IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v6y2002i1d10.1023_a1013333232691.html
   My bibliography  Save this article

On the Robust Single Machine Scheduling Problem

Author

Listed:
  • Jian Yang

    (New Jersey Institute of Technology)

  • Gang Yu

    (The University of Texas at Austin)

Abstract

The single machine scheduling problem with sum of completion times criterion (SS) can be solved easily by the Shortest Processing Time (SPT) rule. In the case of significant uncertainty of the processing times, a robustness approach is appropriate. In this paper, we show that the robust version of the (SS) problem is NP-complete even for very restricted cases. We present an algorithm for finding optimal solutions for the robust (SS) problem using dynamic programming. We also provide two polynomial time heuristics and demonstrate their effectiveness.

Suggested Citation

  • Jian Yang & Gang Yu, 2002. "On the Robust Single Machine Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 17-33, March.
    • Handle: RePEc:spr:jcomop:v:6:y:2002:i:1:d:10.1023_a:1013333232691
    DOI: 10.1023/A:1013333232691
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1013333232691
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1013333232691?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Emmons, Hamilton & Pinedo, Michael, 1990. "Scheduling stochastic jobs with due dates on parallel machines," European Journal of Operational Research, Elsevier, vol. 47(1), pages 49-55, July.
    2. Allahverdi, Ali & Mittenthal, John, 1995. "Scheduling on a two-machine flowshop subject to random breakdowns with a makespan objective function," European Journal of Operational Research, Elsevier, vol. 81(2), pages 376-387, March.
    3. Thomas Kämpke, 1989. "Optimal Scheduling of Jobs with Exponential Service Times on Identical Parallel Processors," Operations Research, INFORMS, vol. 37(1), pages 126-133, February.
    4. J. Birge & J. B. G. Frenk & J. Mittenthal & A. H. G. Rinnooy Kan, 1990. "Single‐machine scheduling subject to stochastic breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 661-677, October.
    5. Richard L. Daniels & Panagiotis Kouvelis, 1995. "Robust Scheduling to Hedge Against Processing Time Uncertainty in Single-Stage Production," Management Science, INFORMS, vol. 41(2), pages 363-376, February.
    6. Charles Du & Michael Pinedo, 1995. "A note on minimizing the expected makespan in flowshops subject to breakdowns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1251-1262, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Choi, Byung-Cheon & Chung, Kwanghun, 2016. "Min–max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 252(2), pages 367-375.
    2. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    3. Miri Gilenson & Dvir Shabtay & Liron Yedidsion & Rohit Malshe, 2021. "Scheduling in multi-scenario environment with an agreeable condition on job processing times," Annals of Operations Research, Springer, vol. 307(1), pages 153-173, December.
    4. Miri Gilenson & Hussein Naseraldin & Liron Yedidsion, 2019. "An approximation scheme for the bi-scenario sum of completion times trade-off problem," Journal of Scheduling, Springer, vol. 22(3), pages 289-304, June.
    5. Mina Roohnavazfar & Daniele Manerba & Lohic Fotio Tiotsop & Seyed Hamid Reza Pasandideh & Roberto Tadei, 2021. "Stochastic single machine scheduling problem as a multi-stage dynamic random decision process," Computational Management Science, Springer, vol. 18(3), pages 267-297, July.
    6. François Clautiaux & Boris Detienne & Henri Lefebvre, 2023. "A two-stage robust approach for minimizing the weighted number of tardy jobs with objective uncertainty," Journal of Scheduling, Springer, vol. 26(2), pages 169-191, April.
    7. Yuri N. Sotskov & Natalja G. Egorova, 2019. "The Optimality Region for a Single-Machine Scheduling Problem with Bounded Durations of the Jobs and the Total Completion Time Objective," Mathematics, MDPI, vol. 7(5), pages 1-21, April.
    8. Semih Atakan & Kerem Bülbül & Nilay Noyan, 2017. "Minimizing value-at-risk in single-machine scheduling," Annals of Operations Research, Springer, vol. 248(1), pages 25-73, January.
    9. Chang, Zhiqi & Ding, Jian-Ya & Song, Shiji, 2019. "Distributionally robust scheduling on parallel machines under moment uncertainty," European Journal of Operational Research, Elsevier, vol. 272(3), pages 832-846.
    10. Subhash C. Sarin & Balaji Nagarajan & Sanjay Jain & Lingrui Liao, 2009. "Analytic evaluation of the expectation and variance of different performance measures of a schedule on a single machine under processing time variability," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 400-416, May.
    11. Yang, Bibo & Geunes, Joseph, 2008. "Predictive-reactive scheduling on a single resource with uncertain future jobs," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1267-1283, September.
    12. Silva, Marco & Poss, Michael & Maculan, Nelson, 2020. "Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 283(1), pages 70-82.
    13. Yuli Zhang & Zuo-Jun Max Shen & Shiji Song, 2018. "Exact Algorithms for Distributionally β -Robust Machine Scheduling with Uncertain Processing Times," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 662-676, November.
    14. Lung-Yu Li & Jian-You Xu & Shuenn-Ren Cheng & Xingong Zhang & Win-Chin Lin & Jia-Cheng Lin & Zong-Lin Wu & Chin-Chia Wu, 2022. "A Genetic Hyper-Heuristic for an Order Scheduling Problem with Two Scenario-Dependent Parameters in a Parallel-Machine Environment," Mathematics, MDPI, vol. 10(21), pages 1-22, November.
    15. Gang Xuan & Win-Chin Lin & Shuenn-Ren Cheng & Wei-Lun Shen & Po-An Pan & Chih-Ling Kuo & Chin-Chia Wu, 2022. "A Robust Single-Machine Scheduling Problem with Two Job Parameter Scenarios," Mathematics, MDPI, vol. 10(13), pages 1-17, June.
    16. Pei, Zhi & Lu, Haimin & Jin, Qingwei & Zhang, Lianmin, 2022. "Target-based distributionally robust optimization for single machine scheduling," European Journal of Operational Research, Elsevier, vol. 299(2), pages 420-431.
    17. Kasperski, Adam & Kurpisz, Adam & Zieliński, Paweł, 2012. "Approximating a two-machine flow shop scheduling under discrete scenario uncertainty," European Journal of Operational Research, Elsevier, vol. 217(1), pages 36-43.
    18. Chin-Chia Wu & Jatinder N. D. Gupta & Win-Chin Lin & Shuenn-Ren Cheng & Yen-Lin Chiu & Juin-Han Chen & Long-Yuan Lee, 2022. "Robust Scheduling of Two-Agent Customer Orders with Scenario-Dependent Component Processing Times and Release Dates," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    19. Chang, Zhiqi & Song, Shiji & Zhang, Yuli & Ding, Jian-Ya & Zhang, Rui & Chiong, Raymond, 2017. "Distributionally robust single machine scheduling with risk aversion," European Journal of Operational Research, Elsevier, vol. 256(1), pages 261-274.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Miri Gilenson & Dvir Shabtay & Liron Yedidsion & Rohit Malshe, 2021. "Scheduling in multi-scenario environment with an agreeable condition on job processing times," Annals of Operations Research, Springer, vol. 307(1), pages 153-173, December.
    2. Xiaoqiang Cai & Sean Zhou, 1999. "Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs," Operations Research, INFORMS, vol. 47(3), pages 422-437, June.
    3. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    4. Allahverdi, Ali, 1999. "Stochastically minimizing total flowtime in flowshops with no waiting space," European Journal of Operational Research, Elsevier, vol. 113(1), pages 101-112, February.
    5. Ali Allahverdi & John Mittenthal, 1994. "Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(5), pages 677-682, August.
    6. Michele E. Pfund & John W. Fowler, 2017. "Extending the boundaries between scheduling and dispatching: hedging and rescheduling techniques," International Journal of Production Research, Taylor & Francis Journals, vol. 55(11), pages 3294-3307, June.
    7. Faicel Hnaien & Taha Arbaoui, 2023. "Minimizing the makespan for the two-machine flow shop scheduling problem with random breakdown," Annals of Operations Research, Springer, vol. 328(2), pages 1437-1460, September.
    8. Brian C. Dean & Michel X. Goemans & Jan Vondrák, 2008. "Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 945-964, November.
    9. Şeker, Merve & Noyan, Nilay, 2012. "Stochastic optimization models for the airport gate assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 438-459.
    10. Adam Kasperski & Paweł Zieliński, 2019. "Risk-averse single machine scheduling: complexity and approximation," Journal of Scheduling, Springer, vol. 22(5), pages 567-580, October.
    11. Zhenpeng Li & Congdian Cheng, 2023. "The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown," Mathematics, MDPI, vol. 11(11), pages 1-12, May.
    12. Li, Wei & Glazebrook, Kevin D., 1998. "On stochastic machine scheduling with general distributional assumptions," European Journal of Operational Research, Elsevier, vol. 105(3), pages 525-536, March.
    13. Gang Xuan & Win-Chin Lin & Shuenn-Ren Cheng & Wei-Lun Shen & Po-An Pan & Chih-Ling Kuo & Chin-Chia Wu, 2022. "A Robust Single-Machine Scheduling Problem with Two Job Parameter Scenarios," Mathematics, MDPI, vol. 10(13), pages 1-17, June.
    14. Igor Averbakh & Oded Berman, 2000. "Minmax Regret Median Location on a Network Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 104-110, May.
    15. Mausser, Helmut E. & Laguna, Manuel, 1999. "A heuristic to minimax absolute regret for linear programs with interval objective function coefficients," European Journal of Operational Research, Elsevier, vol. 117(1), pages 157-174, August.
    16. Silva, Marco & Poss, Michael & Maculan, Nelson, 2020. "Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 283(1), pages 70-82.
    17. Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy & Julia Resch & Giovanni Righini, 2021. "Optimally rescheduling jobs with a Last-In-First-Out buffer," Journal of Scheduling, Springer, vol. 24(6), pages 663-680, December.
    18. Xiaoqiang Cai & Xianyi Wu & Xian Zhou, 2009. "Stochastic Scheduling Subject to Preemptive-Repeat Breakdowns with Incomplete Information," Operations Research, INFORMS, vol. 57(5), pages 1236-1249, October.
    19. Lin, Jun & Ng, Tsan Sheng, 2011. "Robust multi-market newsvendor models with interval demand data," European Journal of Operational Research, Elsevier, vol. 212(2), pages 361-373, July.
    20. Pei, Zhi & Lu, Haimin & Jin, Qingwei & Zhang, Lianmin, 2022. "Target-based distributionally robust optimization for single machine scheduling," European Journal of Operational Research, Elsevier, vol. 299(2), pages 420-431.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:6:y:2002:i:1:d:10.1023_a:1013333232691. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.