IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v296y2022i2p423-439.html
   My bibliography  Save this article

Single-machine scheduling with machine unavailability periods and resource dependent processing times

Author

Listed:
  • Shabtay, Dvir

Abstract

We study a single-machine scheduling problem, where each of the job processing times is a bounded linear decreasing function of the amount of resource allocated to its processing operation, and there is a single and fixed machine-unavailability interval that begins at time T. A solution is given by (i) partitioning the jobs into two sets, corresponding to the set of jobs to be processed before and after the unavailability period; and (ii) defining the amount of resource allocated to the processing operation of each of the jobs. A solution is feasible if the total processing time of all jobs assigned to be processed before the unavailability period does not exceed T. Our aim is to find a feasible solution that minimizes the makespan plus the total resource consumption cost. As the problem is known to be NP-hard even for constant processing times, we focus on the design of pseudo-polynomial time and approximation algorithms. Extension to the case of a fixed number of unavailability intervals is also provided.

Suggested Citation

  • Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    • Handle: RePEc:eee:ejores:v:296:y:2022:i:2:p:423-439
    DOI: 10.1016/j.ejor.2021.03.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721002605
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.03.034?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. Allaoui, H. & Artiba, A. & Elmaghraby, S.E. & Riane, F., 2006. "Scheduling of a two-machine flowshop with availability constraints on the first machine," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 16-27, February.
    2. J. Breit & G. Schmidt & V. A. Strusevich, 2003. "Non-preemptive two-machine open shop scheduling with non-availability constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 217-234, May.
    3. Oron, Daniel, 2016. "Scheduling controllable processing time jobs with position-dependent workloads," International Journal of Production Economics, Elsevier, vol. 173(C), pages 153-160.
    4. Nowicki, Eugeniusz & Zdrzalka, Stanislaw, 1988. "A two-machine flow shop scheduling problem with controllable job processing times," European Journal of Operational Research, Elsevier, vol. 34(2), pages 208-220, March.
    5. Dvir Shabtay & Omri Dover & Moshe Kaspi, 2015. "Single-machine two-agent scheduling involving a just-in-time criterion," International Journal of Production Research, Taylor & Francis Journals, vol. 53(9), pages 2590-2604, May.
    6. Janiak, Adam & Kovalyov, Mikhail Y. & Kubiak, Wieslaw & Werner, Frank, 2005. "Positive half-products and scheduling with controllable processing times," European Journal of Operational Research, Elsevier, vol. 165(2), pages 416-422, September.
    7. Chung-Yee Lee & Lei Lei, 2001. "Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases," Annals of Operations Research, Springer, vol. 102(1), pages 287-307, February.
    8. Yang, Dar-Li & Lai, Chien-Jung & Yang, Suh-Jenq, 2014. "Scheduling problems with multiple due windows assignment and controllable processing times on a single machine," International Journal of Production Economics, Elsevier, vol. 150(C), pages 96-103.
    9. Kacem, Imed & Chu, Chengbin, 2008. "Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint," International Journal of Production Economics, Elsevier, vol. 112(1), pages 138-150, March.
    10. Liao, Ching-Jong & Shyur, Der-Lin & Lin, Chien-Hung, 2005. "Makespan minimization for two parallel machines with an availability constraint," European Journal of Operational Research, Elsevier, vol. 160(2), pages 445-456, January.
    11. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    12. Breit, Joachim, 2007. "Improved approximation for non-preemptive single machine flow-time scheduling with an availability constraint," European Journal of Operational Research, Elsevier, vol. 183(2), pages 516-524, December.
    13. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    14. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    15. C. Ng & T. Cheng & Adam Janiak & Mikhail Kovalyov, 2005. "Group Scheduling with Controllable Setup and Processing Times: Minimizing Total Weighted Completion Time," Annals of Operations Research, Springer, vol. 133(1), pages 163-174, January.
    16. Michael A. Trick, 1994. "Scheduling Multiple Variable-Speed Machines," Operations Research, INFORMS, vol. 42(2), pages 234-248, April.
    17. Janiak, Adam & Kovalyov, Mikhail Y., 1996. "Single machine scheduling subject to deadlines and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 94(2), pages 284-291, October.
    18. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    19. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
    20. Shabtay, Dvir & Bensoussan, Yaron & Kaspi, Moshe, 2012. "A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 67-74.
    21. Liu, Peihai & Lu, Xiwen, 2016. "Integrated production and job delivery scheduling with an availability constraint," International Journal of Production Economics, Elsevier, vol. 176(C), pages 1-6.
    22. Sadfi, Cherif & Penz, Bernard & Rapine, Christophe & Blazewicz, Jacek & Formanowicz, Piotr, 2005. "An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints," European Journal of Operational Research, Elsevier, vol. 161(1), pages 3-10, February.
    23. Kayan, Rabia K. & Akturk, M. Selim, 2005. "A new bounding mechanism for the CNC machine scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(3), pages 624-643, December.
    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. Shi-Sheng Li & Ren-Xia Chen, 2022. "Minimizing total weighted late work on a single-machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1330-1355, September.
    2. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.

    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. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    2. Yaron Leyvand & Dvir Shabtay & George Steiner & Liron Yedidsion, 2010. "Just-in-time scheduling with controllable processing times on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 347-368, April.
    3. Leyvand, Yaron & Shabtay, Dvir & Steiner, George, 2010. "A unified approach for scheduling with convex resource consumption functions using positional penalties," European Journal of Operational Research, Elsevier, vol. 206(2), pages 301-312, October.
    4. 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.
    5. Yim, Seho & Hong, Sung-Pil & Park, Myoung-Ju & Chung, Yerim, 2022. "Inverse interval scheduling via reduction on a single machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 541-549.
    6. Shabtay, Dvir & Bensoussan, Yaron & Kaspi, Moshe, 2012. "A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 67-74.
    7. Dvir Shabtay & George Steiner, 2007. "Optimal Due Date Assignment and Resource Allocation to Minimize the Weighted Number of Tardy Jobs on a Single Machine," Manufacturing & Service Operations Management, INFORMS, vol. 9(3), pages 332-350, March.
    8. Seyed Habib A. Rahmati & Abbas Ahmadi & Kannan Govindan, 2018. "A novel integrated condition-based maintenance and stochastic flexible job shop scheduling problem: simulation-based optimization approach," Annals of Operations Research, Springer, vol. 269(1), pages 583-621, October.
    9. Hans Kellerer & Vitaly A. Strusevich, 2016. "Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications," Annals of Operations Research, Springer, vol. 240(1), pages 39-94, May.
    10. Kellerer, Hans & Kubzin, Mikhail A. & Strusevich, Vitaly A., 2009. "Two simple constant ratio approximation algorithms for minimizing the total weighted completion time on a single machine with a fixed non-availability interval," European Journal of Operational Research, Elsevier, vol. 199(1), pages 111-116, November.
    11. Kacem, Imed & Chu, Chengbin, 2008. "Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint," International Journal of Production Economics, Elsevier, vol. 112(1), pages 138-150, March.
    12. Jing Fan & Xiwen Lu, 2015. "Supply chain scheduling problem in the hospital with periodic working time on a single machine," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 892-905, November.
    13. 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.
    14. Dvir Shabtay & Moshe Kaspi, 2006. "Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 204-216, April.
    15. Dujuan Wang & Yunqiang Yin & T.C.E. Cheng, 2017. "A bicriterion approach to common flow allowances due window assignment and scheduling with controllable processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 41-63, February.
    16. Oron, Daniel, 2016. "Scheduling controllable processing time jobs with position-dependent workloads," International Journal of Production Economics, Elsevier, vol. 173(C), pages 153-160.
    17. Yunqiang Yin & Du-Juan Wang & T C E Cheng & Chin-Chia Wu, 2016. "Bi-criterion single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(9), pages 1169-1183, September.
    18. Byung-Cheon Choi & Myoung-Ju Park, 2022. "Single-machine scheduling with resource-dependent processing times and multiple unavailability periods," Journal of Scheduling, Springer, vol. 25(2), pages 191-202, April.
    19. Choi, Byung-Cheon & Yoon, Suk-Hun & Chung, Sung-Jin, 2007. "Single machine scheduling problem with controllable processing times and resource dependent release times," European Journal of Operational Research, Elsevier, vol. 181(2), pages 645-653, September.
    20. Shi-Sheng Li & Ren-Xia Chen, 2022. "Minimizing total weighted late work on a single-machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1330-1355, September.

    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:296:y:2022:i:2:p:423-439. 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.