We introduce a new variant of the well-known vehicle routing problem (VRP): the VRP with time windows and flexible delivery locations (VRPTW-FL). Generally, in the VRP each customer is served in one fixed service location. However, in the VRPTW-FL each customer is served in one of a set of potential service locations, each of which has a certain capacity. From a practical point of view, the VRPTW-FL is highly relevant due to its numerous applications, e.g. parcel delivery, routing with limited parking space, and hospital-wide scheduling of physical therapists. Theoretically, the VRPTW-FL is challenging to solve due to the limited location capacities. When serving a customer, location availability must be ensured at every time. To solve this problem, we present a mathematical model and a tailored hybrid adaptive large neighborhood search. Our heuristic makes use of an innovative backtracking approach during the construction phase to alter unsatisfactory decisions at an early stage. In the meta-heuristic phase, we employ novel neighborhoods and dynamic updates of the objective violation weights. For our computational analysis, we use hospital data to evaluate the utility of flexible delivery locations and various cost functions. Our algorithmic features improve the solution quality considerably.

我们介绍了著名的车辆出行问题(VRP) 的一个新变体：具有时间窗口和灵活交付l的VRP地点（VRPTW-FL）。通常，在 VRP 中，每个客户都在一个固定的服务地点得到服务。然而，在 VRPTW-FL 中，每个客户都在一组潜在服务地点中的一个服务，每个地点都有一定的容量。从实用的角度来看，VRPTW-FL 因其众多应用而具有高度相关性，例如包裹递送、停车位有限的路由以及物理治疗师在医院范围内的调度。从理论上讲，由于定位能力有限，VRPTW-FL 很难解决。在为客户提供服务时，必须始终确保位置可用性。为了解决这个问题，我们提出了一个数学模型和一个定制的混合自适应大邻域搜索。我们的启发式方法在构建阶段使用创新的回溯方法来在早期阶段改变不满意的决策。在元启发式阶段，我们采用新的邻域和客观违规权重的动态更新。对于我们的计算分析，我们使用医院数据来评估灵活分娩地点和各种成本函数的效用。我们的算法功能大大提高了解决方案的质量。