IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v34y2017i04ns0217595917500154.html
   My bibliography  Save this article

Proportionate Flow Shop Scheduling with Rejection

Author

Listed:
  • Shi-Sheng Li

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou 450007, P. R. China)

  • De-Liang Qian

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou 450007, P. R. China)

  • Ren-Xia Chen

    (Department of Information and Computation Science, Zhongyuan University of Technology, Zhengzhou 450007, P. R. China)

Abstract

We consider the problem of scheduling n jobs with rejection on a set of m machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is 𝒩𝒫-hard, then we construct a pseudo-polynomial time algorithm to solve it and an O(n3log n) time for the case where the jobs have the same processing time. For the second problem, we first show that it is 𝒩𝒫-hard, then we design O(n2) time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

Suggested Citation

  • Shi-Sheng Li & De-Liang Qian & Ren-Xia Chen, 2017. "Proportionate Flow Shop Scheduling with Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-13, August.
    • Handle: RePEc:wsi:apjorx:v:34:y:2017:i:04:n:s0217595917500154
    DOI: 10.1142/S0217595917500154
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595917500154
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595917500154?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. M. L. Smith & S. S. Panwalkar & R. A. Dudek, 1975. "Flowshop Sequencing Problem with Ordered Processing Time Matrices," Management Science, INFORMS, vol. 21(5), pages 544-549, January.
    2. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    3. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    4. Choi, Byung-Cheon & Chung, Jibok, 2011. "Two-machine flow shop scheduling problem with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(1), pages 66-72, August.
    5. Zhong, Xueling & Ou, Jinwen & Wang, Guoqing, 2014. "Order acceptance and scheduling with machine availability constraints," European Journal of Operational Research, Elsevier, vol. 232(3), pages 435-441.
    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. Kuo-Ching Ying & Pourya Pourhejazy & Chuan-En Sung, 2024. "Two-agent proportionate flowshop scheduling with deadlines: polynomial-time optimization algorithms," Annals of Operations Research, Springer, vol. 343(1), pages 543-558, December.
    2. Zhang, Yufeng & Khani, Alireza, 2021. "Integrating transit systems with ride-sourcing services: A study on the system users’ stochastic equilibrium problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 150(C), pages 95-123.
    3. Baruch Mor, 2023. "Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection," Operational Research, Springer, vol. 23(1), pages 1-19, March.
    4. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.

    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. Tarhan, İstenç & Oğuz, Ceyda, 2022. "A matheuristic for the generalized order acceptance and scheduling problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 87-103.
    2. Lingfa Lu & Liqi Zhang & Jinwen Ou, 2021. "In-house production and outsourcing under different discount schemes on the total outsourcing cost," Annals of Operations Research, Springer, vol. 298(1), pages 361-374, March.
    3. Byung-Cheon Choi & Joseph Y.-T. Leung & Michael L. Pinedo, 2011. "Minimizing makespan in an ordered flow shop with machine-dependent processing times," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 797-818, November.
    4. 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.
    5. Lingfa Lu & Liqi Zhang & Jie Zhang & Lili Zuo, 2020. "Single Machine Scheduling with Outsourcing Under Different Fill Rates or Quantity Discount Rates," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-15, January.
    6. Lili Zuo & Zhenxia Sun & Lingfa Lu & Liqi Zhang, 2019. "Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval," Mathematics, MDPI, vol. 7(8), pages 1-8, July.
    7. Ou, Jinwen & Zhong, Xueling & Wang, Guoqing, 2015. "An improved heuristic for parallel machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 241(3), pages 653-661.
    8. Jinwen Ou & Xueling Zhong, 2017. "Order acceptance and scheduling with consideration of service level," Annals of Operations Research, Springer, vol. 248(1), pages 429-447, January.
    9. S. S. Panwalkar & Christos Koulamas, 2019. "The evolution of schematic representations of flow shop scheduling problems," Journal of Scheduling, Springer, vol. 22(4), pages 379-391, August.
    10. Shi-Sheng Li & Ren-Xia Chen, 2017. "Scheduling with Rejection and a Deteriorating Maintenance Activity on a Single Machine," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(02), pages 1-17, April.
    11. Chung, Dae-Young & Choi, Byung-Cheon, 2013. "Outsourcing and scheduling for two-machine ordered flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 226(1), pages 46-52.
    12. Xueling Zhong & Zhangming Pan & Dakui Jiang, 2017. "Scheduling with release times and rejection on two parallel machines," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 934-944, April.
    13. Koulamas, Christos, 1998. "On the complexity of two-machine flowshop problems with due date related objectives," European Journal of Operational Research, Elsevier, vol. 106(1), pages 95-100, April.
    14. Shabtay, Dvir & Gerstl, Enrique, 2024. "Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 316(3), pages 887-898.
    15. Choi, Byung-Cheon & Lee, Kangbok & Leung, Joseph Y.-T. & Pinedo, Michael L., 2010. "Flow shops with machine maintenance: Ordered and proportionate cases," European Journal of Operational Research, Elsevier, vol. 207(1), pages 97-104, November.
    16. Choi, Byung-Cheon & Chung, Jibok, 2011. "Two-machine flow shop scheduling problem with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(1), pages 66-72, August.
    17. S.S. Panwalkar & Milton L. Smith & Christos Koulamas, 2013. "Review of the ordered and proportionate flow shop scheduling research," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 46-55, February.
    18. Mehravaran, Yasaman & Logendran, Rasaratnam, 2012. "Non-permutation flowshop scheduling in a supply chain with sequence-dependent setup times," International Journal of Production Economics, Elsevier, vol. 135(2), pages 953-963.
    19. Lunardi, Willian T. & Birgin, Ernesto G. & Ronconi, Débora P. & Voos, Holger, 2021. "Metaheuristics for the online printing shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 293(2), pages 419-441.
    20. Zhengcai Cao & Lijie Zhou & Biao Hu & Chengran Lin, 2019. "An Adaptive Scheduling Algorithm for Dynamic Jobs for Dealing with the Flexible Job Shop Scheduling Problem," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 61(3), pages 299-309, June.

    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:wsi:apjorx:v:34:y:2017:i:04:n:s0217595917500154. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.