Maximum Coverage Location Model for Fire Stations with Top Corporate Risk Locations

Abstract

The fire station location is a critical decision to optimize the coverage level as measured in terms of the response time. This paper focuses on optimizing the coverage problem, especially in the fire protection field, with new model features to incorporate realistic business challenges such as location criticality and secondary coverage. We extend the deterministic Maximum Coverage Location Problem to account for Top Corporate Risk locations being covered by different fire stations as primary and secondary coverage. To deal with the response time uncertainty arising in practice, we propose a new binary linear problem based on the Maximum Expected Covering Location Problem. By exploiting the model structural characteristics, we prove that the model complexity can be substantially reduced to yield an efficient solution. In the numerical experiments, we use a real case study with five years of historical data. The optimization results of the models yield a priority ranking of the fire stations to open and show the value of incorporating the coverage uncertainty. Finally, we also compare our model with uncertainty with the standard scenario-based optimization to extend the numerical results.