Abstract
Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that changes only little when variations in the input parameters arise. This paper presents a model for single-machine scheduling with stability objective and a common deadline. We propose a branch-and-bound algorithm for solving an approximate formulation of the model. The algorithm is exact when exactly one job is disrupted during schedule execution.
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Adiri, I., Bruno, J., Frostig, E., & Rinnooy Kan, A. H. G. (1989). Single machine flow-time scheduling with a single breakdown. Acta Informatica, 36, 679–696.
Ahuja, R., Magnanti, T., & Orlin, J. (1993). Network flows. New York: Prentice-Hall.
Akturk, M., & Gorgulu, E. (1999). Match-up scheduling under a machine breakdown. European Journal of Operational Research, 112, 81–97.
Aytug, H., Lawley, M., McKay, K., Mohan, S., & Uzsoy, R. (2005). Executing production schedules in the face of uncertainties: a review and some future directions. European Journal of Operational Research, 161, 86–110.
Bean, J., Birge, J., Mittenthal, J., & Noon, C. (1991). Match-up scheduling with multiple resources, release dates and disruptions. Operations Research, 39, 470–483.
Britney, R. R. (1976). Bayesian point estimation and the PERT scheduling of stochastic activities. Management Science, 22, 938–948.
Bruno, J., Coffmann, E., & Sethi, R. (1974). Scheduling independent tasks to reduce mean finishing time. Communications of the ACM, 17, 382–387.
Calhoun, K., Deckro, R., Moore, J., Chrissis, J., & Hove, J. V. (2002). Planning and re-planning in project and production planning. Omega, 30, 155–170.
Christy, D. P., & Kanet, J. J. (1990). Manufacturing systems with forbidden early shipment: implications for choice of scheduling rules. International Journal of Production Research, 28, 91–100.
Daniels, R., & Carrillo, J. (1997). β-robust scheduling for single-machine systems with uncertain processing times. IIE Transactions, 29, 977–985.
Daniels, R., & Kouvelis, P. (1995). Robust scheduling to hedge against processing time uncertainty in single-stage production. Management Science, 41, 363–376.
Dasdan, A., & Gupta, R. (1998). Faster maximum and minimum mean cycle algorithms for system performance analysis. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 17, 889–899.
Elmaghraby, S. E. (2005). On the fallacy of averages in project risk management. European Journal of Operational Research, 165, 307–313.
Fearnhead, P., & Meligkotsidou, L. (2004). Exact filtering for partially observed continuous time models. Journal of the Royal Statistical Society: Series B, 66, 771–789.
Herroelen, W., & Leus, R. (2004). The construction of stable project baseline schedules. European Journal of Operational Research, 156, 550–565.
Kanet, J. J., & Christy, D. P. (1984). Manufacturing systems with forbidden early departure. International Journal of Production Research, 22, 41–50.
Kanet, J., & Sridharan, V. (2000). Scheduling with inserted idle time: problem taxonomy and literature review. Operations Research, 48, 99–110.
Karp, R. (1978). A characterization of the minimum cycle mean in a digraph. Discrete Mathematics, 23, 309–311.
Kouvelis, P., & Yu, G. (1997). Robust discrete optimization and its applications. Dordrecht: Kluwer Academic.
Kouvelis, P., Daniels, R. L., & Vairaktarakis, G. (2000). Robust scheduling of a two-machine flow shop with uncertain processing times. IIE Transactions, 32, 421–432.
Leon, V., Wu, S., & Storer, R. (1994). Robustness measures and robust scheduling for job shops. IIE Transactions, 26, 343–362.
Leus, R. (2003). The generation of stable project plans. Complexity and exact algorithms. PhD thesis, Katholieke Universiteit Leuven, Leuven, Belgium.
Leus, R., & Herroelen, W. (2005). The complexity of machine scheduling for stability with a single disrupted job. Operations Research Letters, 33, 151–156.
Mehta, S., & Uzsoy, R. (1998). Predictable scheduling of a job shop subject to breakdowns. IEEE Transactions on Robotics and Automation, 14, 365–378.
O’Donovan, R., Uzsoy, R., & McKay, K. (1999). Predictable scheduling on a single machine with breakdowns and sensitive jobs. International Journal of Production Research, 37, 4217–4233.
Parker, R., & Rardin, R. (1988). Discrete optimization. New York: Academic.
Pinedo, M. (2002). Scheduling. Theory, algorithms, and systems. New York: Prentice-Hall.
Raheja, A., & Subramaniam, V. (2002). Reactive recovery of job shop schedules—a review. International Journal of Advanced Manufacturing Technology, 19, 756–763.
Rangsaritratsamee, R., Ferrel, W., & Kurz, M. (2004). Dynamic rescheduling that simultaneously considers efficiency and stability. Computers & Industrial Engineering, 46, 1–15.
Stork, F. (2001). Stochastic resource-constrained project scheduling. PhD thesis, TU Berlin, Berlin, Germany.
Wu, S., Storer, H., & Chang, P.-C. (1993). One-machine rescheduling heuristics with efficiency and stability as criteria. Computers and Operations Research, 20, 1–14.
Yáñez, J., & Ramírez, J. (2003). The robust coloring problem. European Journal of Operational Research, 148, 546–558.
Yano, C. A. (1987). Setting planned leadtimes in serial production systems with tardiness costs. Management Science, 33, 95–106.
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Leus, R., Herroelen, W. Scheduling for stability in single-machine production systems. J Sched 10, 223–235 (2007). https://doi.org/10.1007/s10951-007-0014-z
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DOI: https://doi.org/10.1007/s10951-007-0014-z