Skip to main content
SpringerLink
Log in

Stochastic single-machine scheduling with workload-dependent maintenance activities

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

This paper studies the stochastic single-machine scheduling problem with workload-dependent maintenance activities, in which the processing times of all jobs are independently subject to a common discrete distribution, and the aim is to find the optimal policy so as to minimize the expected total discounted holding cost. Based on the definition of Markov process, for each of the two cases with the discount rate being zero or a positive number, we present two dynamic programming algorithms to produce the optimal static policy and the optimal dynamic policy, respectively.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adiri, I., Bruno, J., Frostig, E., Kan, R.: Single machine flow-time scheduling with a single breakdown. Acta Inform. 26, 679–696 (1989)

    Article  MathSciNet  Google Scholar 

  2. Bagga, P.C.: n-job, 2-machine sequencing problem with stochastic service times. Mathematics 7, 184–197 (1970)

    MathSciNet  Google Scholar 

  3. Ball, M., Barnhart, C., Nemhauser, G., Odoni, A.: Air transportation: irregular operations and control. In: Barnhart, C., Laporte, G. (eds.) Handbooks in Operations Research and Management Science, Transportation, vol. 14, pp. 1–68. Elsevier, Amsterdam (2007)

    Google Scholar 

  4. Cai, X., Sun, X., Zhou, X.: Stochastic scheduling subject to machine breakdowns: the preemptive-repeat model with discounted reward and other criteria. Nav. Res. Logist. 51(6), 800–817 (2004)

    Article  MathSciNet  Google Scholar 

  5. Cai, X., Wu, X., Zhou, X.: Dynamically optimal policies for stochastic scheduling subject to preemptive-repeat machine breakdowns. IEEE Trans. Autom. Sci. Eng. 2(2), 158–172 (2005)

    Article  Google Scholar 

  6. Cai, X., Wu, X., Zhou, X.: Stochastic scheduling on parallel machines to minimize discounted holding costs. J. Sched. 12(4), 375–388 (2009)

    Article  MathSciNet  Google Scholar 

  7. Cai, X., Wu, X., Zhou, X.: Stochastic scheduling subject to preemptive-repeat breakdowns with incomplete information. Oper. Res. 57(5), 1236–1249 (2009)

    Article  MathSciNet  Google Scholar 

  8. Cai, X., Wu, X., Zhou, X.: Optimal Stochastic Scheduling. International Series in Operations Research & Management Science, vol. 207. Springer, New York (2014)

    Google Scholar 

  9. Cai, X., Wu, X., Zhou, X.: Optimal unrestricted dynamic stochastic scheduling with partial losses of work due to breakdowns. Ann. Oper. Res. 298, 43–64 (2021)

    Article  MathSciNet  Google Scholar 

  10. Chou, M., Liu, H., Queyranne, M., Simchi-Levi, D.: On the asymptotic optimality of a simple on-line algorithm for the stochastic single-machine weighted completion time problem and its extensions. Oper. Res. 54, 464–474 (2006)

    Article  MathSciNet  Google Scholar 

  11. Graham, R.L., Lawer, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discret. Math. 5, 287–326 (1979)

    Article  MathSciNet  Google Scholar 

  12. Haleh, H., Maghsoudlou, H., Hadipour, H., Nabovati, H.: Scheduling single machine with random breakdown and preemptive jobs. J. Ind. Prod. Eng. 34(4), 289–299 (2017)

    Google Scholar 

  13. Lee, C.Y., Yu, G.: Single machine scheduling under potential disruption. Oper. Res. Lett. 35, 541–548 (2007)

    Article  MathSciNet  Google Scholar 

  14. Luo, W., Cheng, T.E., Ji, M.: Single-machine scheduling with a variable maintenance activity. Comput. Ind. Eng. 79, 168–174 (2015)

    Article  Google Scholar 

  15. Luo, W., Liu, F.: On single-machine scheduling with workload-dependent maintenance duration. Omega 68, 119–122 (2017)

    Article  Google Scholar 

  16. Luo, W., Ji, M.: Scheduling a variable maintenance and linear deteriorating jobs on a single machine. Inf. Process. Lett. 115(1), 33–39 (2015)

    Article  MathSciNet  Google Scholar 

  17. Megow, N., Vredeveld, T.: A tight 2-approximation for preemptive stochastic scheduling. Math. Oper. Res. 39(4), 1297–1310 (2014)

    Article  MathSciNet  Google Scholar 

  18. Pinedo, M.: A note on the two-machine job shop with exponential processing times. Naval Res. Log. Q. 28, 693–696 (1981)

    Article  Google Scholar 

  19. Pinedo, M.: A note on the flow time and number of tardy jobs in stochastich open shops. Eur. J. Oper. Res. 18, 81–85 (1984)

    Article  MathSciNet  Google Scholar 

  20. Pinedo, M.: Scheduling: Theory, Algorithms, and Systems, 5th edn. Prentice-Hall, New York (2016)

    Book  Google Scholar 

  21. Rothkopf, M.H., Smith, S.A.: There are no undiscovered priority index sequencing rules for minimizing total delay costs. Oper. Res. 32(2), 451–456 (1984)

    Article  MathSciNet  Google Scholar 

  22. Stefano, N., Nessah, R.: Time-flexible min completion time variance in a single machine by quadratic programming. Eur. J. Oper. Res. 312(2), 427–444 (2024)

    Article  MathSciNet  Google Scholar 

  23. Tang, D., Dai, M., Salido, M.A., Giret, A.: Energy-efficient dynamic scheduling for a flexible flow shop using an improved particle swarm optimization. Comput. Ind. 81, 82–95 (2016)

    Article  Google Scholar 

  24. Tang, H., Zhao, C.: Stochastic single machine scheduling subject to machines breakdowns with quadratic early-tardy penalties for the preemptive-repeat model. J. Appl. Math. Comput. 25, 183–199 (2007)

    Article  MathSciNet  Google Scholar 

  25. Wei, W.: Single machine scheduling with stochastically dependent times. J. Sched. 22, 677–689 (2019)

    Article  MathSciNet  Google Scholar 

  26. Xu, Z., Xu, D.: Single-machine scheduling with workload-dependent tool change durations and equal processing time jobs to minimize total completion time. J. Sched. 21, 461–482 (2018)

    Article  MathSciNet  Google Scholar 

  27. Xu, D., Yin, Y., Li, H.: Scheduling jobs under increasing linear machine maintenance time. J. Sched. 13(4), 443–449 (2010)

    Article  MathSciNet  Google Scholar 

  28. Zhang, Y., Wu, X., Zhou, X.: Stochastic scheduling problems with general position-based learning effects and stochastic breakdowns. J. Sched. 16, 331–336 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Manzhan Gu & Weitao Yang

  2. School of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Peihai Liu

Authors
  1. Manzhan Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weitao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peihai Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manzhan Gu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gu, M., Yang, W. & Liu, P. Stochastic single-machine scheduling with workload-dependent maintenance activities. Optim Lett (2024). https://doi.org/10.1007/s11590-024-02102-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11590-024-02102-3

Keywords

Search

Navigation