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On reformulations for the one-warehouse multi-retailer problem

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  • Jesus Cunha
  • Rafael Melo

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. Copyright Springer Science+Business Media New York 2016

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  • 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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    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.
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    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.

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