Two-stage optimization for site selection and resource allocation of metro rescue stations

Metro systems serve as the backbone of modern urban transportation, with elevators being critical facilities within metro stations. Considering the problem of elevator emergency rescue in an urban subway, a two-stage optimization model of location selection and resource allocation is proposed. In the first stage, based on the distribution and coverage of metro stations, a minimum site selection model and a maximum coverage model with a fixed number of rescue stations are constructed. Utilizing a mixed-integer programming approach, the optimal layout for rescue stations is determined, ensuring that the minimum number of stations covers all target locations. In the second stage, a resource allocation model is developed that optimizes the distribution of limited resources among rescue stations by balancing utility and cost. To address this non-linear mixed-integer programming problem, the authors conduct a comparative analysis of the efficiency and effectiveness of five heuristic algorithms in resource allocation. The results indicate that particle swarm optimization and tabu search achieve the highest benefits under a concentrated resource allocation strategy, while the genetic algorithm and ant colony optimization perform well in balanced resource distribution. This research provides theoretical support for emergency management in urban metro systems.