Skip to main content
Log in

Scheduling for stability in single-machine production systems

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • 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.

    Article  Google Scholar 

  • Ahuja, R., Magnanti, T., & Orlin, J. (1993). Network flows. New York: Prentice-Hall.

    Google Scholar 

  • Akturk, M., & Gorgulu, E. (1999). Match-up scheduling under a machine breakdown. European Journal of Operational Research, 112, 81–97.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Bean, J., Birge, J., Mittenthal, J., & Noon, C. (1991). Match-up scheduling with multiple resources, release dates and disruptions. Operations Research, 39, 470–483.

    Google Scholar 

  • Britney, R. R. (1976). Bayesian point estimation and the PERT scheduling of stochastic activities. Management Science, 22, 938–948.

    Google Scholar 

  • Bruno, J., Coffmann, E., & Sethi, R. (1974). Scheduling independent tasks to reduce mean finishing time. Communications of the ACM, 17, 382–387.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Daniels, R., & Carrillo, J. (1997). β-robust scheduling for single-machine systems with uncertain processing times. IIE Transactions, 29, 977–985.

    Article  Google Scholar 

  • Daniels, R., & Kouvelis, P. (1995). Robust scheduling to hedge against processing time uncertainty in single-stage production. Management Science, 41, 363–376.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Elmaghraby, S. E. (2005). On the fallacy of averages in project risk management. European Journal of Operational Research, 165, 307–313.

    Article  Google Scholar 

  • Fearnhead, P., & Meligkotsidou, L. (2004). Exact filtering for partially observed continuous time models. Journal of the Royal Statistical Society: Series B, 66, 771–789.

    Article  Google Scholar 

  • Herroelen, W., & Leus, R. (2004). The construction of stable project baseline schedules. European Journal of Operational Research, 156, 550–565.

    Article  Google Scholar 

  • Kanet, J. J., & Christy, D. P. (1984). Manufacturing systems with forbidden early departure. International Journal of Production Research, 22, 41–50.

    Google Scholar 

  • Kanet, J., & Sridharan, V. (2000). Scheduling with inserted idle time: problem taxonomy and literature review. Operations Research, 48, 99–110.

    Article  Google Scholar 

  • Karp, R. (1978). A characterization of the minimum cycle mean in a digraph. Discrete Mathematics, 23, 309–311.

    Google Scholar 

  • Kouvelis, P., & Yu, G. (1997). Robust discrete optimization and its applications. Dordrecht: Kluwer Academic.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Leon, V., Wu, S., & Storer, R. (1994). Robustness measures and robust scheduling for job shops. IIE Transactions, 26, 343–362.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Mehta, S., & Uzsoy, R. (1998). Predictable scheduling of a job shop subject to breakdowns. IEEE Transactions on Robotics and Automation, 14, 365–378.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Parker, R., & Rardin, R. (1988). Discrete optimization. New York: Academic.

    Google Scholar 

  • Pinedo, M. (2002). Scheduling. Theory, algorithms, and systems. New York: Prentice-Hall.

    Google Scholar 

  • Raheja, A., & Subramaniam, V. (2002). Reactive recovery of job shop schedules—a review. International Journal of Advanced Manufacturing Technology, 19, 756–763.

    Article  Google Scholar 

  • Rangsaritratsamee, R., Ferrel, W., & Kurz, M. (2004). Dynamic rescheduling that simultaneously considers efficiency and stability. Computers & Industrial Engineering, 46, 1–15.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Yáñez, J., & Ramírez, J. (2003). The robust coloring problem. European Journal of Operational Research, 148, 546–558.

    Article  Google Scholar 

  • Yano, C. A. (1987). Setting planned leadtimes in serial production systems with tardiness costs. Management Science, 33, 95–106.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Roel Leus.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-007-0014-z

Keywords

Navigation