IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v170y2015ipap88-96.html
   My bibliography  Save this article

An informative column generation and decomposition method for a production planning and facility location problem

Author

Listed:
  • Liang, Zhe
  • He, Yan
  • Wu, Tao
  • Zhang, Canrong

Abstract

This paper develops an informative column generation and decomposition method for a capacitated multi-item lot sizing and facility location problem with backlogging. The method hybridizes column generation to achieve a relaxed linear solution and a lower bound and a decomposition method (i.e., relax-and-fix) to achieve a feasible solution. The two solutions are used for a neighborhood search procedure that fixes a subset of setup decision variables to iteratively reduce problem sizes. The relax-and-fix method is applied again to solve these smaller-size restricted problems with a purpose of progressively improving solution qualities. To show the effectiveness of the method, a number of computational tests are performed using newly-generated benchmark problems. Computational comparisons with a commercial solver (CPLEX) show that the proposed method provides competitive solution results.

Suggested Citation

  • Liang, Zhe & He, Yan & Wu, Tao & Zhang, Canrong, 2015. "An informative column generation and decomposition method for a production planning and facility location problem," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 88-96.
    • Handle: RePEc:eee:proeco:v:170:y:2015:i:pa:p:88-96
    DOI: 10.1016/j.ijpe.2015.08.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527315003205
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2015.08.024?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. Christopher Suerie & Hartmut Stadtler, 2003. "The Capacitated Lot-Sizing Problem with Linked Lot Sizes," Management Science, INFORMS, vol. 49(8), pages 1039-1054, August.
    2. William W. Trigeiro & L. Joseph Thomas & John O. McClain, 1989. "Capacitated Lot Sizing with Setup Times," Management Science, INFORMS, vol. 35(3), pages 353-366, March.
    3. Millar, Harvey H. & Yang, Minzhu, 1994. "Lagrangian heuristics for the capacitated multi-item lot-sizing problem with backordering," International Journal of Production Economics, Elsevier, vol. 34(1), pages 1-15, February.
    4. Hasan Pirkul & Vaidyanathan Jayaraman, 1996. "Production, Transportation, and Distribution Planning in a Multi-Commodity Tri-Echelon System," Transportation Science, INFORMS, vol. 30(4), pages 291-302, November.
    5. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
    6. Sahling, Florian & Buschkühl, Lisbeth & Tempelmeier, Horst & Helber, Stefan, 2008. "Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic," Hannover Economic Papers (HEP) dp-400, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    7. Zeger Degraeve & Raf Jans, 2007. "A New Dantzig-Wolfe Reformulation and Branch-and-Price Algorithm for the Capacitated Lot-Sizing Problem with Setup Times," Operations Research, INFORMS, vol. 55(5), pages 909-920, October.
    8. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    9. Merce, C. & Fontan, G., 2003. "MIP-based heuristics for capacitated lotsizing problems," International Journal of Production Economics, Elsevier, vol. 85(1), pages 97-111, July.
    10. Wu, Tao & Shi, Leyuan & Geunes, Joseph & AkartunalI, Kerem, 2011. "An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging," European Journal of Operational Research, Elsevier, vol. 214(2), pages 428-441, October.
    11. Suerie, Christopher & Stadtler, Hartmut, 2003. "The Capacitated lot-sizing problem with linked lot sizes," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20206, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    12. Song, Yuyue & Chan, Gin Hor, 2005. "Single item lot-sizing problems with backlogging on a single machine at a finite production rate," European Journal of Operational Research, Elsevier, vol. 161(1), pages 191-202, February.
    13. Drexl, A. & Kimms, A., 1997. "Lot sizing and scheduling -- Survey and extensions," European Journal of Operational Research, Elsevier, vol. 99(2), pages 221-235, June.
    14. AkartunalI, Kerem & Miller, Andrew J., 2009. "A heuristic approach for big bucket multi-level production planning problems," European Journal of Operational Research, Elsevier, vol. 193(2), pages 396-411, March.
    15. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, 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. Raoul Fonkoua Fofou & Zhigang Jiang & Qingshan Gong & Yihua Yang, 2022. "A Decision-Making Model for Remanufacturing Facility Location in Underdeveloped Countries: A Capacitated Facility Location Problem Approach," Sustainability, MDPI, vol. 14(22), pages 1-18, November.
    2. Correia, Isabel & Melo, Teresa, 2016. "A computational comparison of formulations for a multi-period facility location problem with modular capacity adjustments and flexible demand fulfillment," Technical Reports on Logistics of the Saarland Business School 11, Saarland University of Applied Sciences (htw saar), Saarland Business School.
    3. Wu, Tao & Huang, Le & Liang, Zhe & Zhang, Xiaoning & Zhang, Canrong, 2022. "A supervised learning-driven heuristic for solving the facility location and production planning problem," European Journal of Operational Research, Elsevier, vol. 301(2), pages 785-796.
    4. Wu, Tao & Xiao, Fan & Zhang, Canrong & Zhang, Defu & Liang, Zhe, 2019. "Regression and extrapolation guided optimization for production–distribution with ship–buy–exchange options," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 129(C), pages 15-37.
    5. Wolfgang Albrecht & Martin Steinrücke, 2020. "Continuous-time scheduling of production, distribution and sales in photovoltaic supply chains with declining prices," Flexible Services and Manufacturing Journal, Springer, vol. 32(3), pages 629-667, September.
    6. Wei, Mingyuan & Qi, Mingyao & Wu, Tao & Zhang, Canrong, 2019. "Distance and matching-induced search algorithm for the multi-level lot-sizing problem with substitutable bill of materials," European Journal of Operational Research, Elsevier, vol. 277(2), pages 521-541.
    7. Zhang, Canrong & Xie, Fanrui & Huang, Kun & Wu, Tao & Liang, Zhe, 2017. "MIP models and a hybrid method for the capacitated air-cargo network planning and scheduling problems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 158-173.
    8. Darvish, Maryam & Coelho, Leandro C., 2018. "Sequential versus integrated optimization: Production, location, inventory control, and distribution," European Journal of Operational Research, Elsevier, vol. 268(1), pages 203-214.

    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. Bruno, Giuseppe & Genovese, Andrea & Piccolo, Carmela, 2014. "The capacitated Lot Sizing model: A powerful tool for logistics decision making," International Journal of Production Economics, Elsevier, vol. 155(C), pages 380-390.
    2. Tao Wu & Leyuan Shi & Jie Song, 2012. "An MIP-based interval heuristic for the capacitated multi-level lot-sizing problem with setup times," Annals of Operations Research, Springer, vol. 196(1), pages 635-650, July.
    3. Sahling, Florian & Hahn, Gerd J., 2019. "Dynamic lot sizing in biopharmaceutical manufacturing," International Journal of Production Economics, Elsevier, vol. 207(C), pages 96-106.
    4. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    5. Nadjib Brahimi & Tarik Aouam, 2016. "Multi-item production routing problem with backordering: a MILP approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1076-1093, February.
    6. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Tao Wu, 2022. "Predictive Search for Capacitated Multi-Item Lot Sizing Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 385-406, January.
    8. Brahimi, Nadjib & Dauzere-Peres, Stephane & Najid, Najib M. & Nordli, Atle, 2006. "Single item lot sizing problems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 1-16, January.
    9. Wei, Mingyuan & Qi, Mingyao & Wu, Tao & Zhang, Canrong, 2019. "Distance and matching-induced search algorithm for the multi-level lot-sizing problem with substitutable bill of materials," European Journal of Operational Research, Elsevier, vol. 277(2), pages 521-541.
    10. Absi, Nabil & van den Heuvel, Wilco, 2019. "Worst case analysis of Relax and Fix heuristics for lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 279(2), pages 449-458.
    11. Tao Wu & Zhe Liang & Canrong Zhang, 2018. "Analytics Branching and Selection for the Capacitated Multi-Item Lot Sizing Problem with Nonidentical Machines," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 236-258, May.
    12. Nadjib Brahimi & Stéphane Dauzère-Pérès & Najib M. Najid, 2006. "Capacitated Multi-Item Lot-Sizing Problems with Time Windows," Operations Research, INFORMS, vol. 54(5), pages 951-967, October.
    13. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    14. Kerem Akartunalı & Ioannis Fragkos & Andrew J. Miller & Tao Wu, 2016. "Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 766-780, November.
    15. Wu, Tao & Shi, Leyuan & Geunes, Joseph & AkartunalI, Kerem, 2011. "An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging," European Journal of Operational Research, Elsevier, vol. 214(2), pages 428-441, October.
    16. Chen, Haoxun, 2015. "Fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems," Omega, Elsevier, vol. 56(C), pages 25-36.
    17. Gislaine Mara Melega & Silvio Alexandre de Araujo & Reinaldo Morabito, 2020. "Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems," Annals of Operations Research, Springer, vol. 295(2), pages 695-736, December.
    18. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
    19. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.
    20. Ríos-Solís, Yasmín Á & Ibarra-Rojas, Omar J. & Cabo, Marta & Possani, Edgar, 2020. "A heuristic based on mathematical programming for a lot-sizing and scheduling problem in mold-injection production," European Journal of Operational Research, Elsevier, vol. 284(3), pages 861-873.

    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:170:y:2015:i:pa:p:88-96. 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.