As a part of the smart urban construction, automated driving is introduced to improve the utilization efficiency of cars and roads, which not only reduces the incidence of traffic accidents, but also improves the environment quality. With the development of the smart urban, it is predictable that, in the city of the future, the service of package pickup and delivery or takeout will be supported mainly by automated vehicles. However, the existing works mainly focus on the variants of the Vehicle Routing Problem (VRP), in which they either take no account of service time of automated vehicle for customers when the automated vehicle arrives at the locations of customers or ignore the impact of rewards gained from customers on path planning of the automated vehicles. In this paper, we also extend a variant of VRP where an automated vehicle is used to package delivery or distribution of food in the smart urban environment, which is called the Delivery Reward Maximization (DRM) problem. The problem aims at designing a route of the automated vehicle while considering the service time for customers before their deadlines and the impact of rewards of the automated vehicle on path planning. We first prove that the DRM problem is NP-hard. Then we study two special cases of the DRM problem, which are called Linear DRM (LDRM) problem and Two-dimensional DRM (TDRM) problem, respectively. In the LDRM and TDRM problems, all customers have the same visiting deadlines and are deployed on the one-dimensional line and two-dimensional plane, respectively. Then we prove that the LDRM and TDRM problems are also NP-hard and propose a constant approximation algorithm for each of them. Afterward, we propose a greedy algorithm to solve the DRM problem, and give the analysis by counterexample.

作为智慧城市建设的一部分，引入了自动驾驶以提高汽车和道路的利用效率，这不仅减少了交通事故的发生，而且还改善了环境质量。随着智能城市的发展，可以预见的是，在未来的城市中，包裹的取送服务将主要由自动车辆来支持。但是，现有的工作主要集中在“车辆路径问题”（VRP）的变体上，其中要么不考虑自动驾驶汽车到达客户位置时对客户的自动驾驶汽车服务时间，要么忽略奖励的影响。从客户那里获得了有关自动车辆路径规划的信息。在本文中，我们还扩展了VRP的一种变体，在这种变体中，自动车辆用于在智能城市环境中包装食物的交付或分发，这称为交付奖励最大化（DRM）问题。该问题旨在设计自动驾驶汽车的路线，同时考虑客户在其截止日期之前的服务时间以及自动驾驶汽车的奖励对路径规划的影响。我们首先证明DRM问题是NP问题。然后，我们研究了DRM问题的两种特殊情况，分别称为线性DRM（LDRM）问题和二维DRM（TDRM）问题。在LDRM和TDRM问题中，所有客户都有相同的访问期限，并且分别部署在一维线和二维平面上。然后，我们证明LDRM和TDRM问题也是NP-难问题，并针对它们分别提出了一个恒定近似算法。然后，提出了一种贪心算法来解决DRM问题，并通过反例进行分析。