IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v19y2021i2d10.1007_s10288-020-00449-8.html
   My bibliography  Save this article

Dynamic programming algorithms and Lagrangian lower bounds for a discrete lot streaming problem in a two-machine flow shop

Author

Listed:
  • Arianna Alfieri

    (DIGEP, Politecnico di Torino)

  • Shuyu Zhou

    (East China University of Science and Technology
    Erasmus University)

  • Rosario Scatamacchia

    (DIGEP, Politecnico di Torino)

  • Steef L. van de Velde

    (Erasmus University)

Abstract

In this paper, we propose exact and heuristic solution approaches based on dynamic programming for an open lot streaming problem. We also present the first application of Lagrangian relaxation to compute strong lower bounds to such a problem. The application concerns the minimization of the total flow time for the discrete version of a single-job lot streaming problem from the literature in a two-machine flow shop with attached setup times. Computational results on benchmark instances illustrate the effectiveness of the proposed approaches and give evidence of the strength of the Lagrangian relaxation lower bounds.

Suggested Citation

  • Arianna Alfieri & Shuyu Zhou & Rosario Scatamacchia & Steef L. van de Velde, 2021. "Dynamic programming algorithms and Lagrangian lower bounds for a discrete lot streaming problem in a two-machine flow shop," 4OR, Springer, vol. 19(2), pages 265-288, June.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:2:d:10.1007_s10288-020-00449-8
    DOI: 10.1007/s10288-020-00449-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-020-00449-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10288-020-00449-8?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. Arianna Alfieri & Celia Glass & Steef van de Velde, 2012. "Two-machine lot streaming with attached setup times," IISE Transactions, Taylor & Francis Journals, vol. 44(8), pages 695-710.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. C. A. Glass & C. N. Potts, 1998. "Structural Properties of Lot Streaming in a Flow Shop," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 624-639, August.
    4. Richard K. Congram & Chris N. Potts & Steef L. van de Velde, 2002. "An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 52-67, February.
    5. Sarin, Subhash C. & Kalir, Adar A. & Chen, Ming, 2008. "A single-lot, unified cost-based flow shop lot-streaming problem," International Journal of Production Economics, Elsevier, vol. 113(1), pages 413-424, May.
    6. D Biskup & M Feldmann, 2006. "Lot streaming with variable sublots: an integer programming formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(3), pages 296-303, March.
    7. Adar A. Kalir & Subhash C. Sarin, 2003. "Constructing Near Optimal Schedules for the Flow-Shop Lot Streaming Problem with Sublot-Attached Setups," Journal of Combinatorial Optimization, Springer, vol. 7(1), pages 23-44, March.
    8. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    9. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    10. Dan Trietsch & Kenneth R. Baker, 1993. "Basic Techniques for Lot Streaming," Operations Research, INFORMS, vol. 41(6), pages 1065-1076, December.
    11. Lika Ben-Dati & Gur Mosheiov & Daniel Oron, 2009. "Batch Scheduling on Two-Machine Flowshop with Machine-Dependent Setup Times," Advances in Operations Research, Hindawi, vol. 2009, pages 1-10, August.
    12. Glass, C. A. & Gupta, J. N. D. & Potts, C. N., 1994. "Lot streaming in three-stage production processes," European Journal of Operational Research, Elsevier, vol. 75(2), pages 378-394, June.
    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. D Biskup & M Feldmann, 2006. "Lot streaming with variable sublots: an integer programming formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(3), pages 296-303, March.
    2. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
    3. Chung‐Lun Li & Wen‐Qiang Xiao, 2004. "Lot streaming with supplier–manufacturer coordination," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 522-542, June.
    4. Liu, Jiyin, 2008. "Single-job lot streaming in m - 1 two-stage hybrid flowshops," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1171-1183, June.
    5. Sarin, Subhash C. & Kalir, Adar A. & Chen, Ming, 2008. "A single-lot, unified cost-based flow shop lot-streaming problem," International Journal of Production Economics, Elsevier, vol. 113(1), pages 413-424, May.
    6. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.
    7. 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.
    8. Ibrahim Muter & Tevfik Aytekin, 2017. "Incorporating Aggregate Diversity in Recommender Systems Using Scalable Optimization Approaches," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 405-421, August.
    9. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    10. Martinhon, Carlos & Lucena, Abilio & Maculan, Nelson, 2004. "Stronger K-tree relaxations for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(1), pages 56-71, October.
    11. Chiu, Huan Neng & Chang, Jen Huei, 2005. "Cost models for lot streaming in a multistage flow shop," Omega, Elsevier, vol. 33(5), pages 435-450, October.
    12. Kouhei Harada, 2021. "A Feasibility-Ensured Lagrangian Heuristic for General Decomposable Problems," SN Operations Research Forum, Springer, vol. 2(4), pages 1-26, December.
    13. Huisman, D. & Jans, R.F. & Peeters, M. & Wagelmans, A.P.M., 2003. "Combining Column Generation and Lagrangian Relaxation," ERIM Report Series Research in Management ERS-2003-092-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.
    14. J. E. Beasley, 1990. "A lagrangian heuristic for set‐covering problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(1), pages 151-164, February.
    15. Lawrence V. Snyder & Mark S. Daskin, 2005. "Reliability Models for Facility Location: The Expected Failure Cost Case," Transportation Science, INFORMS, vol. 39(3), pages 400-416, August.
    16. Marcel Turkensteen & Dmitry Malyshev & Boris Goldengorin & Panos M. Pardalos, 2017. "The reduction of computation times of upper and lower tolerances for selected combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 68(3), pages 601-622, July.
    17. X-Y Li & Y P Aneja & F Baki, 2010. "An ant colony optimization metaheuristic for single-path multicommodity network flow problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1340-1355, September.
    18. Ahmadi, Reza H. & Kouvelis, Panagiotis, 1999. "Design of electronic assembly lines: An analytical framework and its application," European Journal of Operational Research, Elsevier, vol. 115(1), pages 113-137, May.
    19. Beasley, J. E. & Cao, B., 1996. "A tree search algorithm for the crew scheduling problem," European Journal of Operational Research, Elsevier, vol. 94(3), pages 517-526, November.
    20. Igor Litvinchev & Socorro Rangel & Jania Saucedo, 2010. "A Lagrangian bound for many-to-many assignment problems," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 241-257, April.

    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:spr:aqjoor:v:19:y:2021:i:2:d:10.1007_s10288-020-00449-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.