IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v300y2022i2p602-614.html
   My bibliography  Save this article

Timed route approaches for large multi-product multi-step capacitated production planning problems

Author

Listed:
  • Beraudy, Sébastien
  • Absi, Nabil
  • Dauzère-Pérès, Stéphane

Abstract

In complex systems that can be found in semiconductor manufacturing, linear programming production planning models must consider many products with hundreds of production steps to be performed on hundreds of machines. To deal with this complexity and solve problems with flexible lead times in a reasonable CPU time, the new concept of timed route is introduced. In a timed route, each production step of a product is associated with a specific time period. A new formulation relying on timed routes is then proposed. Because the number of feasible timed routes can grow exponentially, a column generation approach is presented. Algorithms to generate relevant timed routes are given, and their complexity analyzed. Computational experiments on industrial data with different lead time profiles, fixed lead times and flexible lead times, show that computational times are very significantly reduced when using our approaches, by 92% on average and even divided by more than 1,000 in some cases. The advantages of timed routes are also discussed.

Suggested Citation

  • Beraudy, Sébastien & Absi, Nabil & Dauzère-Pérès, Stéphane, 2022. "Timed route approaches for large multi-product multi-step capacitated production planning problems," European Journal of Operational Research, Elsevier, vol. 300(2), pages 602-614.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:2:p:602-614
    DOI: 10.1016/j.ejor.2021.08.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721006780
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.08.011?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. Lasse Nisted & David Pisinger & Avri Altman, 2011. "Optimal wafer cutting in shuttle layout problems," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 202-216, August.
    2. Peter J. Billington & John O. McClain & L. Joseph Thomas, 1983. "Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction," Management Science, INFORMS, vol. 29(10), pages 1126-1141, October.
    3. Bredstrom, David & Lundgren, Jan T. & Ronnqvist, Mikael & Carlsson, Dick & Mason, Andrew, 2004. "Supply chain optimization in the pulp mill industry--IP models, column generation and novel constraint branches," European Journal of Operational Research, Elsevier, vol. 156(1), pages 2-22, July.
    4. Dauzere-Peres, Stephane & Lasserre, Jean-Bernard, 1994. "Integration of lotsizing and scheduling decisions in a job-shop," European Journal of Operational Research, Elsevier, vol. 75(2), pages 413-426, June.
    5. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    6. Missbauer, Hubert, 2020. "Order release planning by iterative simulation and linear programming: Theoretical foundation and analysis of its shortcomings," European Journal of Operational Research, Elsevier, vol. 280(2), pages 495-507.
    7. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
    8. Jacques Desrosiers & Marco E. Lübbecke, 2005. "A Primer in Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 1-32, Springer.
    9. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    10. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    11. Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2010. "An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles," European Journal of Operational Research, Elsevier, vol. 202(3), pages 756-763, May.
    12. Matthew J. Liberatore & Tan Miller, 1985. "A Hierarchical Production Planning System," Interfaces, INFORMS, vol. 15(4), pages 1-11, August.
    13. 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.
    14. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    15. Pereira Lopes, Manuel J. & de Carvalho, J.M. Valerio, 2007. "A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1508-1527, February.
    16. Ng, Tsan Sheng & Sun, Yang & Fowler, John, 2010. "Semiconductor lot allocation using robust optimization," European Journal of Operational Research, Elsevier, vol. 205(3), pages 557-570, September.
    17. Michel Gamache & François Soumis & Gérald Marquis & Jacques Desrosiers, 1999. "A Column Generation Approach for Large-Scale Aircrew Rostering Problems," Operations Research, INFORMS, vol. 47(2), pages 247-263, April.
    18. Erinc Albey & Ümit Bilge & Reha Uzsoy, 2017. "Multi-dimensional clearing functions for aggregate capacity modelling in multi-stage production systems," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 4164-4179, July.
    19. Stephen C. Graves, 1986. "A Tactical Planning Model for a Job Shop," Operations Research, INFORMS, vol. 34(4), pages 522-533, August.
    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. Ioannis Fragkos & Zeger Degraeve & Bert De Reyck, 2016. "A Horizon Decomposition Approach for the Capacitated Lot-Sizing Problem with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 465-482, August.
    2. Jans, Raf, 2010. "Classification of Dantzig-Wolfe reformulations for binary mixed integer programming problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 251-254, July.
    3. 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.
    4. 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.
    5. Degraeve, Z. & Jans, R.F., 2003. "A New Dantzig-Wolfe Reformulation And Branch-And-Price Algorithm For The Capacitated Lot Sizing Problem With Set Up Times," ERIM Report Series Research in Management ERS-2003-010-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.
    6. Dziuba, Daryna & Almeder, Christian, 2023. "New construction heuristic for capacitated lot sizing problems," European Journal of Operational Research, Elsevier, vol. 311(3), pages 906-920.
    7. Gondzio, Jacek & González-Brevis, Pablo & Munari, Pedro, 2013. "New developments in the primal–dual column generation technique," European Journal of Operational Research, Elsevier, vol. 224(1), pages 41-51.
    8. 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.
    9. 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.
    10. Fırat, M. & Briskorn, D. & Laugier, A., 2016. "A Branch-and-Price algorithm for stable workforce assignments with hierarchical skills," European Journal of Operational Research, Elsevier, vol. 251(2), pages 676-685.
    11. Rauchecker, Gerhard & Schryen, Guido, 2019. "An exact branch-and-price algorithm for scheduling rescue units during disaster response," European Journal of Operational Research, Elsevier, vol. 272(1), pages 352-363.
    12. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    13. Julia Pahl & Stefan Voß & David Woodruff, 2007. "Production planning with load dependent lead times: an update of research," Annals of Operations Research, Springer, vol. 153(1), pages 297-345, September.
    14. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    15. 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.
    16. Raf Jans, 2009. "Solving Lot-Sizing Problems on Parallel Identical Machines Using Symmetry-Breaking Constraints," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 123-136, February.
    17. Issmail Elhallaoui & Daniel Villeneuve & François Soumis & Guy Desaulniers, 2005. "Dynamic Aggregation of Set-Partitioning Constraints in Column Generation," Operations Research, INFORMS, vol. 53(4), pages 632-645, August.
    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. 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.
    20. Sami Gabteni & Mattias Grönkvist, 2009. "Combining column generation and constraint programming to solve the tail assignment problem," Annals of Operations Research, Springer, vol. 171(1), pages 61-76, October.

    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:300:y:2022:i:2:p:602-614. 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.