## 3 Research Method  
This study developed a distance matrix that encompasses the warehouses from which delivery vehicles depart and all the stores served. Moreover, it determined the distances and travel times between each two points in the matrix. If \(N\) is the total number of stores, then the total number of points in a road network is \(N+1\) (including the warehouse). The number of combinations of data on travel distances and times is \((N+1)\times N\) (the travel distance and travel time between a point and itself are 0). For delivery task scheduling, the developed two-dimensional matrix allowed for quick checks on the travel time and distance between any two points within them, according to which the route and sequence of deliveries can be determined to minimize the total travel time of the fleet and to ensure that deliveries arrive at each store by the expected delivery time. Assume that unloading time is proportional to the number of goods to be unloaded at each store. In this case, the time of a vehicle's arrival at a store should be accurately estimated by summing the vehicle's unloading time at the preceding store and the time required to travel to the particular store. All the vehicles in the target fleet have a GPS device on board that sends the vehicle's GPS information, including GPS time, speed, latitude and longitude, and azimuth, to the management system every 30 s. According to this information, the management system detects abnormal vehicle activities, such as speeding, prolonged stop at a location, or deviation from the scheduled route. The information relevant to this study is the times a vehicle enters and exits a location, including the warehouse and stores. The management system delineates the areas of the warehouse and stores to establish geofences for them. A vehicle is considered to have arrived at and departed from a location at the moment it drives into and outside the geofence, respectively. Given that many convenience stores are located near a crossroad, the management system might incorrectly detect a vehicle's arrival at a store if it enters the store's geofence as it drives past the store. To address this problem, this study included two additional factors--pulling the parking brake and stopping for 3 min or longer--for determining a vehicle's arrival. Specifically, a vehicle was determined to have arrived at a store for unloading the delivery if it entered the store's geofence if the parking brake was pulled, and if it had stopped at the spot for 3 min or longer, with the arrival time being recorded as the time the vehicle first entered the geofence. The vehicle was determined to have completed unloading the delivery and leaving the store if the parking brake was released and the vehicle had driven out of the store's geofence, with the departure time being recorded as the time the vehicle drove out of the geofence. The duration between a vehicle's departure time from a store and its arrival time at the next store is the travel time between the two stores. After adequate travel time data were collected, the average travel time between a departure location and an arrival location was calculated according to the historical travel data between these locations. The travel times of all vehicles that had traveled between the two locations were used for the calculation. Therefore, the vehicle numbers were not included in the travel time calculation, with the only factors considered being the locations of departure and arrival and the times of departure and arrival. Some vehicles had a relatively long travel time because of road conditions, vehicle malfunctions, or traffic incidents, whereas other vehicles had a relatively short travel time because their drivers drove fast. Travel time records that were excessively long or short, which represented abnormal records, were removed to prevent them from affecting the average travel time. According to the normal distribution theory, the distribution of the collected data can be accurately estimated using the data's mean and standard deviation.