IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v17y2009i4d10.1007_s10878-007-9122-0.html
   My bibliography  Save this article

Analytic evaluation of the expectation and variance of different performance measures of a schedule on a single machine under processing time variability

Author

Listed:
  • Subhash C. Sarin

    (Virginia Tech.)

  • Balaji Nagarajan

    (Virginia Tech.)

  • Sanjay Jain

    (Virginia Tech.)

  • Lingrui Liao

    (Virginia Tech.)

Abstract

In this paper, we present closed-form expressions, wherever possible, or devise algorithms otherwise, to determine the expectation and variance of a given schedule on a single machine. We consider a variety of completion time and due date-based objectives. The randomness in the scheduling process is due to variable processing times with known means and variances of jobs and, in some cases, a known underlying processing time distribution. The results that we present in this paper can enable evaluation of a schedule in terms of both the expectation and variance of a performance measure considered, and thereby, aid in obtaining a stable schedule. Additionally, the expressions and algorithms that are presented, can be incorporated in existing scheduling algorithms in order to determine expectation-variance efficient schedules.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:4:d:10.1007_s10878-007-9122-0
    DOI: 10.1007/s10878-007-9122-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-007-9122-0
    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/s10878-007-9122-0?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. Rajendran, Chandrasekharan, 1995. "Heuristics for scheduling in flowshop with multiple objectives," European Journal of Operational Research, Elsevier, vol. 82(3), pages 540-555, May.
    2. Kenneth N. McKay & Frank R. Safayeni & John A. Buzacott, 1988. "Job-Shop Scheduling Theory: What Is Relevant?," Interfaces, INFORMS, vol. 18(4), pages 84-90, August.
    3. Jian Yang & Gang Yu, 2002. "On the Robust Single Machine Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 17-33, March.
    4. Charles E. Clark, 1961. "The Greatest of a Finite Set of Random Variables," Operations Research, INFORMS, vol. 9(2), pages 145-162, April.
    5. Hayriye Ayhan & Tava Lennon Olsen, 2000. "Scheduling of Multi-Class Single-Server Queues Under Nontraditional Performance Measures," Operations Research, INFORMS, vol. 48(3), pages 482-489, June.
    6. De, Prabuddha & Ghosh, Jay B. & Wells, Charles E., 1992. "Expectation-variance analyss of job sequences under processing time uncertainty," International Journal of Production Economics, Elsevier, vol. 28(3), pages 289-297, December.
    7. 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.
    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. M. Urgo & J. Váncza, 2019. "A branch-and-bound approach for the single machine maximum lateness stochastic scheduling problem to minimize the value-at-risk," Flexible Services and Manufacturing Journal, Springer, vol. 31(2), pages 472-496, June.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Ilkyeong Moon & Sanghyup Lee & Moonsoo Shin & Kwangyeol Ryu, 2016. "Evolutionary resource assignment for workload-based production scheduling," Journal of Intelligent Manufacturing, Springer, vol. 27(2), pages 375-388, April.
    19. Lof, Matthijs & van Bommel, Jos, 2023. "Asymmetric information and the distribution of trading volume," Journal of Corporate Finance, Elsevier, vol. 82(C).
    20. P J Kalczynski & J Kamburowski, 2004. "Generalization of Johnson's and Talwar's scheduling rules in two-machine stochastic flow shops," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1358-1362, December.

    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:17:y:2009:i:4:d:10.1007_s10878-007-9122-0. 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.