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The one-warehouse multi-retailer problem: reformulation, classification, and computational results

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  • Oğuz Solyalı

    ()

  • Haldun Süral

    ()

Abstract

We consider the one-warehouse multi-retailer problem where a warehouse replenishes multiple retailers with deterministic dynamic demands over a horizon. The problem is to determine when and how much to order to the warehouse and retailers such that the total system-wide costs are minimized. We propose a new (combined transportation and shortest path based) integer programming reformulation for the problem in addition to the echelon stock and transportation based formulations in the literature. We analyze the strength of the LP relaxations of three formulations and show that the new formulation is stronger than others. We also show that the new and transportation based formulations are equivalent for the joint replenishment problem, where the warehouse is a crossdocking facility. We extend all formulations to the case with initial inventory at the warehouse and reveal the relation among their LP relaxations. We present our computational experiments with all formulations over a set of randomly generated test instances. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:517-541:10.1007/s10479-011-1022-0
    DOI: 10.1007/s10479-011-1022-0
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    References listed on IDEAS

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    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. Lap Mui Ann Chan & Ana Muriel & Zuo-Jun Max Shen & David Simchi-Levi & Chung-Piaw Teo, 2002. "Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures," Management Science, INFORMS, vol. 48(11), pages 1446-1460, November.
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    6. E. Powell Robinson, Jr. & Li-Lian Gao, 1996. "A Dual Ascent Procedure for Multiproduct Dynamic Demand Coordinated Replenishment with Backlogging," Management Science, INFORMS, vol. 42(11), pages 1556-1564, November.
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    8. Stadtler, Hartmut, 1997. "Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 7096, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    13. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2005. "Integrated Lot Sizing in Serial Supply Chains with Production Capacities," Management Science, INFORMS, vol. 51(11), pages 1706-1719, November.
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    Cited by:

    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. 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.
    3. repec:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2073-4 is not listed on IDEAS

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