New strategies for stochastic resource-constrained project scheduling

Abstract

We study the stochastic resource-constrained project scheduling problem or SRCPSP, where project activities have stochastic durations. A solution is a scheduling policy, and we propose a new class of policies that is a generalization of most of the classes described in the literature. A policy in this new class makes a number of a priori decisions in a preprocessing phase, while the remaining scheduling decisions are made online. A two-phase local search algorithm is proposed to optimize within the class. Our computational results show that the algorithm has been efficiently tuned toward finding high-quality solutions and that it outperforms all existing algorithms for large instances. The results also indicate that the optimality gap even within the larger class of elementary policies is very small.

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References

  1. Al-Bahar, J. F., & Crandall, K. C. (1990). Systematic risk management approach for construction projects. Journal of Construction Engineering and Management, 116, 533–546.

    Article  Google Scholar 

  2. Artigues, C., Leus, R., & Talla Nobibon, F. (2013). Robust optimization for resource-constrained project scheduling with uncertain activity durations. Flexible Services and Manufacturing Journal, 25(1–2), 175–205.

    Article  Google Scholar 

  3. Ashtiani, B., Leus, R., & Aryanezhad, M. (2011). New competitive results for the stochastic resource-constrained project scheduling problem: Exploring the benefits of pre-processing. Journal of Scheduling, 14(2), 157–171.

    Article  Google Scholar 

  4. Ballestín, F. (2007). When it is worthwhile to work with the stochastic RCPSP? Journal of Scheduling, 10(3), 153–166.

    Article  Google Scholar 

  5. Ballestín, F., & Leus, R. (2009). Resource-constrained project scheduling for timely project completion with stochastic activity durations. Production and Operations Management, 18, 459–474.

    Article  Google Scholar 

  6. Bendavid, I., & Golany, B. (2011). Predetermined intervals for start times of activities in the stochastic project scheduling problem. Annals of Operations Research, 186, 429–442.

    Article  Google Scholar 

  7. Bianchi, L., Dorigo, M., Gambardella, L. M., & Gutjahr, W. J. (2009). A survey on metaheuristics for stochastic combinatorial optimization. Natural Computing, 8(2), 239–287.

    Article  Google Scholar 

  8. Blazewicz, J., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1983). Scheduling subject to resource constraints. Discrete Applied Mathematics, 5, 11–24.

    Article  Google Scholar 

  9. Bruni, M. E., Beraldi, P., Guerriero, F., & Pinto, E. (2011). A heuristic approach for resource constrained project scheduling with uncertain activity durations. Computers & Operations Research, 38, 1305–1318.

    Article  Google Scholar 

  10. Buss, A. H., & Rosenblatt, M. J. (1997). Activity delay in stochastic project networks. Operations Research, 45(1), 126–139.

    Article  Google Scholar 

  11. Chapman, C., & Ward, S. (2000). Estimation and evaluation of uncertainty: A minimalist first pass approach. International Journal of Project Management, 18, 369–383.

    Article  Google Scholar 

  12. Chtourou, H., & Haouari, M. (2008). A two-stage-priority-rule-based algorithm for robust resource-constrained project scheduling. Computers & Industrial Engineering, 55, 183–194.

    Article  Google Scholar 

  13. Creemers, S. (2015). Minimizing the expected makespan of a project with stochastic activity durations under resource constraints. Journal of Scheduling, 18(3), 263–273.

    Article  Google Scholar 

  14. Creemers, S., Leus, R., & Lambrecht, M. (2010). Scheduling Markovian PERT networks to maximize the net present value. Operations Research Letters, 38(1), 51–56.

    Article  Google Scholar 

  15. Dawood, N. (1998). Estimating project and activity duration: A risk management approach using network analysis. Construction Management and Economics, 16, 41–48.

    Article  Google Scholar 

  16. Deblaere, F. (2010). Resource constrained project scheduling under uncertainty. Ph.D. thesis, Department of Applied Economics, KU Leuven, Belgium.

  17. Deblaere, F., Demeulemeester, E., & Herroelen, W. (2011). Proactive policies for the stochastic resource-constrained project scheduling problem. European Journal of Operational Research, 214(2), 308–316.

    Article  Google Scholar 

  18. Demeulemeester, E., & Herroelen, W. (2002). Project scheduling: A research handbook. Boston: Kluwer Academic Publishers.

    Google Scholar 

  19. Escudero, L. F., Kamesam, P. V., King, A. J., & Wets, R. J. B. (1993). Production planning via scenario modelling. Annals of Operations Research, 43, 311–335.

    Google Scholar 

  20. Fang, C., Kolisch, R., Wang, L., & Mu, C. (2015). An estimation of distribution algorithm and new computational results for the stochastic resource-constrained project scheduling problem. Flexible Services and Manufacturing Journal, 27(4), 585–605.

    Article  Google Scholar 

  21. Feo, T. A., & Resende, M. G. C. (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization, 6(2), 109–133.

    Article  Google Scholar 

  22. Fernandez, A. A., Armacost, R. L., & Pet-Edwards, J. (1996). The role of the non-anticipativity constraint in commercial software for stochastic project scheduling. Computers and Industrial Engineering, 31, 233–236.

    Article  Google Scholar 

  23. Fernandez, A. A., Armacost, R. L., & Pet-Edwards, J. (1998). Understanding simulation solutions to resource constrained project scheduling problems with stochastic task durations. Engineering Management Journal, 10, 5–13.

    Article  Google Scholar 

  24. Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley.

    Google Scholar 

  25. Graham, R. L. (1966). Bounds on multiprocessing timing anomalies. Bell System Technical Journal, 45, 1563–1581.

    Article  Google Scholar 

  26. Hartmann, S., & Kolisch, R. (2000). Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem. European Journal of Operational Research, 127, 394–407.

    Article  Google Scholar 

  27. Holland, H. J. (1975). Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press.

    Google Scholar 

  28. Igelmund, G., & Radermacher, F. J. (1983). Preselective strategies for the optimization of stochastic project networks under resource constraints. Networks, 13, 1–28.

    Article  Google Scholar 

  29. Kolisch, R. (1996a). Efficient priority rules for the resource-constrained project scheduling problem. Journal of Operations Management, 14, 172–192.

    Article  Google Scholar 

  30. Kolisch, R. (1996b). Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation. European Journal of Operational Research, 90, 320–333.

    Article  Google Scholar 

  31. Kolisch, R., & Sprecher, A. (1996). PSPLIB—A project scheduling problem library. European Journal of Operational Research, 96, 205–216.

    Article  Google Scholar 

  32. Kulkarni, V. G., & Adlakha, V. G. (1986). Markov and Markov-regenerative PERT networks. Operations Research, 34(5), 769–781.

    Article  Google Scholar 

  33. Lambrechts, O. (2007). Robust project scheduling subject to resource breakdowns. Ph.D. thesis, KU Leuven, Belgium.

  34. Leus, R. (2003). The generation of stable project plans. Ph.D. thesis, Department of Applied Economics, KU Leuven, Belgium.

  35. Leus, R., & Herroelen, W. (2004). Stability and resource allocation in project planning. IIE Transactions, 36(7), 667–682.

    Article  Google Scholar 

  36. Li, H., & Womer, N. K. (2015). Solving stochastic resource-constrained project scheduling problems by closed-loop approximate dynamic programming. European Journal of Operational Research, 246(1), 20–33.

    Article  Google Scholar 

  37. Li, K. Y., & Willis, R. J. (1992). An iterative scheduling technique for resource-constrained project scheduling. European Journal of Operational Research, 56, 370–379.

    Article  Google Scholar 

  38. Malcolm, D. G., Rosenbloom, J. M., Clark, C. E., & Fazar, W. (1959). Application of a technique for research and development program evaluation. Operations Research, 7, 646–669.

    Article  Google Scholar 

  39. Möhring, R. H. (2000). Scheduling under uncertainty: Optimizing against a randomizing adversary. In Lecture Notes in Computer Science (Vol. 1913/2000), pp. 651–670.

  40. Möhring, R. H., & Radermacher, F. J. (1989). The order-theoretic approach to scheduling: The stochastic case. In R. Slowinski, J. Weglarz (Eds.), Advances in Project Scheduling, chapter III.4. Elsevier.

  41. Möhring, R., Radermacher, F., & Weiss, G. (1984). Stochastic scheduling problems I—General strategies. ZOR: Zeitschrift für Operations Research, 28, 193–260.

    Google Scholar 

  42. Neumann, K., Schwindt, C., & Zimmermann, J. (2006). Project scheduling with time windows. Berlin: Springer.

    Google Scholar 

  43. Özdamar, L., & Ulusoy, G. (1996). A note on an iterative forward/backward scheduling technique with reference to a procedure by Li and Willis. European Journal of Operational Research, 89, 400–407.

    Article  Google Scholar 

  44. Pinedo, M. L. (2008). Scheduling: Theory, algorithms, and systems. Berlin: Springer.

    Google Scholar 

  45. Project Management Institute. (2013). A guide to the project management body of knowledge (PMBOK \(^{\textregistered }\) Guide). Project Management Institute Inc.

  46. Radermacher, F. J. (1981). Cost-dependent essential systems of ES-strategies for stochastic scheduling problems. Methods of Operations Research, 42, 17–31.

    Google Scholar 

  47. Radermacher, F. J. (1985). Scheduling of project networks. Annals of Operations Research, 4, 227–252.

    Article  Google Scholar 

  48. Radermacher, F. J. (1986). Analytical vs. combinatorial characterizations of well-behaved strategies in stochastic scheduling. Methods of Operations Research, 53, 467–475.

    Google Scholar 

  49. Rockafellar, R. T., & Wets, R. J. B. (1991). Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16, 119–147.

    Article  Google Scholar 

  50. Saliby, E. (1990). Descriptive sampling: A better approach to Monte Carlo simulation. Journal of the Operational Research Society, 41, 1133–1142.

    Article  Google Scholar 

  51. Schatteman, D., Herroelen, W., Van de Vonder, S., & Boone, A. (2008). A methodology for integrated risk management and proactive scheduling of construction projects. Journal of Construction Engineering and Management, 134, 885–893.

  52. Shtub, A., Bard, J. F., & Globerson, S. (2005). Project management: Processes, methodologies, and economics. New Jersey: Pearson Prentice Hall.

    Google Scholar 

  53. Sprecher, A. (2000). Scheduling resource-constrained projects competitively at modest memory requirements. Management Science, 46, 710–723.

    Article  Google Scholar 

  54. Stork, F. (2001). Stochastic resource-constrained project scheduling. Ph.D. thesis, Technische Universität Berlin.

  55. Valls, V., Ballestín, F., & Quintanilla, S. (2005). Justification and RCPSP: A technique that pays. European Journal of Operational Research, 165, 375–386.

    Article  Google Scholar 

  56. Van de Vonder, S., Demeulemeester, E., & Herroelen, W. (2008). Proactive heuristic procedures for robust project scheduling: An experimental analysis. European Journal of Operational Research, 189(3), 723–733.

    Article  Google Scholar 

  57. Van de Vonder, S., Demeulemeester, E., Herroelen, W., & Leus, R. (2005). The use of buffers in project management: The trade-off between stability and makespan. International Journal of Production Economics, 97, 227–240.

    Article  Google Scholar 

  58. Wang, J. (2004). A fuzzy robust scheduling approach for product development projects. European Journal of Operational Research, 152, 180–194.

    Article  Google Scholar 

  59. Wets, R. J. B. (1989). The aggregation principle in scenario analysis and stochastic optimization, volume F51 of Nato ASI Series (pp. 91–113). Springer.

  60. Yu, G., & Qi, X. (2004). Disruption management—Framework, models and applications. New Jersey: World Scientific.

    Google Scholar 

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Correspondence to Roel Leus.

Appendix: Exact evaluation of GP-policies for exponential distributions

Appendix: Exact evaluation of GP-policies for exponential distributions

In this appendix, we describe an exact evaluation procedure for the expected makespan of a feasible GP-policy \({\varPi }(L,X,Y)\), when each activity i has an exponentially distributed duration with rate parameter \(\lambda _{i}\).

We use a Markov chain in which a state is represented by a pair (IO), where I and O are the sets of idle and ongoing activities, respectively. The set F of finished activities is fully defined by given choices for I and O. In a state (IO), an activity \(i \in N\) is eligible to start if the following three conditions hold:

  1. 1.

    \(i \in I\),

  2. 2.

    \(j \in F\) for all j for which \((j,i) \in A\),

  3. 3.

    \(r_{ik} \le \left( a_{k} - \sum _{j \in O} r_{jk} \right) \) for all \(k \in K\).

For a given state (IO), let H denote the set of eligible activities and \(W\subseteq H\) the set of activities to be started in that state (following the given policy \({\varPi }(L,X,Y)\)). Activities \(i\in H\) are considered in order of L for inclusion into W and are included if the following two conditions apply:

  1. 1.

    \(j \in \left( O \cup F \right) \) for all j for which \((j,i) \in Y\),

  2. 2.

    \(j \in F\) for all j for which \((j,i) \in X\).

If \(\left| W \right| > 0\), then an immediate transition is made toward state \((I{\setminus }W, O \cup W)\). Otherwise (if W is empty), no activities are started and a transition takes place after completion of the first activity in O. The probability that an activity \(i \in O\) finishes first equals \(\lambda _{i}/\sum _{j \in O} \lambda _{j}\). The time until the first completion is exponentially distributed and has expected value \(\left( \sum _{i \in O} \lambda _{i} \right) ^{-1}\).

With each state (IO), we associate a value function G(IO) that represents the expected time when state (IO) is visited, and \(\pi (I,O)\) denotes the probability that the state is visited. We stepwise update both values. If \(W\ne \emptyset \), then \(\pi (I{\setminus }W, O \cup W)\) is increased by \(\pi (I,O)\) and \(G(I{\setminus }W, O \cup W)\) is increased by \(G(I,O)\pi (I,O)\). Otherwise (\(W=\emptyset \)), probability \(\pi (I , O{\setminus }\left\{ i \right\} )\) is increased by \(\pi (I,O)\lambda _{i}/\sum _{j \in O} \lambda _{j}\), and value function \(G(I , O{\setminus }\left\{ i \right\} )\) is augmented with \(\left( G(I,O) + \left( \sum _{i \in O} \lambda _{i} \right) ^{-1} \right) \pi (I,O)\lambda _{i}/\sum _{j \in O} \lambda _{j}\).

Memory rather than computation time is typically the bottleneck when evaluating a Markovian PERT network. In our implementation, we have used techniques described in Creemers et al. (2010) and Creemers (2015) to delete states from memory when they are no longer needed.

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Rostami, S., Creemers, S. & Leus, R. New strategies for stochastic resource-constrained project scheduling. J Sched 21, 349–365 (2018). https://doi.org/10.1007/s10951-016-0505-x

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Keywords

  • Project scheduling
  • Uncertainty
  • Stochastic activity durations
  • Scheduling policies