# Drone-Based Parcel Delivery Using the Rooftops of City Buildings: Model and Solution
## 3 Model Development
### Assumptions and Problem Description  
Rooftop-based drone operations have the following potential advantages over other drone operations in terms of operability. It would be much easier for drones to find, follow, and land on the rooftops of buildings than to perform those actions with moving destinations such as delivery vans. In other words, the rooftops of buildings, particularly flat rooftops, can provide safe landing zones for drones. Real-time identification and selection of safe landing zones on rooftops based on light detection and ranging and camera sensor feedback have already been developed. Additionally, some trials to check the accuracy of rooftop-based drone operation have been conducted using a downward-facing camera to implement vision-guided rooftop landing [33]. In line with the abovementioned progress in the related technologies, we develop a MILP-based mathematical model for drone scheduling for parcel delivery using rooftops. To formulate the model, the following general assumptions are needed. * There are several buildings, each of which has a rooftop with sufficient space. * One of the rooftops of any building or the rooftop of a delivery center (e.g., post office building) is designated a drone operation center. * Drones are operated on a hub-and-spoke network, and each drone can carry at most one package due to their fixed payloads; thus, they can move between the drone operation center to one of the delivery locations only [24]. * Multiple drones are used, and the number of drones for parcel delivery is given. * Drones are not used to replace conventional delivery modes but to supplement them. * The demand is represented as the number of parcels, which is known and given for each building,
* The delivery location for each building is set to the center of the rooftop, and the delivery distance can be calculated by checking the straight-line distance between each destination and the drone operation center. In addition to the above assumptions, because the weight of the loadable item is limited to approximately 2 kg, it is difficult for most commercial parcel delivery drones to complete a delivery route with multiple parcels. The available moving distance of a drone is only approximately 10-15 km when there are weak winds and a clear line of sight. The battery can be recharged at any time when the battery is not fully charged. The general specifications of the drones manufactured for parcel delivery are summarized in Table 1. If such specifications are altered in accordance with improvements in the related technologies, they can be considered in our proposed model without modifying any of the model's constraints. Among the various specifications of the drones in Table 1, the worst-case battery consumption scenario was calculated using the equation proposed by [PERSON] [34]. Since battery consumption is critical to the safe flight of drones, we use the worst-case battery consumption to avoid any battery problems during the flight. The drone operating hours are set from 9:00 am to 6:00 pm (9 h) given the visibility condition of the drones. The take-off and landing of the drones and the loading/unloading of the goods are regarded as additional work, and we assume that this additional work takes approximately 15 min (0.25 h). Finally, the effects of weather, such as strong winds, are not taken into consideration because drones will not be operated for delivery in such conditions. In the beginning, drones start to deliver parcels to one target destination (i.e., rooftop) with a full battery capacity. Drones must choose either delivery or battery recharging as the next operation whenever they finish their previous operation. Additionally, drones need to recharge their batteries to amounts greater than the minimum recharging ratio to prevent full discharge, up to its full capacity. The accumulated operation time after the final operation should be less than the available hours (i.e., the drone operating hours).