Abstract: There is a risk of disruption in each transportation route of the real supply chain network. Only the reasonable choice of the supply facilities and the transportation route can guarantee the transportation reliability of the whole network to some extent. Firstly, under facilities capacity constraints, a new two-objective mixed integer programming model for the design of a three-echelon supply chain network is proposed to minimize the total operating cost and maximize the transportation reliability of the whole network. Then, Non-dominated Sorting Genetic Algorithm II（NSGA-II） is used to solve the proposed model, and a new method of chromosome decoding is designed according to the relationship between decision variables. Finally, through the comparison experiment of routes reliability and example scales, it not only analyzes the sensitivity of the model and the effectiveness of algorithm, but also discusses the influence of facilities capacity constraints on the result of examples. The research of LRP model and algorithm in this paper can effectively help the decision maker to design a three echelon supply chain network with low cost and high reliability.

Key words: location-routing problem, operating cost, transportation reliability, Non-dominated Sorting Genetic Algorithm II（NSGA-II）

摘要： 现实供应链网络中每条运输路径都存在中断风险，只有合理地选择供应设施及其运输路径才能在一定程度上保证整个网络的运输可靠性。在设施能力约束下，为了保证总运营成本的最小化和整个网络的运输可靠性的最大化，提出了一个新的三级供应链网络设计的两目标混合整数规划模型。利用改进的非支配排序遗传算法（NSGA-II）求解提出的模型，并根据决策变量之间的关系设计新的染色体解码方法。通过路径可靠度对比实验和算例规模对比实验，不仅分析了模型的灵敏度和算法的有效性，还讨论了设施能力约束对算例结果的影响。构建的LRP模型及算法的研究能有效地帮助决策者设计出低成本、高可靠性的三级供应链网络。

关键词: 选址路径问题, 运营成本, 运输可靠性, 改进的非支配排序遗传算法