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A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem


  • Retsef Levi

    () (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Robin Roundy

    () (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • David Shmoys

    () (School of Operations Research and Information Engineering and Department of Computer Science, Cornell University, Ithaca, New York 14853)

  • Maxim Sviridenko

    () (IBM T. J. Watson Research Center, Yorktown Heights, New York 10598)


Deterministic inventory theory provides streamlined optimization models that attempt to capture trade-offs in managing the flow of goods through a supply chain. We will consider two well-studied deterministic inventory models, called the one-warehouse multiretailer (OWMR) problem and its special case the joint replenishment problem (JRP), and give approximation algorithms with worst-case performance guarantees. That is, for each instance of the problem, our algorithm produces a solution with cost that is guaranteed to be at most 1.8 times the optimal cost; this is called a 1.8-approximation algorithm. Our results are based on an LP-rounding approach; we provide the first constant approximation algorithm for the OWMR problem and improve the previous results for the JRP.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:4:p:763-776

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    References listed on IDEAS

    1. Leroy B. Schwarz, 1973. "A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem," Management Science, INFORMS, vol. 19(5), pages 555-566, January.
    2. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
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    Cited by:

    1. 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.
    2. repec:spr:mathme:v:88:y:2018:i:3:d:10.1007_s00186-018-0642-4 is not listed on IDEAS
    3. 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.
    4. Sainathuni, Bhanuteja & Parikh, Pratik J. & Zhang, Xinhui & Kong, Nan, 2014. "The warehouse-inventory-transportation problem for supply chains," European Journal of Operational Research, Elsevier, vol. 237(2), pages 690-700.
    5. repec:eee:ejores:v:277:y:2019:i:2:p:561-573 is not listed on IDEAS
    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. Hossein Abouee-Mehrizi & Opher Baron & Oded Berman, 2014. "Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 561-577, October.
    8. Takahashi, Katsuhiko & Aoi, Takahiko & Hirotani, Daisuke & Morikawa, Katsumi, 2011. "Inventory control in a two-echelon dual-channel supply chain with setup of production and delivery," International Journal of Production Economics, Elsevier, vol. 133(1), pages 403-415, September.
    9. repec:spr:annopr:v:273:y:2019:i:1:d:10.1007_s10479-016-2338-6 is not listed on IDEAS
    10. 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.
    11. repec:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2073-4 is not listed on IDEAS
    12. 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.
    13. 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.
    14. Retsef Levi & Cong Shi, 2013. "Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times," Operations Research, INFORMS, vol. 61(3), pages 593-602, June.


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