IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v19y2016i6d10.1007_s10951-016-0472-2.html
   My bibliography  Save this article

Scheduling with time-dependent discrepancy times

Author

Listed:
  • Florian Jaehn

    (University of Augsburg)

  • Helmut A. Sedding

    (University of Augsburg)

Abstract

In time-dependent scheduling, various processing time functions are studied, yet absolute value functions have surprisingly been omitted from the discussion. Such a processing time function increases linearly with a job’s discrepancy from its ideal midtime. The objective is to find a schedule that minimizes the makespan, introducing the discrepancy time minimization problem. This single-machine scheduling problem with time-dependent processing times is motivated by optimization of walking times on a car assembly line. Its decision version is NP hard, as we show by reduction of the even–odd partition problem. For the variant with known start time, we develop several heuristics. Further insights form lower bounds and dominance rules for a branch-and-bound search. Numerical experiments show the performance of our algorithms on problem instances of up to 60 jobs. For the variant with common ideal midtime and flexible start time, we present a polynomial-time algorithm.

Suggested Citation

  • Florian Jaehn & Helmut A. Sedding, 2016. "Scheduling with time-dependent discrepancy times," Journal of Scheduling, Springer, vol. 19(6), pages 737-757, December.
    • Handle: RePEc:spr:jsched:v:19:y:2016:i:6:d:10.1007_s10951-016-0472-2
    DOI: 10.1007/s10951-016-0472-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-016-0472-2
    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/s10951-016-0472-2?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. Andres, Carlos & Miralles, Cristobal & Pastor, Rafael, 2008. "Balancing and scheduling tasks in assembly lines with sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1212-1223, June.
    2. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    3. Boysen, Nils & Emde, Simon & Hoeck, Michael & Kauderer, Markus, 2015. "Part logistics in the automotive industry: Decision problems, literature review and research agenda," European Journal of Operational Research, Elsevier, vol. 242(1), pages 107-120.
    4. Kunnathur, Anand S. & Gupta, Sushil K., 1990. "Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem," European Journal of Operational Research, Elsevier, vol. 47(1), pages 56-64, July.
    5. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2007. "A classification of assembly line balancing problems," European Journal of Operational Research, Elsevier, vol. 183(2), pages 674-693, December.
    6. Bautista, Joaquin & Pereira, Jordi, 2007. "Ant algorithms for a time and space constrained assembly line balancing problem," European Journal of Operational Research, Elsevier, vol. 177(3), pages 2016-2032, March.
    7. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    8. Chryssi Malandraki & Mark S. Daskin, 1992. "Time Dependent Vehicle Routing Problems: Formulations, Properties and Heuristic Algorithms," Transportation Science, INFORMS, vol. 26(3), pages 185-200, August.
    9. Jean-Claude Picard & Maurice Queyranne, 1978. "The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling," Operations Research, INFORMS, vol. 26(1), pages 86-110, February.
    10. Nicholas G. Hall & Wieslaw Kubiak & Suresh P. Sethi, 1991. "Earliness–Tardiness Scheduling Problems, II: Deviation of Completion Times About a Restrictive Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 847-856, October.
    11. Boysen, Nils & Emde, Simon & Hoeck, Michael & Kauderer, Markus, 2015. "Part logistics in the automotive industry: Decision problems, literature review and research agenda," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 79443, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    12. Biskup, Dirk, 2008. "A state-of-the-art review on scheduling with learning effects," European Journal of Operational Research, Elsevier, vol. 188(2), pages 315-329, July.
    13. Michael R. Garey & Robert E. Tarjan & Gordon T. Wilfong, 1988. "One-Processor Scheduling with Symmetric Earliness and Tardiness Penalties," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 330-348, May.
    14. 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.
    15. 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.
    16. Nicholas G. Hall & Marc E. Posner, 1991. "Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date," Operations Research, INFORMS, vol. 39(5), pages 836-846, October.
    17. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, 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. Helmut A. Sedding, 2020. "Scheduling jobs with a V-shaped time-dependent processing time," Journal of Scheduling, Springer, vol. 23(6), pages 751-768, December.
    2. 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. Helmut A. Sedding, 2020. "Scheduling jobs with a V-shaped time-dependent processing time," Journal of Scheduling, Springer, vol. 23(6), pages 751-768, December.
    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. Dar-Li Yang & Wen-Hung Kuo, 2009. "Single-machine scheduling with both deterioration and learning effects," Annals of Operations Research, Springer, vol. 172(1), pages 315-327, November.
    4. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    5. 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.
    6. Boysen, Nils & Schulze, Philipp & Scholl, Armin, 2022. "Assembly line balancing: What happened in the last fifteen years?," European Journal of Operational Research, Elsevier, vol. 301(3), pages 797-814.
    7. 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.
    8. 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.
    9. Baals, Julian & Emde, Simon & Turkensteen, Marcel, 2023. "Minimizing earliness-tardiness costs in supplier networks—A just-in-time truck routing problem," European Journal of Operational Research, Elsevier, vol. 306(2), pages 707-741.
    10. 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.
    11. Qian, Jianbo & Steiner, George, 2013. "Fast algorithms for scheduling with learning effects and time-dependent processing times on a single machine," European Journal of Operational Research, Elsevier, vol. 225(3), pages 547-551.
    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. 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.
    14. Wang, Xiuli & Edwin Cheng, T.C., 2007. "Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 178(1), pages 57-70, April.
    15. Xing Chai & Wenhua Li & Hang Yuan & Libo Wang, 0. "Online scheduling on a single machine with linear deteriorating processing times and delivery times," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.
    16. Delorme, Maxence & Iori, Manuel & Mendes, Nilson F.M., 2021. "Solution methods for scheduling problems with sequence-dependent deterioration and maintenance events," European Journal of Operational Research, Elsevier, vol. 295(3), pages 823-837.
    17. Xing Chai & Wenhua Li & Hang Yuan & Libo Wang, 2022. "Online scheduling on a single machine with linear deteriorating processing times and delivery times," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1900-1912, October.
    18. Ocetkiewicz, Krzysztof M., 2010. "A FPTAS for minimizing total completion time in a single machine time-dependent scheduling problem," European Journal of Operational Research, Elsevier, vol. 203(2), pages 316-320, June.
    19. Cheng, Yushao & Sun, Shijie, 2009. "Scheduling linear deteriorating jobs with rejection on a single machine," European Journal of Operational Research, Elsevier, vol. 194(1), pages 18-27, April.
    20. W-H Kuo & D-L Yang, 2011. "A note on due-date assignment and single-machine scheduling with deteriorating jobs and learning effects," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 206-210, January.

    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:jsched:v:19:y:2016:i:6:d:10.1007_s10951-016-0472-2. 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.