IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v33y2016i06ns0217595916500482.html
   My bibliography  Save this article

Scheduling Deteriorating Jobs with Availability Constraints to Minimize the Makespan

Author

Listed:
  • Chuanli Zhao

    (School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, Liaoning 110034, People’s Republic of China)

  • Hengyong Tang

    (School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, Liaoning 110034, People’s Republic of China)

Abstract

In this paper, we consider the scheduling problem in which the processing time of a job is a linear increasing function of its starting time and machine with availability constraints. The objective is to minimize the makespan. We first present a fully polynomial-time approximation scheme (FPTAS) for the case with a single machine. We then show that there exists no polynomial time approximation algorithm with a constant worst-case bound for the case with two identical machines unless P = NP.

Suggested Citation

  • Chuanli Zhao & Hengyong Tang, 2016. "Scheduling Deteriorating Jobs with Availability Constraints to Minimize the Makespan," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-10, December.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:06:n:s0217595916500482
    DOI: 10.1142/S0217595916500482
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595916500482
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595916500482?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. Mikhail Y. Kovalyov & Wieslaw Kubiak, 1999. "A Fully Polynomial Approximation Scheme for the Weighted Earliness–Tardiness Problem," Operations Research, INFORMS, vol. 47(5), pages 757-761, October.
    2. Gawiejnowicz, Stanislaw, 2007. "Scheduling deteriorating jobs subject to job or machine availability constraints," European Journal of Operational Research, Elsevier, vol. 180(1), pages 472-478, July.
    3. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    4. Ng, C.T. & Barketau, M.S. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2010. ""Product Partition" and related problems of scheduling and systems reliability: Computational complexity and approximation," European Journal of Operational Research, Elsevier, vol. 207(2), pages 601-604, December.
    5. Chuan-Li Zhao & Heng-Yong Tang, 2011. "Single Machine Scheduling With Linear Deteriorating Jobs Under Predictive Disruption," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 28(03), pages 419-429.
    6. B Alidaee & N K Womer, 1999. "Scheduling with time dependent processing times: Review and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 711-720, July.
    7. Alberto Bosio & Giovanni Righini, 2009. "A dynamic programming algorithm for the single-machine scheduling problem with release dates and deteriorating processing times," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(2), pages 271-280, May.
    8. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    9. Shisheng Li, 2011. "Scheduling Proportionally Deteriorating Jobs In Two-Machine Open Shop With A Non-Bottleneck Machine," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 28(05), pages 623-631.
    10. Chin-Chia Wu & Wen-Chiung Lee & Yau-Ren Shiau, 2011. "A Single-Machine Deteriorating Job Scheduling Problem With A Non-Regular Criterion," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 28(03), pages 349-359.
    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. 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.
    2. Min Ji & Chou-Jung Hsu & Dar-Li Yang, 2013. "Single-machine scheduling with deteriorating jobs and aging effects under an optional maintenance activity consideration," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 437-447, October.
    3. Li, Shisheng & Ng, C.T. & Cheng, T.C.E. & Yuan, Jinjiang, 2011. "Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 210(3), pages 482-488, May.
    4. Ming Liu & Feifeng Zheng & Chengbin Chu & Jiantong Zhang, 2012. "An FPTAS for uniform machine scheduling to minimize makespan with linear deterioration," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 483-492, May.
    5. C-C He & C-C Wu & W-C Lee, 2009. "Branch-and-bound and weight-combination search algorithms for the total completion time problem with step-deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1759-1766, December.
    6. Wang, Ling & Sun, Lin-Yan & Sun, Lin-Hui & Wang, Ji-Bo, 2010. "On three-machine flow shop scheduling with deteriorating jobs," International Journal of Production Economics, Elsevier, vol. 125(1), pages 185-189, May.
    7. Wu, Chin-Chia & Lee, Wen-Chiung, 2006. "Two-machine flowshop scheduling to minimize mean flow time under linear deterioration," International Journal of Production Economics, Elsevier, vol. 103(2), pages 572-584, October.
    8. T C E Cheng & L Kang & C T Ng, 2004. "Due-date assignment and single machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 198-203, February.
    9. Shakeri, Shakib & Logendran, Rasaratnam, 2007. "A mathematical programming-based scheduling framework for multitasking environments," European Journal of Operational Research, Elsevier, vol. 176(1), pages 193-209, January.
    10. Hongfeng Wang & Min Huang & Junwei Wang, 2019. "An effective metaheuristic algorithm for flowshop scheduling with deteriorating jobs," Journal of Intelligent Manufacturing, Springer, vol. 30(7), pages 2733-2742, October.
    11. Cheng, T.C.E. & Shafransky, Y. & Ng, C.T., 2016. "An alternative approach for proving the NP-hardness of optimization problems," European Journal of Operational Research, Elsevier, vol. 248(1), pages 52-58.
    12. Wang, Ji-Bo, 2007. "Single-machine scheduling problems with the effects of learning and deterioration," Omega, Elsevier, vol. 35(4), pages 397-402, August.
    13. Min Kong & Xinbao Liu & Jun Pei & Panos M. Pardalos & Nenad Mladenovic, 2020. "Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines," Journal of Global Optimization, Springer, vol. 78(4), pages 693-715, December.
    14. Zhao, Chuan-Li & Tang, Heng-Yong, 2010. "Scheduling deteriorating jobs under disruption," International Journal of Production Economics, Elsevier, vol. 125(2), pages 294-299, June.
    15. Sawik, Tadeusz, 2010. "An integer programming approach to scheduling in a contaminated area," Omega, Elsevier, vol. 38(3-4), pages 179-191, June.
    16. Cheng He & Joseph Y.-T. Leung, 2017. "Two-agent scheduling of time-dependent jobs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 362-377, August.
    17. Yang, Suh-Jenq & Yang, Dar-Li, 2010. "Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities," Omega, Elsevier, vol. 38(6), pages 528-533, December.
    18. Shi-Sheng Li & Ren-Xia Chen & Qi Feng & Cheng-Wen Jiao, 2019. "Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 957-971, October.
    19. Ma, Ran & Tao, Jiping & Yuan, Jinjiang, 2016. "Online scheduling with linear deteriorating jobs to minimize the total weighted completion time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 570-583.
    20. Jin, Xianfei & Li, Kunpeng & Sivakumar, Appa Iyer, 2013. "Scheduling and optimal delivery time quotation for customers with time sensitive demand," International Journal of Production Economics, Elsevier, vol. 145(1), pages 349-358.

    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:33:y:2016:i:06:n:s0217595916500482. 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.