IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v22y2019i5d10.1007_s10951-019-00599-6.html
   My bibliography  Save this article

Risk-averse single machine scheduling: complexity and approximation

Author

Listed:
  • Adam Kasperski

    (Wrocław University of Science and Technology)

  • Paweł Zieliński

    (Wrocław University of Science and Technology)

Abstract

In this paper, a class of single machine scheduling problems is considered. It is assumed that job processing times and due dates can be uncertain and they are specified in the form of discrete scenario set. A probability distribution in the scenario set is known. In order to choose a schedule, some risk criteria such as the value at risk and conditional value at risk are used. Various positive and negative complexity results are provided for basic single machine scheduling problems. In this paper, new complexity results are shown and some known complexity results are strengthened.

Suggested Citation

  • Adam Kasperski & Paweł Zieliński, 2019. "Risk-averse single machine scheduling: complexity and approximation," Journal of Scheduling, Springer, vol. 22(5), pages 567-580, October.
    • Handle: RePEc:spr:jsched:v:22:y:2019:i:5:d:10.1007_s10951-019-00599-6
    DOI: 10.1007/s10951-019-00599-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-019-00599-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10951-019-00599-6?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. E. L. Lawler, 1973. "Optimal Sequencing of a Single Machine Subject to Precedence Constraints," Management Science, INFORMS, vol. 19(5), pages 544-546, January.
    2. Włodzimierz Ogryczak, 2012. "Robust Decisions under Risk for Imprecise Probabilities," Lecture Notes in Economics and Mathematical Systems, in: Yuri Ermoliev & Marek Makowski & Kurt Marti (ed.), Managing Safety of Heterogeneous Systems, edition 127, pages 51-66, Springer.
    3. Martin Skutella & Maxim Sviridenko & Marc Uetz, 2016. "Unrelated Machine Scheduling with Stochastic Processing Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 851-864, August.
    4. Karthik Natarajan & Dongjian Shi & Kim-Chuan Toh, 2014. "A Probabilistic Model for Minmax Regret in Combinatorial Optimization," Operations Research, INFORMS, vol. 62(1), pages 160-181, February.
    5. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
    6. 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.
    7. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    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. 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.
    10. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    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. Matthew Bold & Marc Goerigk, 2025. "Recoverable robust single machine scheduling with polyhedral uncertainty," Journal of Scheduling, Springer, vol. 28(3), pages 269-287, June.
    2. Lei Liu & Marcello Urgo, 2024. "Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type dis," Annals of Operations Research, Springer, vol. 338(1), pages 741-764, July.
    3. Fatemeh Rezaei & Amir Abbas Najafi & Erik Demeulemeester & Reza Ramezanian, 2024. "A stochastic bi-objective project scheduling model under failure of activities," Annals of Operations Research, Springer, vol. 338(1), pages 453-476, July.

    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. 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.
    2. Carlo Meloni & Marco Pranzo, 2020. "Expected shortfall for the makespan in activity networks under imperfect information," Flexible Services and Manufacturing Journal, Springer, vol. 32(3), pages 668-692, September.
    3. Yin, Yunqiang & Luo, Zunhao & Wang, Dujuan & Cheng, T.C.E., 2023. "Wasserstein distance‐based distributionally robust parallel‐machine scheduling," Omega, Elsevier, vol. 120(C).
    4. Enrique Gerstl & Gur Mosheiov, 2020. "Single machine scheduling to maximize the number of on-time jobs with generalized due-dates," Journal of Scheduling, Springer, vol. 23(3), pages 289-299, June.
    5. Meloni, Carlo & Pranzo, Marco & Samà, Marcella, 2022. "Evaluation of VaR and CVaR for the makespan in interval valued blocking job shops," International Journal of Production Economics, Elsevier, vol. 247(C).
    6. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    7. Conde, Eduardo, 2012. "On a constant factor approximation for minmax regret problems using a symmetry point scenario," European Journal of Operational Research, Elsevier, vol. 219(2), pages 452-457.
    8. 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.
    9. Cohen, Izack & Postek, Krzysztof & Shtern, Shimrit, 2023. "An adaptive robust optimization model for parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 306(1), pages 83-104.
    10. Zhi Pei & Mingzhong Wan & Ziteng Wang, 2020. "A new approximation algorithm for unrelated parallel machine scheduling with release dates," Annals of Operations Research, Springer, vol. 285(1), pages 397-425, February.
    11. Santiago R. Balseiro & David B. Brown, 2019. "Approximations to Stochastic Dynamic Programs via Information Relaxation Duality," Operations Research, INFORMS, vol. 67(2), pages 577-597, March.
    12. Tugba Saraç & Feristah Ozcelik & Mehmet Ertem, 2023. "Unrelated parallel machine scheduling problem with stochastic sequence dependent setup times," Operational Research, Springer, vol. 23(3), pages 1-19, September.
    13. Varun Gupta & Benjamin Moseley & Marc Uetz & Qiaomin Xie, 2020. "Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 497-516, May.
    14. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 2022. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1796-1811, October.
    15. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    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. Nadia Brauner & Gerd Finke & Yakov Shafransky, 2017. "Lawler’s minmax cost problem under uncertainty," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 31-46, July.
    18. Hongmin Li & Woonghee T. Huh & Matheus C. Sampaio & Naiping Keng, 2021. "Planning Production and Equipment Qualification under High Process Flexibility," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3369-3390, October.
    19. 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.
    20. Lu, Haimin & Pei, Zhi, 2023. "Single machine scheduling with release dates: A distributionally robust approach," European Journal of Operational Research, Elsevier, vol. 308(1), pages 19-37.

    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:jsched:v:22:y:2019:i:5:d:10.1007_s10951-019-00599-6. 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.