Multi-resource allocation in stochastic project scheduling
We propose a resource allocation model for project scheduling. Our model accommodates multiple resources and decision-dependent activity durations inspired by microeconomic theory. First, we elaborate a deterministic problem formulation. In a second stage, we enhance this model to account for uncertain problem parameters. Assuming that the first and second moments of these parameters are known, the stochastic model minimises an approximation of the value-at-risk of the project makespan. As a salient feature, our approach employs a scenario-free formulation which is based on normal approximations of the activity path durations. We extend our model to situations in which the moments of the random parameters are ambiguous and describe an iterative solution procedure. Extensive numerical results are provided.
KeywordsResource allocation problem Project scheduling Value-at-risk
Unable to display preview. Download preview PDF.
- Demeulemeester, E. L., & Herroelen, W. S. (2002). Project scheduling—a research handbook. Dordrecht: Kluwer Academic. Google Scholar
- Eppstein, D. (1994). Finding the k shortest paths. In IEEE symposium on foundations of computer science (pp. 154–165). Google Scholar
- Horst, R., Pardalos, P. M., & Thoai, N. V. (2000). Introduction to global optimization (2nd ed.). Dordrecht: Kluwer Academic. Google Scholar
- Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory. London: Oxford University Press. Google Scholar
- Neumann, K. (1999). Scheduling of projects with stochastic evolution structure. In J. Weglarz (Ed.), Project scheduling: recent models, algorithms, and applications (pp. 309–332). Dordrecht: Kluwer Academic. Google Scholar
- Petrov, V. V. (1975). Sums of independent random variables. Berlin: Springer. Google Scholar
- Prékopa, A. (1995). Stochastic programming. Dordrecht: Kluwer Academic. Google Scholar
- Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21–41. Google Scholar
- Zhu, S.-S., & Fukushima, M. (2006). Worst-case conditional value-at-risk with application to robust portfolio management (Working Paper). Google Scholar