1287/opre.12.3.395
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    Cited by:

    1. Wan-An Cui, 2018. "Critical Sequences and Resource Links Optimization in Resource-Constrained Project Scheduling," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-26, October.
    2. Jan Böttcher & Andreas Drexl & Rainer Kolisch & Frank Salewski, 1999. "Project Scheduling Under Partially Renewable Resource Constraints," Management Science, INFORMS, vol. 45(4), pages 543-559, April.
    3. Kolisch, Rainer & Padman, Rema, 1997. "An integrated survey of project scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 463, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Kolisch, R. & Padman, R., 2001. "An integrated survey of deterministic project scheduling," Omega, Elsevier, vol. 29(3), pages 249-272, June.
    5. Valls, Vicente & Ballestin, Francisco & Quintanilla, Sacramento, 2005. "Justification and RCPSP: A technique that pays," European Journal of Operational Research, Elsevier, vol. 165(2), pages 375-386, September.
    6. 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.
    7. Mabrouka Shahat Younis Elfargani & Ahmed Fthallh Mhmmed & Aimen Emragha Abd alati Abd allah & Abd aullah Mansor Algedo & Hamad Fryaj Hamad Amer & Youssf Tiher Abobker Hasan, 2022. "Application Of Primavera P6 Software For Scheduling Single Constrained Resource In Small Gas Station Project," Engineering Heritage Journal (GWK), Zibeline International Publishing, vol. 6(2), pages 65-72, October.
    8. Lova, Antonio & Maroto, Concepcion & Tormos, Pilar, 2000. "A multicriteria heuristic method to improve resource allocation in multiproject scheduling," European Journal of Operational Research, Elsevier, vol. 127(2), pages 408-424, December.
    9. Kyunghwan Kim, 2020. "Generalized Resource-Constrained Critical Path Method to Improve Sustainability in Construction Project Scheduling," Sustainability, MDPI, vol. 12(21), pages 1-19, October.
    10. Böttcher, Jan & Drexl, Andreas & Kolisch, Rainer & Salewski, Frank, 1996. "Project scheduling under partially renewable resource constraints," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 398, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    11. Ballestí­n, Francisco & Valls, Vicente & Quintanilla, Sacramento, 2008. "Pre-emption in resource-constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1136-1152, September.
    12. Scott E. Sampson & Elliott N. Weiss, 1993. "Local search techniques for the generalized resource constrained project scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 665-675, August.
    13. Drexl, Andreas & Kolisch, Rainer, 1994. "Model-based assembly management in machine tool manufacturing," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 346, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    14. Demeulemeester, Erik L. & Herroelen, Willy S., 1996. "An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 90(2), pages 334-348, April.
    15. W Herroelen & R Leus, 2005. "Identification and illumination of popular misconceptions about project scheduling and time buffering in a resource-constrained environment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 102-109, January.
    16. Dumez, Dorian & Tilk, Christian & Irnich, Stefan & Lehuédé, Fabien & Olkis, Katharina & Péton, Olivier, 2023. "A matheuristic for a 2-echelon vehicle routing problem with capacitated satellites and reverse flows," European Journal of Operational Research, Elsevier, vol. 305(1), pages 64-84.
    17. Sprecher, Arno & Kolisch, Rainer & Drexl, Andreas, 1993. "Semi-active, active and non-delay schedules for the resource-constrained project scheduling problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 307, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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