The Robust Vehicle Routing Problem with Time Window Assignments
研究了物流企业在出发前同时确定配送路线和服务时间窗的问题，目标是最小化预期行驶时间和违反时间窗的风险，适用于包裹配送、零售和维修服务等场景。
In practice, there are several applications in which logistics service providers determine the service time windows at the customers, for example, in parcel delivery, retail, and repair services. These companies face uncertain travel times and service times that have to be taken into account when determining the time windows and routes prior to departure. The objective of the proposed robust vehicle routing problem with time window assignments (RVRP-TWA) is to simultaneously determine routes and time window assignments such that the expected travel time and the risk of violating the time windows are minimized. We assume that the travel time probability distributions are not completely known but that some statistics, such as the mean, minimum, and maximum, can be estimated. We extend the robust framework based on the requirements’ violation index, which was originally developed for the case where the specific requirements (time windows) are given as inputs, to the case where they are also part of the decisions. The subproblem of finding the optimal time window assignment for the customers in a given route is shown to be convex, and the subgradients can be derived. The RVRP-TWA is solved by iteratively generating subgradient cuts from the subproblem that are added in a branch-and-cut fashion. Experiments address the performance of the proposed solution approach and examine the trade-off between expected travel time and risk of violating the time windows.