Abstract
We consider an extension of the classical resource-constrained project scheduling problem (RCPSP), which covers discrete resource-resource and time-resource tradeoffs. As a result a project scheduler is permitted to identify several alternatives or modes of accomplishment for each activity of the project. The solution procedure to be presented is a considerable generalization of the branch-and-bound algorithm proposed by Demeulemeester and Herroelen, which is currently the most powerful method for optimally solving the RCPSP. More precisely, we extend their concept of delay alternatives by introducing mode alternatives. The basic enumeration scheme is enhanced by dominance rules which increase the performance of the algorithm. We then report on our computational results obtained from the comparison with the most rapid procedure reported in the literature.
Zusammenfassung
Wir betrachten eine Erweiterung des klassischen Resource-Constrained Project Scheduling Problems (RCPSP), die die Abbildung von Ressourcen-Ressourcen- und Zeit-Ressourcen-Tradeoffs ermöglicht. Damit ist der Projektplaner in der Lage, für jeden Vorgang des Projekts mehrere Ausführungsalternativen (Modi) anzugeben. Der von uns vorgestellte Algorithmus ist eine Verallgemeinerung des derzeit schnellsten Branch-and-Bound-Verfahrens für das RCPSP von Demeulemeester und Herroelen. Wir erweitern deren Konzept der Delay-Alternativen um sogenannte Modus-Alternativen. Die Enumeration wird mit Hilfe von Dominanzregeln beschleunigt. Schließlich fassen wir unsere Rechenergebnise zusammen, in denen wir unser Verfahren mit dem derzeit schnellsten aus der Literatur bekannten Algorithmus vergleichen.
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References
Bartusch M, Möhring RH, Radermacher, FJ (1988) Scheduling project networks with resource constraints and time windows. Ann Oper Res 16:201–240
Boctor FF (1993) Heuristics for scheduling projects with resource restrictions and several resource-duration modes. Int J Prod Res 31:2547–2558
Brucker P, Schoo A, Thiele O (1996) A branch-and-bound algorithm for the resource-constrained project scheduling problem. Osnabrücker Schriften zur Mathematik, No. 178, University of Osnabrück, Germany
Christofides N, Alvarez-Valdes R, Tamarit JM (1987) Project scheduling with resource constraints: A branch and bound approach. Eur J Oper Res 29:262–273
Demeulemeester E (1992) Optimal algorithms for various classes of multiple resource-constrained project scheduling problems. PhD Dissertation, Katholieke Universiteit Leuven, Belgium
Demeulemeester E, Herroelen W (1992) A branch-and-bound procedure for the multiple resource-constrained project scheduling problem. Manag Sci 38:1803–1818
Drexl A (1991) Scheduling of project networks by job assignment. Manag Sci 37:1590–1602
French S (1982) Sequencing and scheduling: An introduction to the mathematics of the job-shop. Wiley, New York
Garey MR, Johnson DS (1979) Computers and intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA
Hartmann S, Sprecher A (1996) A note on “Hierarchical models for multi-project planning and scheduling”. Europ J Oper Res 94:377–383
Kolisch R (1995) Project scheduling under resource constraints — Efficient heuristics for several problem classes. Physica, Heidelberg
Kolisch R, Sprecher A, Drexl A (1995) Characterization and generation of a general class of resource-constrained project scheduling problems. Manag Sci 41, No. 11
Mingozzi A, Maniezzo V, Ricciardelli S, Bianco L (1994) An exact algorithm for project scheduling with resource constraints based on a new mathematical formulation. University of Bologna, Department of Mathematics, Technical Report No. 32, Bologna
Patterson JH, Slowinski R, Talbot FB, Weglarz J (1989) An algorithm for a general class of precedence and resource constrained scheduling problems. In: Slowinski R, Weglarz J (eds.): Advances in project scheduling. Elsevier, Amsterdam, pp. 3–28
Radermacher FJ (1985/86) Scheduling of project networks. Ann Oper Res 4:227–252
Schräge L (1971) Solving resource-constrained network problems by implicit enumeration — nonpreemptive case. Oper Res 18:263–278
Slowinski R (1980) Two approaches to problems of resource allocation among project activities: A comparative study. J Oper Res Soc 31:711–723
Speranza MG, Vercellis C (1993) Hierarchical models for multiproject planning and scheduling. Europ J Oper Res 64:312–325
Sprecher A (1994) Resource-constrained project scheduling: Exact methods for the multi-mode case. Lecture Notes in Economics and Mathematical Systems, Vol. 409, Springer, Berlin et al.
Sprecher A, Hartmann S, Drexl A (1994) Project scheduling with discrete time-resource and resource-resource tradeoffs. Manuskripte aus den Instituten für Betriebswirtschaftslehre, No. 357, University of Kiel, Germany
Sprecher A, Kolisch R, Drexl A (1995) Semi-active, active and non-delay schedules for the resource-constrained project scheduling problem. Europ J Oper Res 80:94–102
Stinson JP, Davis EW, Khumawala BM (1978) Multiple resourceconstrained scheduling using branch and bound. AIIE Trans 10:252–259
Talbot FB (1982) Resource-constrained project scheduling with time-resource tradeoffs: The nonpreemptive case. Manag Sci 28:1197–1210
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Sprecher, A., Hartmann, S. & Drexl, A. An exact algorithm for project scheduling with multiple modes. OR Spektrum 19, 195–203 (1997). https://doi.org/10.1007/BF01545587
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DOI: https://doi.org/10.1007/BF01545587
Key words
- Project management/scheduling
- discrete resource-resource and time-resource tradeoffs
- mode and delay alternatives
- branch-and-bound
- dominance rules
- computational results