IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i8p1314-d395994.html
   My bibliography  Save this article

Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times

Author

Listed:
  • Yuri N. Sotskov

    (United Institute of Informatics Problems, National Academy of Sciences of Belarus, Surganova Street 6, 220012 Minsk, Belarus)

  • Natalja M. Matsveichuk

    (Belorussian State Agrarian Technical University, Nezavisimosti Avenue 99, 220023 Minsk, Belarus)

  • Vadzim D. Hatsura

    (Belorussian State University of Informatics and Radioelectronics, P. Brovki Street 6, 220013 Minsk, Belarus)

Abstract

This study addresses a two-machine job-shop scheduling problem with fixed lower and upper bounds on the job processing times. An exact value of the job duration remains unknown until completing the job. The objective is to minimize a schedule length (makespan). It is investigated how to best execute a schedule, if the job processing time may be equal to any real number from the given (closed) interval. Scheduling decisions consist of the off-line phase and the on-line phase of scheduling. Using the fixed lower and upper bounds on the job processing times available at the off-line phase, a scheduler may determine a minimal dominant set of schedules (minimal DS), which is based on the proven sufficient conditions for a schedule dominance. The DS optimally covers all possible realizations of the uncertain (interval) processing times, i.e., for each feasible scenario, there exists at least one optimal schedule in the minimal DS. The DS enables a scheduler to make the on-line scheduling decision, if a local information on completing some jobs becomes known. The stability approach enables a scheduler to choose optimal schedules for most feasible scenarios. The on-line scheduling algorithms have been developed with the asymptotic complexity O ( n 2 ) for n given jobs. The computational experiment shows the effectiveness of these algorithms.

Suggested Citation

  • Yuri N. Sotskov & Natalja M. Matsveichuk & Vadzim D. Hatsura, 2020. "Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times," Mathematics, MDPI, vol. 8(8), pages 1-51, August.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1314-:d:395994
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/8/1314/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/8/1314/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. James R. Jackson, 1956. "An extension of Johnson's results on job IDT scheduling," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(3), pages 201-203, September.
    2. Cheng, T.C. Edwin & Kovalyov, Mikhail Y. & Shakhlevich, Natalia V., 2006. "Scheduling with controllable release dates and processing times: Total completion time minimization," European Journal of Operational Research, Elsevier, vol. 175(2), pages 769-781, December.
    3. Zigao Wu & Shaohua Yu & Tiancheng Li, 2019. "A Meta-Model-Based Multi-Objective Evolutionary Approach to Robust Job Shop Scheduling," Mathematics, MDPI, vol. 7(6), pages 1-19, June.
    4. Kuroda, Mitsuru & Wang, Zeng, 1996. "Fuzzy job shop scheduling," International Journal of Production Economics, Elsevier, vol. 44(1-2), pages 45-51, June.
    5. Lai, Tsung-Chyan & Sotskov, Yuri N. & Sotskova, Nadezhda & Werner, Frank, 2004. "Mean flow time minimization with given bounds of processing times," European Journal of Operational Research, Elsevier, vol. 159(3), pages 558-573, December.
    6. Peng-Sheng Ku & Shun-Chen Niu, 1986. "On Johnson's Two-Machine Flow Shop with Random Processing Times," Operations Research, INFORMS, vol. 34(1), pages 130-136, February.
    7. J. Carlier & E. Pinson, 1989. "An Algorithm for Solving the Job-Shop Problem," Management Science, INFORMS, vol. 35(2), pages 164-176, February.
    8. Xiong, Jian & Xing, Li-ning & Chen, Ying-wu, 2013. "Robust scheduling for multi-objective flexible job-shop problems with random machine breakdowns," International Journal of Production Economics, Elsevier, vol. 141(1), pages 112-126.
    9. Cheng, T.C. Edwin & Kovalyov, Mikhail Y. & Shakhlevich, Natalia V., 2006. "Scheduling with controllable release dates and processing times: Makespan minimization," European Journal of Operational Research, Elsevier, vol. 175(2), pages 751-768, December.
    10. C. T. Ng & Natalja M. Matsveichuk & Yuri N. Sotskov & T. C. Edwin Cheng, 2009. "Two-Machine Flow-Shop Minimum-Length Scheduling With Interval Processing Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(06), pages 715-734.
    11. Ali Allahverdi & Tariq Aldowaisan & Yuri N. Sotskov, 2003. "Two-machine flowshop scheduling problem to minimize makespan or total completion time with random and bounded setup times," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
    12. Kamburowski, Jerzy, 1999. "Stochastically minimizing the makespan in two-machine flow shops without blocking," European Journal of Operational Research, Elsevier, vol. 112(2), pages 304-309, January.
    13. Jansen, Klaus & Mastrolilli, Monaldo & Solis-Oba, Roberto, 2005. "Approximation schemes for job shop scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(2), pages 297-319, December.
    14. R Tavakkoli-Moghaddam & N Safaei & M M O Kah, 2008. "Accessing feasible space in a generalized job shop scheduling problem with the fuzzy processing times: a fuzzy-neural approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(4), pages 431-442, April.
    15. Iwona Paprocka, 2019. "The model of maintenance planning and production scheduling for maximising robustness," International Journal of Production Research, Taylor & Francis Journals, vol. 57(14), pages 4480-4501, July.
    16. Tsung-Chyan Lai & Yuri N. Sotskov & Natalja G. Egorova & Frank Werner, 2018. "The optimality box in uncertain data for minimising the sum of the weighted job completion times," International Journal of Production Research, Taylor & Francis Journals, vol. 56(19), pages 6336-6362, October.
    17. Ozelkan, Ertunga C. & Duckstein, Lucien, 1999. "Optimal fuzzy counterparts of scheduling rules," European Journal of Operational Research, Elsevier, vol. 113(3), pages 593-609, March.
    18. 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.
    19. Portougal, Victor & Trietsch, Dan, 2006. "Johnson's problem with stochastic processing times and optimal service level," European Journal of Operational Research, Elsevier, vol. 169(3), pages 751-760, March.
    20. T-C Lai & Y N Sotskov, 1999. "Sequencing with uncertain numerical data for makespan minimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(3), pages 230-243, March.
    21. 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.
    22. Y N Sotskov & A Allahverdi & T-C Lai, 2004. "Flowshop scheduling problem to minimize total completion time with random and bounded processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 277-286, March.
    Full references (including those not matched with items on IDEAS)

    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. Y N Sotskov & A Allahverdi & T-C Lai, 2004. "Flowshop scheduling problem to minimize total completion time with random and bounded processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 277-286, March.
    2. 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.
    3. 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.
    4. 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.
    5. Evgeny Gurevsky & Sergey Kovalev & Mikhail Y. Kovalyov, 2021. "Min-max controllable risk problems," 4OR, Springer, vol. 19(1), pages 93-101, March.
    6. Leyvand, Yaron & Shabtay, Dvir & Steiner, George, 2010. "A unified approach for scheduling with convex resource consumption functions using positional penalties," European Journal of Operational Research, Elsevier, vol. 206(2), pages 301-312, October.
    7. Monaci, Marta & Agasucci, Valerio & Grani, Giorgio, 2024. "An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents," European Journal of Operational Research, Elsevier, vol. 312(3), pages 910-926.
    8. 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.
    9. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh & Jin-Hwa Song, 2012. "The Fixed-Charge Shortest-Path Problem," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 578-596, November.
    10. Wieslaw Kubiak & Yanling Feng & Guo Li & Suresh P. Sethi & Chelliah Sriskandarajah, 2020. "Efficient algorithms for flexible job shop scheduling with parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 272-288, June.
    11. Abdelhamid Boudjelida, 2019. "On the robustness of joint production and maintenance scheduling in presence of uncertainties," Journal of Intelligent Manufacturing, Springer, vol. 30(4), pages 1515-1530, April.
    12. Dauzère-Pérès, Stéphane & Ding, Junwen & Shen, Liji & Tamssaouet, Karim, 2024. "The flexible job shop scheduling problem: A review," European Journal of Operational Research, Elsevier, vol. 314(2), pages 409-432.
    13. 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.
    14. Xiong, Jian & Leus, Roel & Yang, Zhenyu & Abbass, Hussein A., 2016. "Evolutionary multi-objective resource allocation and scheduling in the Chinese navigation satellite system project," European Journal of Operational Research, Elsevier, vol. 251(2), pages 662-675.
    15. Gueret, Christelle & Jussien, Narendra & Prins, Christian, 2000. "Using intelligent backtracking to improve branch-and-bound methods: An application to Open-Shop problems," European Journal of Operational Research, Elsevier, vol. 127(2), pages 344-354, December.
    16. J Jackman & Z Guerra de Castillo & S Olafsson, 2011. "Stochastic flow shop scheduling model for the Panama Canal," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 69-80, January.
    17. Sels, Veronique & Craeymeersch, Kjeld & Vanhoucke, Mario, 2011. "A hybrid single and dual population search procedure for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 215(3), pages 512-523, December.
    18. Pan, Yunpeng & Shi, Leyuan, 2006. "Branch-and-bound algorithms for solving hard instances of the one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 168(3), pages 1030-1039, February.
    19. Siyun Zhang & Kameng Nip & Zhenbo Wang, 0. "Related machine scheduling with machine speeds satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.
    20. Jacomine Grobler & Andries Engelbrecht & Schalk Kok & Sarma Yadavalli, 2010. "Metaheuristics for the multi-objective FJSP with sequence-dependent set-up times, auxiliary resources and machine down time," Annals of Operations Research, Springer, vol. 180(1), pages 165-196, November.

    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:gam:jmathe:v:8:y:2020:i:8:p:1314-:d:395994. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.