IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v243y2015i1p70-74.html
   My bibliography  Save this article

The three-machine proportionate open shop and mixed shop minimum makespan problems

Author

Listed:
  • Koulamas, Christos
  • Kyparisis, George J.

Abstract

We first consider the ordinary NP-hard three-machine proportionate open shop minimum makespan O3|prpt|Cmax problem and show that it is solvable in O(nlog n) time when certain conditions on the total machine load are met. When these conditions are not met, we derive an approximate solution by implementing the optimal solution for the O3|prpt|Cmax problem when the two longest jobs are of equal length. In that case, both absolute and ratio worst-case bounds are derived. We also consider the more general mixed shop problem M3|prpt|Cmax in which a given job subset must be processed as in a flow shop while the remaining jobs can be processed as in the O3|prpt|Cmax problem. We show that our open shop solution techniques can be implemented to derive exact and approximate solutions for the M3|prpt|Cmax problem. Finally, we discuss the applicability of our open shop results to the proportionate open shop problem with unequal machine speeds.

Suggested Citation

  • Koulamas, Christos & Kyparisis, George J., 2015. "The three-machine proportionate open shop and mixed shop minimum makespan problems," European Journal of Operational Research, Elsevier, vol. 243(1), pages 70-74.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:1:p:70-74
    DOI: 10.1016/j.ejor.2014.11.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714009606
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.11.037?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. A. Kononov & S. Sevastianov & I. Tchernykh, 1999. "When difference in machine loads leadsto efficient scheduling in open shops," Annals of Operations Research, Springer, vol. 92(0), pages 211-239, January.
    2. Shakhlevich, Natalia V. & Sotskov, Yuri N. & Werner, Frank, 2000. "Complexity of mixed shop scheduling problems: A survey," European Journal of Operational Research, Elsevier, vol. 120(2), pages 343-351, January.
    3. Bo Chen & Vitaly A. Strusevich, 1993. "Approximation Algorithms for Three-Machine Open Shop Scheduling," INFORMS Journal on Computing, INFORMS, vol. 5(3), pages 321-326, August.
    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. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. Yu, Tae-Sun & Pinedo, Michael, 2020. "Flow shops with reentry: Reversibility properties and makespan optimal schedules," European Journal of Operational Research, Elsevier, vol. 282(2), pages 478-490.
    3. S. Knust & N. V. Shakhlevich & S. Waldherr & C. Weiß, 2019. "Shop scheduling problems with pliable jobs," Journal of Scheduling, Springer, vol. 22(6), pages 635-661, December.

    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. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. Liaw, Ching-Fang, 2000. "A hybrid genetic algorithm for the open shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 124(1), pages 28-42, July.
    3. Inna G. Drobouchevitch, 2021. "Three-machine open shop with a bottleneck machine revisited," Journal of Scheduling, Springer, vol. 24(2), pages 197-208, April.
    4. Drobouchevitch, Inna G. & Strusevich, Vitaly A., 2001. "Two-stage open shop scheduling with a bottleneck machine," European Journal of Operational Research, Elsevier, vol. 128(1), pages 159-174, January.
    5. Mati, Yazid & Xie, Xiaolan, 2004. "The complexity of two-job shop problems with multi-purpose unrelated machines," European Journal of Operational Research, Elsevier, vol. 152(1), pages 159-169, January.
    6. Eranda Çela & Vladimir G. Deineko & Gerhard J. Woeginger, 2017. "The multi-stripe travelling salesman problem," Annals of Operations Research, Springer, vol. 259(1), pages 21-34, December.
    7. Burak Cankaya & Ezra Wari & Berna Eren Tokgoz, 2019. "Practical approaches to chemical tanker scheduling in ports: a case study on the Port of Houston," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 21(4), pages 559-575, December.
    8. Mosheiov, Gur & Sarig, Assaf & Strusevich, Vitaly A & Mosheiff, Jonathan, 2018. "Two-machine flow shop and open shop scheduling problems with a single maintenance window," European Journal of Operational Research, Elsevier, vol. 271(2), pages 388-400.
    9. Jianming Dong & Yong Chen & An Zhang & Qifan Yang, 2013. "A new three-machine shop scheduling: complexity and approximation algorithm," Journal of Combinatorial Optimization, Springer, vol. 26(4), pages 799-810, November.
    10. Xiong, Hegen & Fan, Huali & Jiang, Guozhang & Li, Gongfa, 2017. "A simulation-based study of dispatching rules in a dynamic job shop scheduling problem with batch release and extended technical precedence constraints," European Journal of Operational Research, Elsevier, vol. 257(1), pages 13-24.
    11. 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.
    12. Kis, Tamas, 2003. "Job-shop scheduling with processing alternatives," European Journal of Operational Research, Elsevier, vol. 151(2), pages 307-332, December.
    13. M.A. Kubzin & V.A. Strusevich & J. Breit & G. Schmidt, 2006. "Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 16-23, February.
    14. Liaw, Ching-Fang, 1998. "An iterative improvement approach for the nonpreemptive open shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 111(3), pages 509-517, December.
    15. Yuan Yuan & Yan Lan & Ning Ding & Xin Han, 2022. "A PTAS for non-resumable open shop scheduling with an availability constraint," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 350-362, March.
    16. Peter Brucker & Yu Sotskov & Frank Werner, 2007. "Complexity of shop-scheduling problems with fixed number of jobs: a survey," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 461-481, June.
    17. Tamer Abdelmaguid & Mohamed Shalaby & Mohamed Awwad, 2014. "A tabu search approach for proportionate multiprocessor open shop scheduling," Computational Optimization and Applications, Springer, vol. 58(1), pages 187-203, May.
    18. Bo Chen & Arjen P.A. Vestjens & Gerhard J. Woeginger, 1998. "On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time," Journal of Combinatorial Optimization, Springer, vol. 1(4), pages 355-365, 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:eee:ejores:v:243:y:2015:i:1:p:70-74. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.