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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 480127, 13 pages
Research Article

On the Transformation Mechanism for Formulating a Multiproduct Two-Layer Supply Chain Network Design Problem as a Network Flow Model

School of Transportation, Traffic and Logistics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China

Received 5 July 2013; Revised 15 December 2013; Accepted 29 December 2013; Published 20 February 2014

Academic Editor: Dongdong Ge

Copyright © 2014 Mi Gan 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.


The multiproduct two-layer supply chain is very common in various industries. In this paper, we introduce a possible modeling and algorithms to solve a multiproduct two-layer supply chain network design problem. The decisions involved are the DCs location and capacity design decision and the initial distribution planning decision. First we describe the problem and give a mixed integer programming (MIP) model; such problem is NP-hard and it is not easy to reduce the complexity. Inspired by it, we develop a transformation mechanism of relaxing the fixed cost and adding some virtual nodes and arcs to the original network. Thus, a network flow problem (NFP) corresponding to the original problem has been formulated. Given that we could solve the NFP as a minimal cost flow problem. The solution procedures and network simplex algorithm (INS) are discussed. To verify the effectiveness and efficiency of the model and algorithms, the performance measure experimental has been conducted. The experiments and result showed that comparing with MIP model solved by genetic algorithm (GA) and Benders, decomposition algorithm (BD) the NFP model and INS are also effective and even more efficient for both small-scale and large-scale problems.