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

Abstract

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.

Designing a supply chain management based on distributers’ efficiency measurement

“…They proposed a hybrid decomposition approach, which heuristically obtains tentative solutions for the vertex facilities number and location and applied these solutions to limit the computational time of a branch-and-cut algorithm. Gan et al (2014) discussed the transformation mechanism for formulating a multiproduct two-layer supply chain network design problem as a network flow model. Georgiadis et al (2011) presented an optimal design of supply chain networks under uncertain transient demand variations.…”

Designing a robust supply chain management based on distributers’ efficiency measurement

“…They applied a path-based formulation, which helps investigate supply-side uncertainties, which are possible disruptions in manufacturers, distribution centers and their connecting links. Gan et al (2014) investigated the transformation mechanism for formulating a multiproduct two-layer problem as a network flow model. Castillo-Villar et al (2014) investigated capacitated model for supply chain network design (SCND), which determines manufacturing, distribution, and quality costs.…”