A multi-period, multi-echelon, multi-product, and multi-modal sustainable supply chain network design problem is considered. The problem is formulated as a multi-objective Mixed-Integer Linear Programming (MILP) model that explicitly considers the environmental footprint and social responsibilities. We introduce the Multi-Neighborhood Descent Traversal Algorithm (MNDTA), which can solve this problem efficiently. The MNDTA begins with a structured initial solution of the model and improves the incumbent solution by sequentially traversing several specifically designed neighborhoods over generations. A lower-bound-based evaluation method is introduced to reduce the computational complexity involved in solving the integer programming problem. Experimental results demonstrate that the proposed MNDTA can provide high-quality solutions that are close to the optimal solutions with a negligibly small (relative) gap and can solve large instances much more quickly than CPLEX can. In addition, the MNDTA outperforms existing solution algorithms. A numerical comparison of the results of the proposed model with those of a model that only considers financial aspects demonstrates that explicitly using our model when designing a supply chain network can substantially reduce the environmental impact and increase social responsibility at a negligible cost increase.

考虑了多周期，多级，多产品，多模式的可持续供应链网络设计问题。该问题被表述为明确考虑环境足迹和社会责任的多目标混合整数线性规划（MILP）模型。我们介绍了多邻域下降遍历算法（MNDTA），可以有效地解决此问题。MNDTA从模型的结构化初始解决方案开始，并通过逐代遍历几个专门设计的邻域来改进现有解决方案。引入了基于下界的评估方法，以减少解决整数规划问题所涉及的计算复杂性。实验结果表明，所提出的MNDTA可以提供接近最佳解决方案的高质量解决方案，并且其相对（相对）的间隙可以忽略不计，并且可以比CPLEX更快地解决大型实例。此外，MNDTA优于现有的解决方案算法。所提议模型的结果与仅考虑财务方面的模型的结果之间的数值比较表明，在设计供应链网络时明确使用我们的模型可以显着降低环境影响并以可忽略的成本增加来提高社会责任感。