Abstract
We present a project scheduling problem subject to general temporal constraints where the utilization of a set of renewable resources has to be smoothed over time. For solving the NP-hard optimization problem, we point out some important structural properties and introduce a new enumeration scheme. Combining this enumeration scheme with some branch-and-bound techniques, we propose an appropriate solution procedure for the project scheduling problem at hand. To outline the practical importance of resource levelling, we sketch exemplary the optimization of mid-term planning schedules with regard to the resource requirements of IT projects. Finally, we present results from a comprehensive computational study on problem instances of the well-known rlp_j10 and rlp_j20 test sets devised by Kolisch et al. (Benchmark Instances for Project Scheduling Problems, Kluwer, Boston, 1999).
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References
Ahuja, H. (1976). Construction performance control by networks. New York: John Wiley and Sons.
Ahuja, R., Magnanti, T., & Orlin, J. (1993). Network flows. Englewood Cliffs: Prentice Hall.
Ballestin, F., Schwindt, C., & Zimmermann, J. (2007). Resource leveling in make-to-order production: modeling and heuristic solution method. International Journal of Operations Research, 4, 50–62.
Bandelloni, M., Tucci, M., & Rinaldi, R. (1994). Optimal resource leveling using non-serial dynamic programming. European Journal of Operations Research, 78, 162–178.
Burgess, A., & Killebrew, J. (1962). Variation in activity level on a cyclical arrow diagram. Journal of Industrial Engineering, 13(2), 76–83.
Easa, S. (1989). Resource leveling in construction by optimization. Journal of Construction Engineering and Management, 115(2), 302–316.
Engelhardt, H., & Zimmermann, J. (1998). Lower bounds and exact methods for resource levelling problems. Report WIOR 517, University of Karlsruhe.
Franck, B., Neumann, K., & Schwindt, C. (2001). Truncated branch-and-bound, schedule construction, and schedule improvement procedures for resource-constrained project scheduling. OR Spektrum, 23, 297–324.
Gabow, H., & Myers, E. (1978). Finding all spanning trees of directed and undirected graphs. SIAM Journal on Computing, 7, 280–287.
Galbreath, R. (1965). Computer program for leveling resource usage. Journal of the Construction Division, 91(1), 107–124.
Harris, R. (1978). Precedence and arrow networks for construction. New York: John Wiley and Sons.
Harris, R. (1990). Packing method for resource leveling (pack). Journal of Construction Engineering and Management, 116, 39–43.
Kolisch, R., Schwindt, C., & Sprecher, A. (1999). Benchmark instances for project scheduling problems. In J. Węglarz (Ed.), Project scheduling: recent models, algorithms and applications. Boston: Kluwer Academic.
Neumann, K., & Zimmermann, J. (2000). Procedures for resource levelling and net present value problems in project scheduling with general temporal and resource constraints. European Journal of Operations Research, 127, 425–443.
Neumann, K., Nübel, H., & Schwindt, C. (2000). Active and stable project scheduling. Mathematical Methods of Operations Research, 52, 441–465.
Neumann, K., Schwindt, C., & Zimmermann, J. (2003). Project scheduling with time windows and scarce resources. Berlin: Springer.
Nübel, H. (1999). Minimierung der Ressourcenkosten für Projekte mit planungsabhängigen Zeitfenstern. Wiesbaden: Gabler.
Nübel, H. (2001). The resource renting problem subject to temporal constraints. OR Spektrum, 23, 359–381.
Petrovic, R. (1969). On optimization of resource leveling in project plans. In H. J. Lombaers (Ed.), Project planning by network analysis: proceedings of the 2nd international congress (pp. 268–273). Amsterdam: North-Holland.
Roy, B. (1964). Les problemes d ordonnancement. Paris: Dunod.
Wiest, J., & Levy, F. (1977). A management guide to PERT/CPM. Englewood Cliffs: Prentice Hall.
Zimmermann, J. (2001). Ablauforientiertes Projektmanagement: Modelle, Verfahren und Anwendungen. Wiesbaden: Gabler.
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Gather, T., Zimmermann, J. & Bartels, JH. Exact methods for the resource levelling problem. J Sched 14, 557–569 (2011). https://doi.org/10.1007/s10951-010-0207-8
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DOI: https://doi.org/10.1007/s10951-010-0207-8