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Project Scheduling with Continuously-Divisible, Doubly Constrained Resources

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  • Jan Weogon glarz

    (Technical University of Poznan, Poland)

Abstract

This paper deals with a class of project scheduling problems concerning the allocation of continuously divisible resources under conditions in which both total usage at every moment and total consumption over the period of project duration are constrained. Typical examples of such resources, called doubly constrained, are money or energy, when the constraint on power or the rate of expenditure cannot be ignored as neither, of course, can. the constraint on resource consumption. Also manpower must often be considered as a doubly constrained resource. Mathematical models of project activities in which performing speeds are continuous functions of resource amounts are considered. The objective is a schedule which minimizes project duration. Thus, the problems considered are generalizations of both the classical project scheduling problem and the time-cost trade-off problem. The properties of optimal schedules are given for strictly concave, concave and convex activity models. On the basis of these properties, methods for finding optimal schedules are described for independent and dependent activities. We also consider the minimum resource consumption ensuring minimum project duration for a given level of resource usage, and the minimum level of resource usage ensuring minimum project duration for a given level of resource consumption. Possible generalizations of the presented results are indicated.

Suggested Citation

  • Jan Weogon glarz, 1981. "Project Scheduling with Continuously-Divisible, Doubly Constrained Resources," Management Science, INFORMS, vol. 27(9), pages 1040-1053, September.
  • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:9:p:1040-1053
    DOI: 10.1287/mnsc.27.9.1040
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    Citations

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    Cited by:

    1. Shewchuk, John P. & Chang, T. C., 1995. "Resource-constrained job scheduling with recyclable resources," European Journal of Operational Research, Elsevier, vol. 81(2), pages 364-375, March.
    2. Joanna Józefowska & Mariusz Nowak & Rafał Różycki & Grzegorz Waligóra, 2022. "Survey on Optimization Models for Energy-Efficient Computing Systems," Energies, MDPI, vol. 15(22), pages 1-20, November.
    3. Azaron, Amir & Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Memariani, Azizollah, 2006. "A multi-objective resource allocation problem in PERT networks," European Journal of Operational Research, Elsevier, vol. 172(3), pages 838-854, August.
    4. Weglarz, Jan & Józefowska, Joanna & Mika, Marek & Waligóra, Grzegorz, 2011. "Project scheduling with finite or infinite number of activity processing modes - A survey," European Journal of Operational Research, Elsevier, vol. 208(3), pages 177-205, February.
    5. Amir Azaron & Hideki Katagiri & Masatoshi Sakawa, 2007. "Time-cost trade-off via optimal control theory in Markov PERT networks," Annals of Operations Research, Springer, vol. 150(1), pages 47-64, March.
    6. Kogan, Konstantin, 2006. "Optimal scheduling of parallel machines with constrained resources," European Journal of Operational Research, Elsevier, vol. 170(3), pages 771-787, May.
    7. R. Różycki & J. Węglarz, 2014. "Power-aware scheduling of preemptable jobs on identical parallel processors to minimize makespan," Annals of Operations Research, Springer, vol. 213(1), pages 235-252, February.
    8. 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.
    9. Drexl, Andreas & Grünewald, Jürgen, 1989. "Nonpreemptive multi-mode resource-constrained project scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 236, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    10. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    11. Azaron, Amir & Tavakkoli-Moghaddam, Reza, 2007. "Multi-objective time-cost trade-off in dynamic PERT networks using an interactive approach," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1186-1200, August.
    12. Kogan, Konstantin & Shtub, Avraham, 1999. "Scheduling projects with variable-intensity activities: The case of dynamic earliness and tardiness costs," European Journal of Operational Research, Elsevier, vol. 118(1), pages 65-80, October.
    13. Różycki, R. & Węglarz, J., 2012. "Power-aware scheduling of preemptable jobs on identical parallel processors to meet deadlines," European Journal of Operational Research, Elsevier, vol. 218(1), pages 68-75.
    14. Tavares, L. V., 2002. "A review of the contribution of Operational Research to Project Management," European Journal of Operational Research, Elsevier, vol. 136(1), pages 1-18, January.
    15. Hua Wang & Jon Dieringer & Steve Guntz & Shankarraman Vaidyaraman & Shekhar Viswanath & Nikolaos H. Lappas & Sal Garcia-Munoz & Chrysanthos E. Gounaris, 2021. "Portfolio-Wide Optimization of Pharmaceutical R&D Activities Using Mathematical Programming," Interfaces, INFORMS, vol. 51(4), pages 262-279, July.
    16. 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.
    17. 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.
    18. 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.
    19. Jozefowska, Joanna & Weglarz, Jan, 1998. "On a methodology for discrete-continuous scheduling," European Journal of Operational Research, Elsevier, vol. 107(2), pages 338-353, June.

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