IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v250y2016i1p155-163.html
   My bibliography  Save this article

Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales

Author

Listed:
  • Gayon, J.-P.
  • Massonnet, G.
  • Rapine, C.
  • Stauffer, G.

Abstract

We consider the One Warehouse Multi-Retailer (OWMR) problem with deterministic time-varying demand in the case where shortages are allowed. Demand may be either backlogged or lost. We present a simple combinatorial algorithm to build an approximate solution from a decomposition of the system into single-echelon subproblems. We establish that the algorithm has a performance guarantee of 3 for the OWMR with backlog under mild assumptions on the cost structure. In addition, we improve this guarantee to 2 in the special case of the Joint-Replenishment Problem (JRP) with backlog. As a by-product of our approach, we show that our decomposition provides a new lower bound of the optimal cost. A similar technique also leads to a 2-approximation for the OWMR problem with lost-sales. In all cases, the complexity of the algorithm is linear in the number of retailers and quadratic in the number of time periods, which makes it a valuable tool for practical applications. To the best of our knowledge, these are the first constant approximations for the OWMR with shortages.

Suggested Citation

  • Gayon, J.-P. & Massonnet, G. & Rapine, C. & Stauffer, G., 2016. "Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales," European Journal of Operational Research, Elsevier, vol. 250(1), pages 155-163.
    • Handle: RePEc:eee:ejores:v:250:y:2016:i:1:p:155-163
    DOI: 10.1016/j.ejor.2015.10.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715009807
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.10.054?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. Absi, Nabil & Kedad-Sidhoum, Safia, 2008. "The multi-item capacitated lot-sizing problem with setup times and shortage costs," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1351-1374, March.
    2. POCHET, Yves & WOLSEY, Laurence A., 1988. "Lot-size models with backlogging: strong reformulations and cutting planes," LIDAM Reprints CORE 791, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. Aksen, Deniz & Altinkemer, Kemal & Chand, Suresh, 2003. "The single-item lot-sizing problem with immediate lost sales," European Journal of Operational Research, Elsevier, vol. 147(3), pages 558-566, June.
    5. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    6. 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.
    7. Richard A. Sandbothe & Gerald L. Thompson, 1990. "A Forward Algorithm for the Capacitated Lot Size Model with Stockouts," Operations Research, INFORMS, vol. 38(3), pages 474-486, June.
    8. 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.
    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. Kaynov, Illya & van Knippenberg, Marijn & Menkovski, Vlado & van Breemen, Albert & van Jaarsveld, Willem, 2024. "Deep Reinforcement Learning for One-Warehouse Multi-Retailer inventory management," International Journal of Production Economics, Elsevier, vol. 267(C).
    2. 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.
    3. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    4. Feng Xue & Qiumin Li, 2024. "Forecast Horizon of Dynamic Lot Sizing Problem with Perishable Inventory and Multiple Chain Stores: Shipping and Stockout Cost," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    5. Jing, Fuying & Chao, Xiangrui, 2021. "A dynamic lot size model with perishable inventory and stockout," Omega, Elsevier, vol. 103(C).
    6. 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.
    7. Weihong Hu & Zhuoting Yu & Alejandro Toriello & Maged M. Dessouky, 2020. "Decomposition‐based approximation algorithms for the one‐warehouse multi‐retailer problem with concave batch order costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 503-523, October.

    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. Absi, Nabil & Kedad-Sidhoum, Safia, 2008. "The multi-item capacitated lot-sizing problem with setup times and shortage costs," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1351-1374, March.
    2. Jing, Fuying & Chao, Xiangrui, 2021. "A dynamic lot size model with perishable inventory and stockout," Omega, Elsevier, vol. 103(C).
    3. 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.
    4. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    5. Hwang, H.C., 2009. "Economic Lot-Sizing Problem with Bounded Inventory and Lost-Sales," Econometric Institute Research Papers EI 2009-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Adam N. Elmachtoub & Retsef Levi, 2016. "Supply Chain Management with Online Customer Selection," Operations Research, INFORMS, vol. 64(2), pages 458-473, April.
    7. Berk, Emre & Toy, Ayhan Ozgur & Hazir, Oncu, 2008. "Single item lot-sizing problem for a warm/cold process with immediate lost sales," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1251-1267, June.
    8. Farhat, Mlouka & Akbalik, Ayse & Hadj-Alouane, Atidel B. & Sauer, Nathalie, 2019. "Lot sizing problem with batch ordering under periodic buyback contract and lost sales," International Journal of Production Economics, Elsevier, vol. 208(C), pages 500-511.
    9. Liu, X. & Tu, Yl., 2008. "Production planning with limited inventory capacity and allowed stockout," International Journal of Production Economics, Elsevier, vol. 111(1), pages 180-191, January.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Danny Segev, 2014. "An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 432-444, May.
    15. 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.
    16. 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.
    17. 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.
    18. Charles, Mehdi & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Mazhoud, Issam, 2022. "Motivations and analysis of the capacitated lot-sizing problem with setup times and minimum and maximum ending inventories," European Journal of Operational Research, Elsevier, vol. 302(1), pages 203-220.
    19. Liu, Tieming, 2008. "Economic lot sizing problem with inventory bounds," European Journal of Operational Research, Elsevier, vol. 185(1), pages 204-215, February.
    20. Zhili Zhou & Yongpei Guan, 2013. "Two-stage stochastic lot-sizing problem under cost uncertainty," Annals of Operations Research, Springer, vol. 209(1), pages 207-230, 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:250:y:2016:i:1:p:155-163. 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.