This paper presents an effective Progressive Hedging algorithm for vehicle routing problem with two-layers time window assignment and stochastic service times (2L-TWAVRPSST). Based on a predefined exogenous time window determined by the customers, an endogenous time window is assigned to each customer. Endogenous time windows have flexible width and composed of two-layers. The outer layer is wider than inner layer and is determined by violation variable. This approach aims to giving more flexibility to career companies for serving more customers using less vehicles. Customers could be visited even after the end of their assigned time windows by paying proportional penalty, while extra violation from the outer layer is not permitted. This problem is formulated as a two-stage stochastic model with the first-stage decisions of assigning inner and outer layers time window. Then in the second stage, routes are planned for each scenario combination of stochastic demand and service time. The validity and effectiveness of the proposed model was examined by various numerical examples. The problem was solved by a Progressive Hedging (PH) algorithm for large-scale instances. The results confirm efficiency of the considered solution approach in different instances.

针对两层时间窗分配和随机服务时间（2L-TWAVRPSST）的车辆路径问题，本文提出了一种有效的渐进式对冲算法。基于客户确定的预定义的外部时间窗口，为每个客户分配一个内部时间窗口。内生时间窗口具有灵活的宽度，由两层组成。外层比内层宽，由违规变量确定。这种方法旨在为职业公司提供更大的灵活性，以使用更少的车辆为更多的客户提供服务。即使在分配的时间窗结束后，也可以通过按比例支付罚款来拜访客户，而不允许外层额外违反。该问题被公式化为两阶段随机模型，其中第一阶段决定分配内层和外层时间窗口。然后在第二阶段，针对随机需求和服务时间的每种情况组合计划路线。通过各种数值例子验证了该模型的有效性和有效性。通过针对大型实例的渐进对冲（PH）算法解决了该问题。结果证实了在不同情况下考虑的解决方案方法的效率。