Multi-echelon Supply Chain Network Design Based On Mixed Integer Programming

The global economy is advancing thoroughly, technology continue to renovate, company competition is increasingly white-hot, the market is gradually becoming complicate and dynamic, the shortness of product lifecycle and the growing variety of customer demand, therefore enterprises should look at the outside to realize the complementary advantages, Building a strong supply chain alliance in order to keep sustainable competitive advantages by re-examining and optimizing supply chain network.This paper, a multi-echelon supply chain network as research object, concluding the following parts:Firstly, the background, significance and main content of supply chain network design are introduced. We summarize the research status, list different focus and determine the framework of this article. Then the paper discuss the related theory of supply chain network design, including the definition, structure, features and so on. We point out the influencing factors, the main principles, main content and the steps of supply chain network design to be followed.Secondly, the paper consider a supply chain network design problem in the fuzzy environment, where the production time and cost are both uncertain and we use fuzzy numbers to describe them. Then we use mathematical language to describe this problem and consider three kinds of cooperation mode, including one-to-one chain case, one-to-many tree case and many-to-many network case. After that, A detailed introduce of the process to construct the supply chain network planning model is present from constraints to objectives.Again, we consider a supply chain network design problem with multiple echelons and multiple periods. Strategic and tactical decisions are considered simultaneously to build a many-to-many supply chain alliance. The strategic decision, which is the selection of companies to form supply chain alliance, and the tactical decisions, which are production, inventory, and transportation of selected companies, are considered as whole. We address the issue by considering bill of materials (BOM) and integrating all decisions to minimize the total costs and total carbon emissions.Finally, we introduce the solving process of the two models in detail and design two examples respectively. The optimal solution of first example obtained directly using LINGO. A Lagrangian relaxation heuristic algorithm is proposed to solve second example because of the second model more complex, Using modified gradient search to optimizing a Lagrangian dual problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of sub-problems each iteration.