IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v135y2012i1p231-241.html
   My bibliography  Save this article

Scheduling jobs with values dependent on their completion times

Author

Listed:
  • Janiak, Adam
  • Krysiak, Tomasz

Abstract

The paper concerns two scheduling problems with job values and losses of job values (costs) dependent on job completion times. In the first problem, we consider scheduling jobs with stepwise values in parallel processor environment. In the stepwise value, there is given a number of moments at which the job value decreases and between them the job value is constant (thus, the value deteriorates over time). The maximized criterion is the total job value. We prove strong NP-hardness of a single processor case of the problem and construct a pseudo-polynomial time algorithm for a special case with fixed number of unrelated parallel processors and fixed number of common moments of job value changes. Additionally, for uniform and unrelated parallel processors we construct and experimentally test several heuristic algorithms based on the list strategy. The second problem is a single processor one with piecewise linear losses of job values (the loss increases over time). The minimized criterion is the total loss of job value. We prove strong NP-hardness of the problem and existence of a pseudo-polynomial time exact algorithm for its special case. We also construct some heuristic algorithms for this problem and verify experimentally their efficiency.

Suggested Citation

  • Janiak, Adam & Krysiak, Tomasz, 2012. "Scheduling jobs with values dependent on their completion times," International Journal of Production Economics, Elsevier, vol. 135(1), pages 231-241.
    • Handle: RePEc:eee:proeco:v:135:y:2012:i:1:p:231-241
    DOI: 10.1016/j.ijpe.2011.07.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S092552731100315X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2011.07.014?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. Wang, Xiuli & Cheng, T.C.E., 2009. "Logistics scheduling to minimize inventory and transport costs," International Journal of Production Economics, Elsevier, vol. 121(1), pages 266-273, September.
    2. Voutsinas, Theodore G. & Pappis, Costas P., 2002. "Scheduling jobs with values exponentially deteriorating over time," International Journal of Production Economics, Elsevier, vol. 79(3), pages 163-169, October.
    3. Bachman, Aleksander & Janiak, Adam, 2000. "Minimizing maximum lateness under linear deterioration," European Journal of Operational Research, Elsevier, vol. 126(3), pages 557-566, November.
    4. J. Michael Moore, 1968. "An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs," Management Science, INFORMS, vol. 15(1), pages 102-109, September.
    5. 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.
    6. Shabtay, Dvir, 2010. "Scheduling and due date assignment to minimize earliness, tardiness, holding, due date assignment and batch delivery costs," International Journal of Production Economics, Elsevier, vol. 123(1), pages 235-242, January.
    7. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 131(2), pages 747-751, June.
    8. Inderfurth, Karl & Kovalyov, Mikhail Y. & Ng, C.T. & Werner, Frank, 2007. "Cost minimizing scheduling of work and rework processes on a single facility under deterioration of reworkables," International Journal of Production Economics, Elsevier, vol. 105(2), pages 345-356, February.
    9. Sourd, Francis, 2005. "Optimal timing of a sequence of tasks with general completion costs," European Journal of Operational Research, Elsevier, vol. 165(1), pages 82-96, August.
    10. 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.
    11. Janiak, Adam & Krysiak, Tomasz & Pappis, Costas P. & Voutsinas, Theodore G., 2009. "A scheduling problem with job values given as a power function of their completion times," European Journal of Operational Research, Elsevier, vol. 193(3), pages 836-848, March.
    12. Mafakheri, Fereshteh & Breton, Michele & Ghoniem, Ahmed, 2011. "Supplier selection-order allocation: A two-stage multiple criteria dynamic programming approach," International Journal of Production Economics, Elsevier, vol. 132(1), pages 52-57, July.
    13. A. H. G. Rinnooy Kan & B. J. Lageweg & J. K. Lenstra, 1975. "Minimizing Total Costs in One-Machine Scheduling," Operations Research, INFORMS, vol. 23(5), pages 908-927, October.
    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. Nikos P. Rachaniotis & Theodore G. Voutsinas & Costas P. Pappis, 2013. "Scheduling periodic preventive maintenance with a single server in a finite horizon," International Journal of Decision Sciences, Risk and Management, Inderscience Enterprises Ltd, vol. 5(1), pages 80-87.
    2. Li, Gang & Wang, Xiao-Yuan & Wang, Ji-Bo & Sun, Lin-Yan, 2013. "Worst case analysis of flow shop scheduling problems with a time-dependent learning effect," International Journal of Production Economics, Elsevier, vol. 142(1), pages 98-104.

    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. Sun, Lin-Hui & Sun, Lin-Yan & Wang, Ming-Zheng & Wang, Ji-Bo, 2012. "Flow shop makespan minimization scheduling with deteriorating jobs under dominating machines," International Journal of Production Economics, Elsevier, vol. 138(1), pages 195-200.
    2. Zhao, Chuanli & Tang, Hengyong, 2012. "Two-machine flow shop scheduling with deteriorating jobs and chain precedence constraints," International Journal of Production Economics, Elsevier, vol. 136(1), pages 131-136.
    3. 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.
    4. Su, Ling-Huey & Tien, Yi-Yu, 2011. "Minimizing mean absolute deviation of completion time about a common due window subject to maximum tardiness for a single machine," International Journal of Production Economics, Elsevier, vol. 134(1), pages 196-203, November.
    5. 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.
    6. Janiak, Adam & Krysiak, Tomasz & Pappis, Costas P. & Voutsinas, Theodore G., 2009. "A scheduling problem with job values given as a power function of their completion times," European Journal of Operational Research, Elsevier, vol. 193(3), pages 836-848, March.
    7. Wen-Chiung Lee, 2004. "A Note on Deteriorating Jobs and Learning in Single-Machine Scheduling Problems," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 3(1), pages 83-89, April.
    8. Nikos P. Rachaniotis & Theodore G. Voutsinas & Costas P. Pappis, 2013. "Scheduling periodic preventive maintenance with a single server in a finite horizon," International Journal of Decision Sciences, Risk and Management, Inderscience Enterprises Ltd, vol. 5(1), pages 80-87.
    9. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    10. Huo, Yumei & Leung, Joseph Y.-T. & Zhao, Hairong, 2007. "Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness," European Journal of Operational Research, Elsevier, vol. 177(1), pages 116-134, February.
    11. Xingong, Zhang & Yong, Wang, 2015. "Single-machine scheduling CON/SLK due window assignment problems with sum-of-processed times based learning effect," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 628-635.
    12. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 131(2), pages 747-751, June.
    13. Ben-Daya, M. & Duffuaa, S. O. & Raouf, A., 1996. "Minimizing mean tardiness subject to unspecified minimum number tardy for a single machine," European Journal of Operational Research, Elsevier, vol. 89(1), pages 100-107, February.
    14. W-H Kuo & D-L Yang, 2008. "A note on due-date assignment and single-machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 857-859, June.
    15. Scott, James & Ho, William & Dey, Prasanta K. & Talluri, Srinivas, 2015. "A decision support system for supplier selection and order allocation in stochastic, multi-stakeholder and multi-criteria environments," International Journal of Production Economics, Elsevier, vol. 166(C), pages 226-237.
    16. 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.
    17. Gupta, Jatinder N. D. & Ho, Johnny C., 1996. "Scheduling with two job classes and setup times to minimize the number of tardy jobs," International Journal of Production Economics, Elsevier, vol. 42(3), pages 205-216, April.
    18. 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.
    19. Du-Juan Wang & Yunqiang Yin & Shuenn-Ren Cheng & T.C.E. Cheng & Chin-Chia Wu, 2016. "Due date assignment and scheduling on a single machine with two competing agents," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1152-1169, February.
    20. 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.

    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:proeco:v:135:y:2012:i:1:p:231-241. 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/ijpe .

    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.