## 1 Background  
Convenience stores have become an integral part of modern life because of changes in lifestyles and consumption habits. Convenience stores are mostly located near commercial areas or communities with convenient transportation. In addition to providing daily supplies, such stores offer other services, including fee collection and e-commerce product delivery, and are open 24 h daily. Since the coronavirus pandemic began in 2019, the importance of convenience stores has increased in Taiwan because they have facilitated the reservation and sale of medical masks through a name-based mask distribution system, the reservation of vaccines, and the reservation and distribution of stimulus vouchers. According to the open data platform of convenience stores in Taiwan [1], Taiwan has 13,173 convenience stores in service as of May 2023, with one store for every 1789 people on average. A single convenience store that runs 24 h daily might receive up to eight deliveries of stocks in a day because of the varying delivery temperature requirements of different products and the need to provide the freshest foods and meals at the store. For example, room-temperature, frozen, refrigerated, fresh, and microwave foods are delivered in separate vehicles at their required storage temperatures. The logistics of chain convenience stores follow a predetermined schedule. With the varying sales levels across convenience stores as well as the opening and closing of stores nearly every week, delivery dispatchers formulate a delivery plan for the following month according to each store's average monthly order quantity and expected monthly delivery. The dispatch process involves three main operations:  
1. Planning a delivery route that connects various stores to be served by a vehicle: The goal is to maximize vehicle capacity without exceeding the loading limit, to minimize the distance between stores along the route, and to arrive at each store at its expected delivery time. Convenience stores are typically located at crossroads or in densely populated areas, which makes deliveries by large vehicles difficult. Therefore, deliveries for these stores are usually completed using medium-sized vehicles that weigh 10 metric tons when loaded. Each delivery route contains approximately 10-20 stores, and the expected time to complete delivery on a route is approximately 3 h.
2. Sequencing the stops at convenience stores: This task involves a traveling salesman problem that requires the route to satisfy each store's expected delivery time and minimize the travel distance by sequencing stops in an appropriate order. 3. Estimating the expected arrival time for each delivery and notifying the corresponding store in advance: This task is particularly helpful for convenience store logistics because convenience stores are typically located at crossroads or in densely populated areas and might have specific requests regarding delivery times because of the nature of deliveries, which makes it difficult for delivery vehicles to avoid traffic. In addition, the absence of storefront space for trucks to park and unload because of these stores' proximity to large roads means that trucks can only park and unload at roadsides. Therefore, upfront notifications to the stores allow them to make space for delivery trucks to park, for delivery to be transported in stores, and for storing the delivery. Operations (1) and (2), which concern the delivery vehicle's route planning, are outside the scope of this study and are thus to be discussed in depth in a separate study. The current study focuses on constructing a model that estimates travel time for logistics vehicles. The currently available online map resources that provide estimated arrival time based on users' departure points and destinations include OpenStreetMap, Google Maps, and navigation applications. Google Maps' estimated travel time is particularly accurate because it included real-time traffic.