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On reformulations for the one-warehouse multi-retailer problem


  • Jesus Cunha


  • Rafael Melo



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. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:p:99-122:10.1007/s10479-015-2073-4
    DOI: 10.1007/s10479-015-2073-4

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    References listed on IDEAS

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. repec:wly:navres:v:46:y:1999:i:5:p:463-486 is not listed on IDEAS
    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," CORE Discussion Papers RP 2235, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. MELO, Rafael A. & WOLSEY, Laurence A., 2012. "MIP formulations and heuristics for two-level production-transportation problems," CORE Discussion Papers RP 2506, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    1. repec:eee:ejores:v:276:y:2019:i:3:p:1013-1033 is not listed on IDEAS
    2. repec:eee:ejores:v:268:y:2018:i:1:p:203-214 is not listed on IDEAS


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