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Mathematical Problems in Engineering
Volume 2016, Article ID 7851625, 9 pages
Research Article

Design of a Distribution Network Using Primal-Dual Decomposition

1Faculty of Engineering, Anahuac University, 52786 Mexico City, MEX, Mexico
2School of Economics, National Polytechnic Institute, 11350 Mexico City, MEX, Mexico
3UAP Nezahualcóyotl, Universidad Autónoma del Estado de México, 57000 Nezahualcoyotl, MEX, Mexico
4Posgrado en Logística y Cadena de Suministro, Universidad Autónoma de Nuevo León, 66450 Monterrey, NL, Mexico

Received 22 October 2015; Revised 1 January 2016; Accepted 10 January 2016

Academic Editor: Young Hae Lee

Copyright © 2016 J. A. Marmolejo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A method to solve the design of a distribution network for bottled drinks company is introduced. The distribution network proposed includes three stages: manufacturing centers, consolidation centers using cross-docking, and distribution centers. The problem is formulated using a mixed-integer programming model in the deterministic and single period contexts. Because the problem considers several elements in each stage, a direct solution is very complicated. For medium-to-large instances the problem falls into large scale. Based on that, a primal-dual decomposition known as cross decomposition is proposed in this paper. This approach allows exploring simultaneously the primal and dual subproblems of the original problem. A comparison of the direct solution with a mixed-integer lineal programming solver versus the cross decomposition is shown for several randomly generated instances. Results show the good performance of the method proposed.