A Mixed-Integer Programming and Branch-and-Cut Approach for Multi-Unmanned Aerial Vehicle Cooperative Scheduling in Mountain Forest Fire Surveillance

Mountainous forest-fire surveillance with multiple UAVs is constrained by rugged terrain, time-varying winds, and temperature-dependent battery derating, which jointly affect endurance and route feasibility. Most existing patrol models simplify these effects through planar routing and constant energy-consumption assumptions. This study develops an energy-aware mixed-integer linear programming model that integrates terrain-induced climbing, period-dependent wind conditions, and battery derating into multi-UAV mission scheduling. Two valid inequalities—a symmetry-breaking cut and a fleet-size lower-bound cut—are embedded in a branch-and-cut framework to improve exact solution efficiency. The proposed method is applicable to year-round patrol planning under season-dependent meteorological conditions. In the Jinyun Mountain, Chongqing, case study, it is evaluated under three representative seasonal scenarios (summer, autumn, and winter), with particular emphasis on the summer pre-fire period as the primary high-risk operating scenario. Within the same computational time limit, the proposed approach reduces total flight distance by approximately 36–49% and energy consumption by approximately 61–74% relative to large neighborhood search and ant colony optimization, while using fewer UAVs to complete the same patrol tasks. These results demonstrate that explicitly coupling environmental and battery constraints can improve the operational efficiency and energy feasibility of multi-UAV wildfire surveillance, and can provide practical decision support for daily wildfire-prevention patrol planning in mountainous environments.