Planning for time-varying volunteer firefighter systems under probabilistic service disruptions

Volunteer firefighters have been incorporated alongside career firefighters to supplement the overall performance and flexibility of fire emergency response systems in many countries. However, volunteer firefighters are more likely to suffer from sub-optimal health conditions during missions than are full-time career firefighters. Thus, they are less reliable in providing consistent emergency response services over time. This paper addresses the time-varying planning problem for volunteer firefighter shifts while considering firefighter service disruptions. We first present a single-period hypercube queuing model for the volunteer service problem under probabilistic disruptions. Then, we propose a two-level volunteer planning model for the multi-period problem by including payments’ budgetary constraints and volunteer health consumption’s effect on service reliability. We validate the hypercube-based optimization model by using the Arena software under various disruption scenarios. Finally, we apply the proposed model to the fire service system in Tangxian, Hebei, China. The numerical results show that our approach provides a promising tool for improving fire emergency response systems’ performance in a time-varying setting.