Abstract
Managers of projects and multi-project programs often face considerable uncertainty in the duration and outcomes of specific tasks, as well as in the overall level of resources required by tasks. They must decide, in these uncertain conditions, how to allocate and manage scarce resources across many projects that have competing needs. This paper develops a nonlinear mixed-integer programming model for optimizing the resource allocations to individual tasks to minimize the completion times of a collection of projects. The model contains a very flexible representation of the effects of changing resource allocations on the probability distribution of task duration, so it can accommodate a wide variety of practical situations. A heuristic solution procedure is proposed that works quite effectively. An illustration involving a collection of bridge construction projects is provided.
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Bertsekas, D., J.N. Tsitsiklis, and C. Wu. (1998). “Rollout Algorithms for Combinatorial Optimization.” Journal of Heuristics 3, 245–262.
Brucker, P., A. Drexel, R. Möhring, K. Neumann, and E. Pesch. (1999). “Resource-Constrained Project Scheduling: Notation, Classification, Models, and Methods.” European Journal of Operational Research 112, 3–41.
Burt, J.M. (1977). “Planning and Dynamic Control of Projects under Uncertainty.” Management Science 24, 249–258.
Fendley, L.G. (1968). “Towards the Development of a Complete Multi-Project Scheduling System.” Journal of Industrial Engineering 19, 505–515.
Gerchak, Y. (2000). “On the Allocation of Uncertainty-Reduction Effort to Minimize Total Variability.” IIE Transactions 32, 403–407.
Golenko-Ginzburg, D. and A. Gonik. (1997). “Stochastic Network Project Scheduling with Non-Con-sumable Limited Resources.” International Journal of Production Economics 48, 29–37.
Gutjahr, W.J., C. Strauss, and E. Wagner. (2000). “A Stochastic Branch-and-Bound Approach to Activity Crashing in Project Management.” INFORMS Journal on Computing 12, 125–135.
Kolisch, R. and A. Sprecher. (1996). “PSLIB-A Project Scheduling Problem Library.” European Journal of Operational Research 96, 205–216.
Kurtulus, I.S. and E.W. Davis. (1982). “Multi-Project Scheduling: Categorization of Heuristic Rules Per-formance.” Management Science 28, 161–172.
Kurtulus, I.S. and S.C. Narula. (1985). “Multi-Project Scheduling: Analysis of Project Performance.” IIE Transactions 17, 58–66.
Leu, S.-S., A.-T. Chen, and C.-H. Yang. (2001). “A GA-Based Fuzzy Optimal Model for Construction Time-Cost Trade-off.” International Journal of Project Management 19, 47–58.
Lova, A., C. Maroto, and P. Tormos. (2000). “A Multicriteria Heuristic Method to Improve Resource Allo-cation in Multiproject Scheduling.” European Journal of Operational Research 127, 408–424.
Lu, M. and S.M. AbouRizk. (2000). “Simplified CPM/PERT Simulation Model.” Journal of Construction Engineering and Management 126, 219–226.
Möhring, R.H., F.J. Radermacher, and G. Weiss. (1984). “Stochastic Scheduling Problems I-General Strategies.” Zeitschrift für Operations Research 28, 193–260.
Möhring, R.H., F.J. Radermacher, and G. Weiss. (1985). “Stochastic Scheduling Problems II-General Strategies.” Zeitschrift für Operations Research 29, 65–104.
Özdamar, L. and E. Alanya. (2001). “Uncertainty Modelling in Software Development Projects (with Case Study).” Annals of Operations Research 102, 157–178.
Özdamar, L. and G. Ulusoy. (1995). “A Survey on the Resource Constrained Project Scheduling Problem.” IIE Transactions 27, 574–586.
Pritsker, A., C. Sigal, and R. Hammesfahr. (1989). SLAM II Network Models for Decision Support. Engle-wood Cliffs, NJ: Prentice Hall.
Tsai, Y. and D. Gemmill. (1998). “Using Tabu Search to Schedule Activities of Stochastic Resource-Constrained Projects.” European Journal of Operational Research 111, 129–141.
van Dorp, J.R. and M.R. Duffey. (1999). “Statistical Dependence in Risk Analysis for Project Networks Using Monte Carlo Methods.” International Journal of Production Economics 58, 17–29.
Yamín, R. and D. Harmelink. (2001). “Comparision of Linear Scheduling Model (LSM) and Critical Path Method (CPM).” Journal of Construction Engineering and Management 127, 374–381.
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Nozick, L.K., Turnquist, M.A. & Xu, N. Managing Portfolios of Projects under Uncertainty. Ann Oper Res 132, 243–256 (2004). https://doi.org/10.1023/B:ANOR.0000045285.12058.03
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DOI: https://doi.org/10.1023/B:ANOR.0000045285.12058.03