Abstract
This paper addresses the problem of scheduling activities in projects with stochastic activity durations. The aim is to determine for each activity a gate—a time before it the activity cannot begin. Setting these gates is analogous to setting inventory levels in the news vendor problem. The resources required for each activity are scheduled to arrive according to its gate. Since activities’ durations are stochastic, the start and finish time of each activity is uncertain. This fact may lead to one of two outcomes: (1) an activity is ready to start its processing as all its predecessors have finished, but it cannot start because the resources required for it were scheduled to arrive at a later time. (2) The resources required for the activity have arrived and are ready to be used but the activity is not ready to start because of precedence constraints. In the first case we will incur a “holding” cost while in the second case, we will incur a “shortage” cost. Our objective is to set gates so as to minimize the sum of the expected holding and shortage costs. We employ the Cross-Entropy method to solve the problem. The paper describes the implementation of the method, compares its results to various heuristic methods and provides some insights towards actual applications.
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References
Alon, G., Kroese, D. P., Raviv, T., & Rubinstein, R. Y. (2005). Application of the Cross-Entropy method to the buffer allocation problem in a simulation-based environment. Annals of Operations Research, 134, 137–151.
Botev, Z., & Kroese, D. P. (2004). Global likelihood optimization via the cross-entropy method with an application to mixture models. In R. G. Ingalls, M. D. Rossetti, J. S. Smith, & B. A. Peters (Eds.), Proceedings of the 2004 winter simulation conference (pp. 529–535). New York: IEEE Press.
Buss, A. H., & Rosenblatt, M. J. (1997). Activity delay in stochastic project networks. Operations Research, 45(1), 126–139.
Cohen, I., Golany, B., & Shtub, A. (2005). Managing stochastic, finite capacity, multi-project systems through the Cross-Entropy methodology. Annals of Operations Research, 134, 189–199.
Demeulemeester, E. L., & Herroelen, W. S. (2002). Project scheduling—a research handbook. Dordrecht: Kluwer Academic.
Denardo, E. V. (1982). Dynamic programming: models and applications. New York: Prentice-Hall.
Elmaghraby, S. E. (1977). Activity networks: project planning and control by network models. New York: Wiley.
Elmaghraby, S. E. (2001). On the optimal release time of jobs with random processing times, with extensions to other criteria. International Journal of Production Economics, 74, 103–113.
Elmaghraby, S. E., Ferreira, A. A., & Tavares, L. V. (2000). Optimal start times under stochastic activity durations. International Journal of Production Economics, 64, 153–164.
Fazar, W. (1959). Program evaluation and review technique. American Statistician, 13(2), 10.
Golany, B., Dar-El, E. M., & Zeev, N. (1999). Controlling shop floor operations in a multi-family, multi-cell manufacturing environment through constant work-in-process. IIE Transactions, 31, 771–781.
Goldratt, E. M. (1997). Critical chain. New York: North River Press.
Heragu, S. (1997). Facilities design. Boston: PWS Publishing Company.
Herroelen, W. S., & Leus, R. (2005). Project scheduling under uncertainty: survey and research potentials. European Journal of Operational Research, 165, 289–306.
Herroelen, W. S., Van Dommelen, P., & Demeulemeester, E. L. (1997). Project network models with discounted cash flows: a guided tour through recent developments. European Journal of Operational Research, 100, 97–121.
Herroelen, W. S., De-Reyck, B., & Demeulemeester, E. L. (1998). Resource-constrained project scheduling: a survey of recent developments. Computers and Operations Research, 25(4), 279–302.
Kimms, A. (2001). Mathematical programming and financial objectives for scheduling projects. Dordrecht: Kluwer Academic.
Kolish, R., & Padman, R. (2001). An integrated survey of deterministic project scheduling. Omega, 29, 249–272.
Kolish, R., Sprecher, A., & Drexl, A. (1995). Characterization and generation of a general class of resource-constrained project scheduling problems. Management Science, 41(10), 1693–1703.
Krishnamoorthy, M. (1968). Critical path method: a review. Technical Report, Michigan Univ., Dept. of Industrial Engineering, Ann-Arbor, MI, USA.
Kroese, D. P., Rubinstein, R. Y., & Porotsky, S. (2006). The cross-entropy method for continuous multi-extremal optimization. Methodology and Computing in Applied Probability, 8, 383–407.
Malcom, D. G., Roseboom, J. H., Clark, C. E., & Fazar, W. (1959). Apllication of a technique for research and development of program evaluation. Operations Research, 7, 646–669.
Rand, G. K. (2000). Critical chain: the theory of constraints applied to project management. International Journal of Project Management, 18, 173–177.
Rubinstein, R. Y., & Kroese, D. P. (2004). The Cross-Entropy method—a unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning. New York: Springer.
Shtub, A., Bard, J. F., & Globerson, S. (2005). Project management—processes, methodologies, and economics. New York: Pearson Prentice Hall.
Sobel, M. J., Szmerekovsky, J. G., & Tilson, V. (2009). Scheduling projects with stochastic activity duration to maximize expected net present value. European Journal of Operational Research, 198(3), 697–705.
Trietsch, D. (2006a). Economically balanced criticalities for robust project scheduling and control. Working Paper, ISOM Department, University of Auckland, New Zealand.
Trietsch, D. (2006b). Optimal feeding buffers for projects or batch supply chains by an exact generalization of the newsvendor result. International Journal of Production Research, 44, 627–637.
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Bendavid, I., Golany, B. Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology. Ann Oper Res 172, 259–276 (2009). https://doi.org/10.1007/s10479-009-0579-3
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DOI: https://doi.org/10.1007/s10479-009-0579-3