IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v196y2018icp113-121.html
   My bibliography  Save this article

Single batch processing machine scheduling with two-dimensional bin packing constraints

Author

Listed:
  • Li, Xueping
  • Zhang, Kaike

Abstract

We study the problem of minimizing the makespan for jobs on a single batch processing machine (BPM). A BMP can process several jobs as a batch simultaneously. Unlike the classic batch processing machine scheduling problems in which the capacity of a machine is modeled as one-dimensional knapsack constraints, in this research, the machine's capacity is represented by a two-dimensional rectangle and a job occupies a rectangle of its dimensions, i.e., width and height, while being processed on the machine. The processing time and the dimensions of the jobs are non-identical. A batch's processing time equals to the longest processing time of jobs in the batch. A batch is feasible only if the jobs can be placed in the machine without overlapping with each other. Arising from practical industrial applications such as advanced manufacturing and wafer fabrication, this problem is a generalization of both the classic single BPM scheduling problem and the two-dimensional bin packing problem (2D-BPP), which are both proven to be NP-hard. Thus, it is NP-hard as well. We present a mixed integer programming (MIP) model for this problem. We also develop heuristic algorithms to tackle this problem, including four single-sequence based heuristics, a biased random-key genetic algorithm (BRKGA), and a hybrid bin loading (HBL) algorithm. The performances of the MIP model and proposed algorithms are compared based on a set of random generated instances.

Suggested Citation

  • Li, Xueping & Zhang, Kaike, 2018. "Single batch processing machine scheduling with two-dimensional bin packing constraints," International Journal of Production Economics, Elsevier, vol. 196(C), pages 113-121.
    • Handle: RePEc:eee:proeco:v:196:y:2018:i:c:p:113-121
    DOI: 10.1016/j.ijpe.2017.11.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527317303997
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2017.11.015?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. Gregory Dobson & Ramakrishnan S. Nambimadom, 2001. "The Batch Loading and Scheduling Problem," Operations Research, INFORMS, vol. 49(1), pages 52-65, February.
    2. Jolai Ghazvini, Fariborz & Dupont, Lionel, 1998. "Minimizing mean flow times criteria on a single batch processing machine with non-identical jobs sizes," International Journal of Production Economics, Elsevier, vol. 55(3), pages 273-280, 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. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    5. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    6. Melouk, Sharif & Damodaran, Purushothaman & Chang, Ping-Yu, 2004. "Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing," International Journal of Production Economics, Elsevier, vol. 87(2), pages 141-147, January.
    7. Andrea Lodi & Silvano Martello & Daniele Vigo, 1999. "Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 345-357, November.
    8. Thiago Noronha & Mauricio Resende & Celso Ribeiro, 2011. "A biased random-key genetic algorithm for routing and wavelength assignment," Journal of Global Optimization, Springer, vol. 50(3), pages 503-518, July.
    9. 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.
    10. Gonçalves, José Fernando & Resende, Mauricio G.C., 2013. "A biased random key genetic algorithm for 2D and 3D bin packing problems," International Journal of Production Economics, Elsevier, vol. 145(2), pages 500-510.
    11. Bennell, Julia A. & Soon Lee, Lai & Potts, Chris N., 2013. "A genetic algorithm for two-dimensional bin packing with due dates," International Journal of Production Economics, Elsevier, vol. 145(2), pages 547-560.
    12. James C. Bean, 1994. "Genetic Algorithms and Random Keys for Sequencing and Optimization," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 154-160, May.
    13. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
    14. 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.
    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. Jae Won Jang & Yong Jae Kim & Byung Soo Kim, 2022. "A Three-Stage ACO-Based Algorithm for Parallel Batch Loading and Scheduling Problem with Batch Deterioration and Rate-Modifying Activities," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    2. Ozturk, Onur, 2020. "A truncated column generation algorithm for the parallel batch scheduling problem to minimize total flow time," European Journal of Operational Research, Elsevier, vol. 286(2), pages 432-443.
    3. Altekin, F. Tevhide & Bukchin, Yossi, 2022. "A multi-objective optimization approach for exploring the cost and makespan trade-off in additive manufacturing," European Journal of Operational Research, Elsevier, vol. 301(1), pages 235-253.
    4. Oğuzhan Ahmet Arık, 2022. "Additive manufacturing scheduling problem considering assembly operations of parts," Operational Research, Springer, vol. 22(3), pages 3063-3087, July.
    5. 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.
    6. Wang, Mengyao & Zhou, Chenhao & Wang, Aihu, 2022. "A cluster-based yard template design integrated with yard crane deployment using a placement heuristic," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 160(C).
    7. Xiaoyu Yu & Jingyi Qian & Yajing Zhang & Min Kong, 2023. "Supply Chain Scheduling Method for the Coordination of Agile Production and Port Delivery Operation," Mathematics, MDPI, vol. 11(15), pages 1-24, July.
    8. Jianxin Fang & Brenda Cheang & Andrew Lim, 2023. "Problems and Solution Methods of Machine Scheduling in Semiconductor Manufacturing Operations: A Survey," Sustainability, MDPI, vol. 15(17), pages 1-44, August.
    9. Gur Mosheiov & Daniel Oron, 2023. "A note on batch scheduling on a two-machine flowshop with machine-dependent processing times," 4OR, Springer, vol. 21(3), pages 457-469, September.

    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. Bayliss, Christopher & Currie, Christine S.M. & Bennell, Julia A. & Martinez-Sykora, Antonio, 2021. "Queue-constrained packing: A vehicle ferry case study," European Journal of Operational Research, Elsevier, vol. 289(2), pages 727-741.
    3. Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.
    4. Nestor M Cid-Garcia & Yasmin A Rios-Solis, 2020. "Positions and covering: A two-stage methodology to obtain optimal solutions for the 2d-bin packing problem," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-22, April.
    5. Gonçalves, José Fernando & Wäscher, Gerhard, 2020. "A MIP model and a biased random-key genetic algorithm based approach for a two-dimensional cutting problem with defects," European Journal of Operational Research, Elsevier, vol. 286(3), pages 867-882.
    6. 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.
    7. A H Kashan & B Karimi, 2008. "Scheduling a single batch-processing machine with arbitrary job sizes and incompatible job families: An ant colony framework," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1269-1280, September.
    8. Polyakovsky, Sergey & M'Hallah, Rym, 2009. "An agent-based approach to the two-dimensional guillotine bin packing problem," European Journal of Operational Research, Elsevier, vol. 192(3), pages 767-781, February.
    9. Bennell, Julia A. & Soon Lee, Lai & Potts, Chris N., 2013. "A genetic algorithm for two-dimensional bin packing with due dates," International Journal of Production Economics, Elsevier, vol. 145(2), pages 547-560.
    10. Önder Aşık & Ender Özcan, 2009. "Bidirectional best-fit heuristic for orthogonal rectangular strip packing," Annals of Operations Research, Springer, vol. 172(1), pages 405-427, November.
    11. Jia, Zhao-hong & Leung, Joseph Y.-T., 2015. "A meta-heuristic to minimize makespan for parallel batch machines with arbitrary job sizes," European Journal of Operational Research, Elsevier, vol. 240(3), pages 649-665.
    12. Francisco Trespalacios & Ignacio E. Grossmann, 2017. "Symmetry breaking for generalized disjunctive programming formulation of the strip packing problem," Annals of Operations Research, Springer, vol. 258(2), pages 747-759, November.
    13. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).
    14. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    15. Gregory S. Taylor & Yupo Chan & Ghulam Rasool, 2017. "A three-dimensional bin-packing model: exact multicriteria solution and computational complexity," Annals of Operations Research, Springer, vol. 251(1), pages 397-427, April.
    16. Andrade, Carlos E. & Toso, Rodrigo F. & Gonçalves, José F. & Resende, Mauricio G.C., 2021. "The Multi-Parent Biased Random-Key Genetic Algorithm with Implicit Path-Relinking and its real-world applications," European Journal of Operational Research, Elsevier, vol. 289(1), pages 17-30.
    17. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    18. M. Muntazir Mehdi & Le Wang & Sean P. Willems, 2022. "Developing a Maximum Inscribed Rectangle Heuristic to Satisfy Rush Orders for Heavy Plate Steel," Interfaces, INFORMS, vol. 52(3), pages 283-294, May.
    19. Gonçalves, José Fernando & Resende, Mauricio G.C., 2015. "A biased random-key genetic algorithm for the unequal area facility layout problem," European Journal of Operational Research, Elsevier, vol. 246(1), pages 86-107.
    20. F. Stefanello & L. S. Buriol & M. J. Hirsch & P. M. Pardalos & T. Querido & M. G. C. Resende & M. Ritt, 2017. "On the minimization of traffic congestion in road networks with tolls," Annals of Operations Research, Springer, vol. 249(1), pages 119-139, February.

    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:196:y:2018:i:c:p:113-121. 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.