IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v238y2016i1d10.1007_s10479-015-2073-4.html
   My bibliography  Save this article

On reformulations for the one-warehouse multi-retailer problem

Author

Listed:
  • Jesus O. Cunha

    (Universidade Federal da Bahia)

  • Rafael A. Melo

    (Universidade Federal da Bahia)

Abstract

We consider the one-warehouse multi-retailer problem (OWMR) and perform both theoretical and computational studies of different formulations for the problem. Several formulations that were not yet directly applied to the OWMR are considered, namely an echelon stock formulation strengthened with valid inequalities, a two-level lot-sizing based formulation strengthened with valid inequalities, a multicommodity formulation and a dynamic programming based formulation. These are also compared with a strengthened echelon stock formulation and the previously best performing formulations available in the literature, a transportation and a shortest path formulations, which were studied in a previous work (Solyali and Süral in Ann Oper Res 196(1):517–541, 2012). The formulations were ordered according to the provided linear relaxation bounds, assuming there is no available stock at the beginning of the planning horizon. Experimental results using a commercial MIP solver indicate that a partial version of the two-level lot-sizing based formulation strengthened with valid inequalities and the multicommodity formulation outperform the others, especially as the sizes of the instances become larger. Besides, these two new best performing formulations allow the solver to prove optimality of instances for which not even the linear relaxation could be solved using the previously best performing formulations.

Suggested Citation

  • Jesus O. Cunha & Rafael A. Melo, 2016. "On reformulations for the one-warehouse multi-retailer problem," Annals of Operations Research, Springer, vol. 238(1), pages 99-122, March.
  • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2073-4
    DOI: 10.1007/s10479-015-2073-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-015-2073-4
    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/s10479-015-2073-4?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. Robinson, Powell & Narayanan, Arunachalam & Sahin, Funda, 2009. "Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms," Omega, Elsevier, vol. 37(1), pages 3-15, February.
    2. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
    3. Oğuz Solyalı & Haldun Süral, 2012. "The one-warehouse multi-retailer problem: reformulation, classification, and computational results," Annals of Operations Research, Springer, vol. 196(1), pages 517-541, July.
    4. MELO, Rafael A. & WOLSEY, Laurence A., 2012. "MIP formulations and heuristics for two-level production-transportation problems," LIDAM Reprints CORE 2506, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Retsef Levi & Robin Roundy & David Shmoys & Maxim Sviridenko, 2008. "A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem," Management Science, INFORMS, vol. 54(4), pages 763-776, April.
    6. Minjiao Zhang & Simge Küçükyavuz & Hande Yaman, 2012. "A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands," Operations Research, INFORMS, vol. 60(4), pages 918-935, August.
    7. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2006. "Primal-Dual Algorithms for Deterministic Inventory Problems," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 267-284, May.
    8. Rardin, Ronald L. & Wolsey, Laurence A., 1993. "Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems," European Journal of Operational Research, Elsevier, vol. 71(1), pages 95-109, November.
    9. MELO, Rafael A. & WOLSEY, Laurence A., 2010. "Uncapacitated two-level lot-sizing," LIDAM Reprints CORE 2235, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Cunha, Jesus O. & Melo, Rafael A., 2021. "Valid inequalities, preprocessing, and an effective heuristic for the uncapacitated three-level lot-sizing and replenishment problem with a distribution structure," European Journal of Operational Research, Elsevier, vol. 295(3), pages 874-892.
    2. Baller, Annelieke C. & Dabia, Said & Dullaert, Wout E.H. & Vigo, Daniele, 2019. "The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1013-1033.
    3. 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. Jesus Cunha & Rafael Melo, 2016. "On reformulations for the one-warehouse multi-retailer problem," Annals of Operations Research, Springer, vol. 238(1), pages 99-122, March.
    2. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    3. Ming Zhao & Minjiao Zhang, 2020. "Multiechelon Lot Sizing: New Complexities and Inequalities," Operations Research, INFORMS, vol. 68(2), pages 534-551, March.
    4. Cunha, Jesus O. & Melo, Rafael A., 2021. "Valid inequalities, preprocessing, and an effective heuristic for the uncapacitated three-level lot-sizing and replenishment problem with a distribution structure," European Journal of Operational Research, Elsevier, vol. 295(3), pages 874-892.
    5. Goisque, Guillaume & Rapine, Christophe, 2017. "An efficient algorithm for the 2-level capacitated lot-sizing problem with identical capacities at both levels," European Journal of Operational Research, Elsevier, vol. 261(3), pages 918-928.
    6. 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.
    7. Gautier Stauffer, 2018. "Approximation algorithms for k-echelon extensions of the one warehouse multi-retailer problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 445-473, December.
    8. Siao-Leu Phouratsamay & Safia Kedad-Sidhoum & Fanny Pascual, 2021. "Coordination of a two-level supply chain with contracts," 4OR, Springer, vol. 19(2), pages 235-264, June.
    9. Minjiao Zhang & Simge Küçükyavuz & Hande Yaman, 2012. "A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands," Operations Research, INFORMS, vol. 60(4), pages 918-935, August.
    10. Oğuz Solyalı & Haldun Süral, 2012. "The one-warehouse multi-retailer problem: reformulation, classification, and computational results," Annals of Operations Research, Springer, vol. 196(1), pages 517-541, July.
    11. Kajjoune, Oussama & Aouam, Tarik & Zouadi, Tarik & Ranjan, Ravi Prakash, 2023. "Dynamic lot-sizing in a two-stage supply chain with liquidity constraints and financing options," International Journal of Production Economics, Elsevier, vol. 258(C).
    12. Hark-Chin Hwang & Wilco van den Heuvel & Albert P. M. Wagelmans, 2023. "Multilevel Lot-Sizing with Inventory Bounds," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1470-1490, November.
    13. Og̀uz Solyalı & Haldun Süral & Meltem Denizel, 2010. "The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 653-666, October.
    14. Laurence A. Wolsey, 2002. "Solving Multi-Item Lot-Sizing Problems with an MIP Solver Using Classification and Reformulation," Management Science, INFORMS, vol. 48(12), pages 1587-1602, December.
    15. Marcin Bienkowski & Martin Böhm & Jaroslaw Byrka & Marek Chrobak & Christoph Dürr & Lukáš Folwarczný & Łukasz Jeż & Jiří Sgall & Nguyen Kim Thang & Pavel Veselý, 2020. "Online Algorithms for Multilevel Aggregation," Operations Research, INFORMS, vol. 68(1), pages 214-232, January.
    16. Niv Buchbinder & Tracy Kimbrel & Retsef Levi & Konstantin Makarychev & Maxim Sviridenko, 2013. "Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms," Operations Research, INFORMS, vol. 61(4), pages 1014-1029, August.
    17. Jean-Philippe Gayon & Guillaume Massonnet & Christophe Rapine & Gautier Stauffer, 2017. "Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 854-875, August.
    18. Lehilton L. C. Pedrosa & Maxim Sviridenko, 2018. "Integrated Supply Chain Management via Randomized Rounding," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 124-136, February.
    19. Levi DeValve & Saša Pekeč & Yehua Wei, 2020. "A Primal-Dual Approach to Analyzing ATO Systems," Management Science, INFORMS, vol. 66(11), pages 5389-5407, November.
    20. Kis, Tamás & Kovács, András, 2013. "Exact solution approaches for bilevel lot-sizing," European Journal of Operational Research, Elsevier, vol. 226(2), pages 237-245.

    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:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2073-4. 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.