IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v58y2011i4p370-388.html
   My bibliography  Save this article

A combination of Lagrangian relaxation and column generation for order batching in steelmaking and continuous‐casting production

Author

Listed:
  • Lixin Tang
  • Gongshu Wang
  • Jiyin Liu
  • Jingyi Liu

Abstract

This article considers the order batching problem in steelmaking and continuous‐casting production. The problem is to jointly specify the slabs needed to satisfy each customer order and group all the slabs of different customer orders into production batches. A novel mixed integer programming model is formulated for the problem. Through relaxing the order assignment constraints, a Lagrangian relaxation model is then obtained. By exploiting the relationship between Lagrangian relaxation and column generation, we develop a combined algorithm that contains nested double loops. At the inner loop, the subgradient method is applied for approximating the Lagrangian dual problem and pricing out columns of the master problem corresponding to the linear dual form of the Lagrangian dual problem. At the outer loop, column generation is employed to solve the master problem exactly and adjust Lagrangian multipliers. Computational experiments are carried out using real data collected from a large steel company, as well as on large‐scaled problem instances randomly generated. The results demonstrate that the combined algorithm can obtain tighter lower bound and higher quality solution within an acceptable computation time as compared to the conventional Lagrangian relaxation algorithm. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • Lixin Tang & Gongshu Wang & Jiyin Liu & Jingyi Liu, 2011. "A combination of Lagrangian relaxation and column generation for order batching in steelmaking and continuous‐casting production," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 370-388, June.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:4:p:370-388
    DOI: 10.1002/nav.20452
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20452
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20452?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
    ---><---

    References listed on IDEAS

    as
    1. Kerem Bülbül & Philip Kaminsky & Candace Yano, 2004. "Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 407-445, April.
    2. Klose, Andreas & Gortz, Simon, 2007. "A branch-and-price algorithm for the capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1109-1125, June.
    3. Zhi‐Long Chen & Warren B. Powell, 2003. "Exact algorithms for scheduling multiple families of jobs on parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 823-840, October.
    4. Ferretti, Ivan & Zanoni, Simone & Zavanella, Lucio, 2006. "Production-inventory scheduling using Ant System metaheuristic," International Journal of Production Economics, Elsevier, vol. 104(2), pages 317-326, December.
    5. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    6. Tang, Lixin & Wang, Gongshu, 2008. "Decision support system for the batching problems of steelmaking and continuous-casting production," Omega, Elsevier, vol. 36(6), pages 976-991, December.
    7. Mathur, Kamlesh & Venkateshan, Prahalad, 2007. "A new lower bound for the linear knapsack problem with general integer variables," European Journal of Operational Research, Elsevier, vol. 178(3), pages 738-754, May.
    8. Ojeong Kwon & Kyungsik Lee & Donghan Kang & Sungsoo Park, 2007. "A branch‐and‐price algorithm for a targeting problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 732-741, October.
    9. Zanoni, Simone & Zavanella, Lucio, 2005. "Model and analysis of integrated production-inventory system: The case of steel production," International Journal of Production Economics, Elsevier, vol. 93(1), pages 197-205, January.
    10. Tang, Lixin & Liu, Jiyin & Rong, Aiying & Yang, Zihou, 2000. "A mathematical programming model for scheduling steelmaking-continuous casting production," European Journal of Operational Research, Elsevier, vol. 120(2), pages 423-435, January.
    11. Şenay Ağca & Burak Eksioglu & Jay B. Ghosh, 2000. "Lagrangian solution of maximum dispersion problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 97-114, March.
    12. X. Zhao & P. B. Luh & J. Wang, 1999. "Surrogate Gradient Algorithm for Lagrangian Relaxation," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 699-712, March.
    13. Marjan van den Akker & Han Hoogeveen & Steef van de Velde, 2002. "Combining Column Generation and Lagrangean Relaxation to Solve a Single-Machine Common Due Date Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 37-51, February.
    14. Dennis Huisman & Raf Jans & Marc Peeters & Albert P.M. Wagelmans, 2005. "Combining Column Generation and Lagrangian Relaxation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 247-270, Springer.
    15. Richard E. Box & Donald G. Herbe, 1988. "A Scheduling Model for LTV Steel's Cleveland Works' Twin Strand Continuous Slab Caster," Interfaces, INFORMS, vol. 18(1), pages 42-56, February.
    16. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "A duality‐based relaxation and decomposition approach for inventory distribution systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 612-631, 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. Çağla Cergibozan & A. Serdar Tasan, 2019. "Order batching operations: an overview of classification, solution techniques, and future research," Journal of Intelligent Manufacturing, Springer, vol. 30(1), pages 335-349, January.
    2. 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.
    3. Lixin Tang & Gongshu Wang & Zhi-Long Chen, 2014. "Integrated Charge Batching and Casting Width Selection at Baosteel," Operations Research, INFORMS, vol. 62(4), pages 772-787, August.
    4. Wang, Zheng & Sheu, Jiuh-Biing, 2019. "Vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 350-364.
    5. Çağla Cergibozan & A. Serdar Tasan, 2022. "Genetic algorithm based approaches to solve the order batching problem and a case study in a distribution center," Journal of Intelligent Manufacturing, Springer, vol. 33(1), pages 137-149, January.
    6. Jing-Quan Li, 2014. "Transit Bus Scheduling with Limited Energy," Transportation Science, INFORMS, vol. 48(4), pages 521-539, November.

    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. Tang, Lixin & Wang, Gongshu, 2008. "Decision support system for the batching problems of steelmaking and continuous-casting production," Omega, Elsevier, vol. 36(6), pages 976-991, December.
    2. Slotnick, Susan A., 2011. "Optimal and heuristic lead-time quotation for an integrated steel mill with a minimum batch size," European Journal of Operational Research, Elsevier, vol. 210(3), pages 527-536, May.
    3. Lixin Tang & Gongshu Wang & Zhi-Long Chen, 2014. "Integrated Charge Batching and Casting Width Selection at Baosteel," Operations Research, INFORMS, vol. 62(4), pages 772-787, August.
    4. Keskin, Muhammed Emre, 2017. "A column generation heuristic for optimal wireless sensor network design with mobile sinks," European Journal of Operational Research, Elsevier, vol. 260(1), pages 291-304.
    5. Liu, Min & Jiang, Shenglong & Wu, Cheng, 2015. "A soft-decision based two-layered scheduling approach for uncertain steelmaking-continuous casting processAuthor-Name: Hao, Jinghua," European Journal of Operational Research, Elsevier, vol. 244(3), pages 966-979.
    6. Eliashberg, Jehoshua & Hegie, Quintus & Ho, Jason & Huisman, Dennis & Miller, Steven J. & Swami, Sanjeev & Weinberg, Charles B. & Wierenga, Berend, 2009. "Demand-driven scheduling of movies in a multiplex," International Journal of Research in Marketing, Elsevier, vol. 26(2), pages 75-88.
    7. X.H. Guan & Q.Z. Zhai & F. Lai, 2002. "New Lagrangian Relaxation Based Algorithm for Resource Scheduling with Homogeneous Subproblems," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 65-82, April.
    8. Wang, Tingsong & Xing, Zheng & Hu, Hongtao & Qu, Xiaobo, 2019. "Overbooking and delivery-delay-allowed strategies for container slot allocation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 433-447.
    9. Tang, Lixin & Liu, Jiyin & Rong, Aiying & Yang, Zihou, 2001. "A review of planning and scheduling systems and methods for integrated steel production," European Journal of Operational Research, Elsevier, vol. 133(1), pages 1-20, August.
    10. Yu-Wei An & Hong-Sen Yan, 2016. "Lagrangean relaxation approach to joint optimization for production planning and scheduling of synchronous assembly lines," International Journal of Production Research, Taylor & Francis Journals, vol. 54(22), pages 6718-6735, November.
    11. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    12. Wolosewicz, Cathy & Dauzère-Pérès, Stéphane & Aggoune, Riad, 2015. "A Lagrangian heuristic for an integrated lot-sizing and fixed scheduling problem," European Journal of Operational Research, Elsevier, vol. 244(1), pages 3-12.
    13. M Diaby & A L Nsakanda, 2006. "Large-scale capacitated part-routing in the presence of process and routing flexibilities and setup costs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(9), pages 1100-1112, September.
    14. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    15. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    16. S Bilgin & M Azizoǧlu, 2006. "Capacity and tool allocation problem in flexible manufacturing systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 670-681, June.
    17. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    18. Peter Francis & Karen Smilowitz & Michal Tzur, 2006. "The Period Vehicle Routing Problem with Service Choice," Transportation Science, INFORMS, vol. 40(4), pages 439-454, November.
    19. Park, Moon-Won & Kim, Yeong-Dae, 2000. "A branch and bound algorithm for a production scheduling problem in an assembly system under due date constraints," European Journal of Operational Research, Elsevier, vol. 123(3), pages 504-518, June.
    20. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:58:y:2011:i:4:p:370-388. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.