Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed dynamically with the goal of maximizing the number of served requests. We model the DVRPSR as a multi-stage optimization problem, where the first-stage decision defines route plans for serving scheduled requests. Our main contributions are knapsack-based linear models to approximate accurately the expected reward-to-go, measured as the number of accepted requests, at any state of the stochastic system. These approximations are based on representing each vehicle as a knapsack with a capacity given by the remaining service time available along the vehicle’s route. We combine these approximations with optimal acceptance and assignment decision rules and derive efficient and high-performing online scheduling policies. We further leverage good predictions of the expected reward-to-go to design initial route plans that facilitate serving dynamic requests. Computational experiments on very large instances based on a real street network demonstrate the effectiveness of the proposed methods in prescribing high-quality offline route plans and online scheduling decisions.

动态车辆路径问题 (DVRP) 出现在多个应用程序中，例如技术人员路径、送餐和包裹运输。我们考虑具有随机客户请求 (DVRPSR) 的 DVRP，其中车辆必须以最大化服务请求数量为目标进行动态路由。我们将 DVRPSR 建模为一个多阶段优化问题，其中第一阶段决策定义了为计划请求提供服务的路线计划。我们的主要贡献是基于背包的线性模型，可以在随机系统的任何状态下准确地近似预期的奖励，以接受的请求数量来衡量。这些近似值基于将每辆车表示为一个背包，其容量由车辆路线上可用的剩余服务时间给出。我们将这些近似与最佳接受和分配决策规则相结合，并推导出高效和高性能的在线调度策略。我们进一步利用对预期奖励的良好预测来设计有助于服务动态请求的初始路线计划。基于真实街道网络的超大型实例的计算实验证明了所提出的方法在制定高质量离线路线计划和在线调度决策方面的有效性。