Mathematical programming applications in the analysis of the deployment and utilization of fire-fighting resources

This paper gives a brief review of some applications of mathematical programming in the analysis of the deployment of fire engines. We discuss a semi-Markov decision process (linear programming) formulation of the problem of deciding how many fire engines to dispatch to a new alarm, a staged integer programming formulation of the problem of relocating fire engines to rebalance city-wide protection when extremely large fires deplete part of the city, and simple non-linear integer programming formulations of strategic resource allocation problems. All analyses have resulted in policy recommendations that have influenced current operations of the New York City Fire Department.