IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v122y2024ics0305048323001226.html
   My bibliography  Save this article

Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine

Author

Listed:
  • Zhang, Hongbin
  • Yang, Yu
  • Wu, Feng

Abstract

We investigate a general single-batch-processing machine scheduling problem of minimizing the total costs of all jobs with general convex piecewise linear cost functions, where the processing time, due dates, and sizes of jobs are non-uniform. Since the studied problem is NP-hard and the objective is irregular, we adopt a practical 3-step method that starts from a specific job sequence, finds the optimal and near-optimal schedules of the given job sequence, and then iteratively improves the schedules. For the restricted problem where the job sequence is given, we propose a dynamic programming algorithm to obtain the optimal schedule. To further reduce the running time, we also devise a span-limit tree search (SLTS) approach to find the near-optimal schedule. We then design a local search method to improve the solutions solved by SLTS. Finally, we design a branch and bound algorithm with a lower bound method for small-sized instances. All proposed methods are based on our analysis of the mathematical properties of the scheduling problem, and extensive numerical experiments are conducted to demonstrate their effectiveness and efficiency.

Suggested Citation

  • Zhang, Hongbin & Yang, Yu & Wu, Feng, 2024. "Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine," Omega, Elsevier, vol. 122(C).
    • Handle: RePEc:eee:jomega:v:122:y:2024:i:c:s0305048323001226
    DOI: 10.1016/j.omega.2023.102958
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048323001226
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2023.102958?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. Polyakovskiy, Sergey & M’Hallah, Rym, 2021. "Just-in-time two-dimensional bin packing," Omega, Elsevier, vol. 102(C).
    2. 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.
    3. Damodaran, Purushothaman & Kumar Manjeshwar, Praveen & Srihari, Krishnaswami, 2006. "Minimizing makespan on a batch-processing machine with non-identical job sizes using genetic algorithms," International Journal of Production Economics, Elsevier, vol. 103(2), pages 882-891, October.
    4. Lixin Tang & Hua Gong & Jiyin Liu & Feng Li, 2014. "Bicriteria scheduling on a single batching machine with job transportation and deterioration considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 269-285, June.
    5. Francis Sourd, 2004. "The Continuous Assignment Problem and Its Application to Preemptive and Non-Preemptive Scheduling with Irregular Cost Functions," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 198-208, May.
    6. Bayi Cheng & Shanlin Yang & Ying Ma, 2012. "Minimising makespan for two batch-processing machines with non-identical job sizes in job shop," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(12), pages 2185-2192.
    7. Guochuan Zhang & Xiaoqiang Cai & C.‐Y Lee & C.K Wong, 2001. "Minimizing makespan on a single batch processing machine with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 226-240, April.
    8. Juan Pablo Vielma & Shabbir Ahmed & George Nemhauser, 2010. "Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions," Operations Research, INFORMS, vol. 58(2), pages 303-315, April.
    9. Artur Alves Pessoa & Teobaldo Bulhões & Vitor Nesello & Anand Subramanian, 2022. "Exact Approaches for Single Machine Total Weighted Tardiness Batch Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1512-1530, May.
    10. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    11. Lixin Tang & Ying Meng & Zhi-Long Chen & Jiyin Liu, 2016. "Coil Batching to Improve Productivity and Energy Utilization in Steel Production," Manufacturing & Service Operations Management, INFORMS, vol. 18(2), pages 262-279, May.
    12. XiaoLin Li & YuPeng Li & Yu Wang, 2017. "Minimising makespan on a batch processing machine using heuristics improved by an enumeration scheme," International Journal of Production Research, Taylor & Francis Journals, vol. 55(1), pages 176-186, January.
    13. Javad H. Ahmadi & Reza H. Ahmadi & Sriram Dasu & Christopher S. Tang, 1992. "Batching and Scheduling Jobs on Batch and Discrete Processors," Operations Research, INFORMS, vol. 40(4), pages 750-763, August.
    14. Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2003. "A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems," Management Science, INFORMS, vol. 49(9), pages 1268-1273, September.
    15. Santha Raja Kumari Upadhyayula & Shanthi Muthuswamy & Purushothaman Damodaran, 2022. "A simulated annealing approach to minimise makespan in a hybrid flowshop with a batch processing machine," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 40(4), pages 513-532.
    16. Zhang, Han & Li, Kai & Jia, Zhao-hong & Chu, Chengbin, 2023. "Minimizing total completion time on non-identical parallel batch machines with arbitrary release times using ant colony optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1024-1046.
    17. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    18. Tang, Lixin & Zhao, Yufang, 2008. "Scheduling a single semi-continuous batching machine," Omega, Elsevier, vol. 36(6), pages 992-1004, December.
    19. Kellerer, Hans & Rustogi, Kabir & Strusevich, Vitaly A., 2020. "A fast FPTAS for single machine scheduling problem of minimizing total weighted earliness and tardiness about a large common due date," Omega, Elsevier, vol. 90(C).
    20. Malapert, Arnaud & Guéret, Christelle & Rousseau, Louis-Martin, 2012. "A constraint programming approach for a batch processing problem with non-identical job sizes," European Journal of Operational Research, Elsevier, vol. 221(3), pages 533-545.
    21. Ruilin Pan & Qiong Wang & Zhenghong Li & Jianhua Cao & Yongjin Zhang, 2022. "Steelmaking-continuous casting scheduling problem with multi-position refining furnaces under time-of-use tariffs," Annals of Operations Research, Springer, vol. 310(1), pages 119-151, March.
    22. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, February.
    23. Husseinzadeh Kashan, Ali & Ozturk, Onur, 2022. "Improved MILP formulation equipped with valid inequalities for scheduling a batch processing machine with non-identical job sizes," Omega, Elsevier, vol. 112(C).
    24. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
    25. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    26. Arbib, Claudio & Marinelli, Fabrizio, 2017. "Maximum lateness minimization in one-dimensional bin packing," Omega, Elsevier, vol. 68(C), pages 76-84.
    27. SOUSA, Jorge P. & WOLSEY, Laurence A., 1992. "A time indexed formulation of non-preemptive single machine scheduling problems," LIDAM Reprints CORE 984, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    28. Hendel, Yann & Sourd, Francis, 2006. "Efficient neighborhood search for the one-machine earliness-tardiness scheduling problem," European Journal of Operational Research, Elsevier, vol. 173(1), pages 108-119, August.
    29. Alidaee, Bahram & Li, Haitao & Wang, Haibo & Womer, Keith, 2021. "Integer programming formulations in sequencing with total earliness and tardiness penalties, arbitrary due dates, and no idle time: A concise review and extension," Omega, Elsevier, vol. 103(C).
    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. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    2. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    3. Husseinzadeh Kashan, Ali & Ozturk, Onur, 2022. "Improved MILP formulation equipped with valid inequalities for scheduling a batch processing machine with non-identical job sizes," Omega, Elsevier, vol. 112(C).
    4. Artur Alves Pessoa & Teobaldo Bulhões & Vitor Nesello & Anand Subramanian, 2022. "Exact Approaches for Single Machine Total Weighted Tardiness Batch Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1512-1530, May.
    5. Lin, Ran & Wang, Jun-Qiang & Oulamara, Ammar, 2023. "Online scheduling on parallel-batch machines with periodic availability constraints and job delivery," Omega, Elsevier, vol. 116(C).
    6. Sang, Yao-Wen & Wang, Jun-Qiang & Sterna, Małgorzata & Błażewicz, Jacek, 2023. "Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work," Omega, Elsevier, vol. 121(C).
    7. Alidaee, Bahram & Li, Haitao & Wang, Haibo & Womer, Keith, 2021. "Integer programming formulations in sequencing with total earliness and tardiness penalties, arbitrary due dates, and no idle time: A concise review and extension," Omega, Elsevier, vol. 103(C).
    8. Jun-Qiang Wang & Guo-Qiang Fan & Zhixin Liu, 2020. "Mixed batch scheduling on identical machines," Journal of Scheduling, Springer, vol. 23(4), pages 487-496, August.
    9. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Discussion Paper 2008-100, Tilburg University, Center for Economic Research.
    10. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    11. Tang, Lixin & Zhao, Yufang, 2008. "Scheduling a single semi-continuous batching machine," Omega, Elsevier, vol. 36(6), pages 992-1004, December.
    12. Lin, Ran & Wang, Jun-Qiang & Liu, Zhixin & Xu, Jun, 2023. "Best possible algorithms for online scheduling on identical batch machines with periodic pulse interruptions," European Journal of Operational Research, Elsevier, vol. 309(1), pages 53-64.
    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. Zhou, Shengchao & Jin, Mingzhou & Du, Ni, 2020. "Energy-efficient scheduling of a single batch processing machine with dynamic job arrival times," Energy, Elsevier, vol. 209(C).
    15. Kedad-Sidhoum, Safia & Solis, Yasmin Rios & Sourd, Francis, 2008. "Lower bounds for the earliness-tardiness scheduling problem on parallel machines with distinct due dates," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1305-1316, September.
    16. Chung Keung Poon & Wenci Yu, 2005. "On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 167-186, March.
    17. Li, Shuguang, 2017. "Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan," European Journal of Operational Research, Elsevier, vol. 260(1), pages 12-20.
    18. Lin, B.M.T. & Cheng, T.C.E. & Chou, A.S.C., 2007. "Scheduling in an assembly-type production chain with batch transfer," Omega, Elsevier, vol. 35(2), pages 143-151, April.
    19. Xu, Rui & Chen, Huaping & Li, Xueping, 2013. "A bi-objective scheduling problem on batch machines via a Pareto-based ant colony system," International Journal of Production Economics, Elsevier, vol. 145(1), pages 371-386.
    20. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Other publications TiSEM ed1f8fce-da76-41a6-9a9e-9, Tilburg University, School of Economics and Management.

    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:jomega:v:122:y:2024:i:c:s0305048323001226. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.