The rapid development of e-commerce has led to increased pressure on the express delivery industry to transport products to customers in a timely manner. The problem of how to deliver an increasing volume of express orders to customer clusters in a timely manner and at low cost with the joint distribution mode is becoming urgent. In this study, an express terminal node optimization and integration model is presented with an option to detach single customer clusters. In addition, the simulated annealing algorithm (SAA) based on neighborhood search that includes four rules is proposed to solve the problem. Contrast experiments are performed with SAA, the immune genetic algorithm (IGA), and the CPLEX solver. The experimental results indicate that IGA is less effective than SAA, and the running time of the IGA is longer. The CPLEX solver is less effective than the SAA, too. Additionally, the experimental results also show that every neighborhood rule proposed in this study plays a role in the optimization process.

中文翻译：

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联合配送模式下快递终端节点优化集成建模与求解算法

电子商务的快速发展，导致快递行业将产品及时运送到客户手中的压力越来越大。如何通过联合配送模式将越来越多的快递订单及时、低成本地送达客户群，成为亟待解决的问题。在这项研究中，提出了一种快递终端节点优化和集成模型，其中包含分离单个客户集群的选项。此外，针对该问题，提出了基于邻域搜索的模拟退火算法（SAA），包括四个规则。使用 SAA、免疫遗传算法 (IGA) 和 CPLEX 求解器执行对比实验。实验结果表明，IGA 的效果不如 SAA，而且 IGA 的运行时间更长。CPLEX 求解器也不如 SAA 有效。此外，实验结果还表明，本研究中提出的每个邻域规则都在优化过程中发挥作用。