## 1 Introduction
The rapid advancement of unmanned aerial vehicle (UAV) logistics distribution technology has highlighted the transportation advantages of UAVs, including their independence from ground conditions, high efficiency, and flexibility, which have garnered increasing attention. Since 2015, the investigation of joint distribution systems that leverage the complementary strengths of vehicles and UAVs has emerged as a prominent area of research. [PERSON] et al. [14] examined the scheduling challenges associated with the joint distribution model of vehicles and UAVs, focusing on minimizing distribution time by establishing a mixed-integer linear programming model, which they solved using a heuristic algorithm. [PERSON] et al. [15] aimed to minimize the combined transportation and vehicle waiting costs, devising a greedy random adaptive search algorithm for this purpose. [PERSON] et al. [16] and [PERSON] et al. [17] introduced a three-stage planning methodology to address the joint distribution problem of vehicles and UAVs. This approach involved constructing vehicle distribution points through an enhanced k-means clustering algorithm, followed by the planning of distribution routes for both vehicles and UAVs. [PERSON] [18] considered scenarios in which vehicles are unable to access certain demand points promptly due to road blockages, proposing a tandem mode problem for vehicles and UAVs in emergency logistics, thereby formulating a mathematical model for the mixed vehicle and UAV routing problem. [PERSON] [19] proposed a combined distribution model for vehicles and UAVs in the context of isolated points within disaster areas resulting from road interruptions following an earthquake. This model aims to minimize total time while accounting for factors such as the urgency of emergency material demand and demand uncertainty, employing a two-stage hybrid algorithm that integrates a tabu search algorithm with an evolutionary algorithm for resolution. The preceding analysis indicates that there exists a substantial body of research concerning the planning of traditional emergency logistics distribution systems in response to emergency situations. A significant portion of the literature on the joint distribution of vehicles and logistics service providers (LSPs) primarily addresses path planning issues under normal conditions, with some studies focusing on the optimization of distribution routes for emergency supplies following natural disasters, such as earthquakes. Noteworthy progress has been made in these areas. However, there remains a notable gap in the research regarding the effective distribution of a high volume of regular express deliveries, which occur with considerable frequency during emergency situations. Given the rapid increase in the quantity and frequency of express deliveries utilized by urban residents, the timeliness of these distributions significantly affects residents' quality of life. The frequent occurrence of emergencies, such as natural disasters, often leads to road blockages that can result in delays and backlogs of express deliveries in certain regions, thereby imposing substantial losses on both delivery companies and residents. While existing studies predominantly emphasize methodological advancements in route planning, they frequently operate under the assumption of static road network reliability, overlooking the dynamic failure risks associated with real-world events. Consequently, it is of considerable practical importance to investigate effective distribution strategies for regular express deliveries in emergency contexts. This paper addresses the express delivery requirements of urban residents in their daily lives, taking into account the challenges posed by disruptions to ground delivery systems. In response to these challenges, a novel location-routing problem (LRP) is introduced, which incorporates a vehicle-unmanned aerial vehicle (UAV) air-ground collaborative delivery model.