An optimization approach integrating coverage and cost in fire unit relocation
针对城市大型火灾中消防站资源耗尽后的重新部署问题，提出了一个整合覆盖与成本的优化模型，并用旧金山消防局数据验证其比启发式方法更有效。
Fire services are a vital part of the public sector, essential for protecting communities by providing rapid emergency response, saving lives, and reducing property damage. Urban growth and aging infrastructure have escalated fire incidents, placing heavy strain on fire departments. Major incidents, such as large-scale fires, are common in urban areas and often deplete multiple nearby fire stations, resulting in unprotected areas and delayed responses. During major incidents, a common practice in fire departments is relocation, moving fire units from staffed stations to empty stations to maintain temporary coverage. However, this relocation problem in fire services is underexplored from an optimization modeling perspective. Thus, this paper aims to develop an optimization model that integrates both coverage and costs to guide relocation decisions. We also analytically demonstrate that the proposed relocation model can be reduced to the classic maximal covering location model, highlighting the connection between relocation and location problems despite their distinctions. Using real data from the San Francisco Fire Department, numerical analyses demonstrate that relocation strategies significantly improve coverage compared with a heuristic method. In summary, this paper provides an integrated analytics and optimization approach to support relocation decisions, enabling fire departments to balance coverage improvement with cost efficiency.