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Firefighter Staffing Including Temporary Absences and Wastage

College of Business, University of Cincinnati, Cincinnati, Ohio 45221
College of Business, University of Cincinnati, Cincinnati, Ohio 45221
College of Business, University of Cincinnati, Cincinnati, Ohio 45221
mike.fry{at}uc.edu
mike.magazine{at}uc.edu
uday.rao{at}uc.edu

We examine the problem of determining the annual staffing level that minimizes total expected costs for a fire department, subject to minimum service-level-based staffing requirements. We develop a quantitative model that allows for stochastic temporary absences, permanent wastage, and limited hiring opportunities, and takes into account the unique firefighter work schedule. Our model is reminiscent of traditional newsvendor-type inventory models, but where the uncertainty is dependent on the decision variable. We derive easily implementable optimal staffing policies for both the continuous and discrete cases. We provide numerical results comparing our optimal solution to several heuristic staffing policies commonly used in practice, which show that our optimal policy can provide significant savings. We perform sensitivity analysis to generate managerial insights. We discuss an application of our model and analysis to the Cincinnati Fire Department.

Subject classifications: workforce staffing; firefighters; emergency services; probability; stochastic model applications.
History: Received July 2003; revision received December 2004; accepted December 2004.