Staffing Healthcare Personnel Combining Petri Nets and Optimisation

Healthcare services are usually delivered by teams, each one composed of individuals working together sharing knowledge, experiences and skills. The staffing problem consists in finding an optimal set of teams with respect to a given performance metrics in such a way to meet a forecasted service demand, which determines the workload level. Various metrics can be used to measure the efficiency of one individual, and to evaluate the overall team performance. The random nature of the problem requires the introduction of random variables, and the characterisation of the overall team behaviour with a stochastic process. We propose hybrid algorithms based on generalised stochastic petri nets (GSPN) and optimisation. The basic idea is to exploit the GSPN model as a black box to evaluate a solution computed by an optimisation algorithm, that is the team performance under several demand scenarios. We test the proposed algorithms on a case study arising from an Italian Emergency Medical Services. The insights from the computational analysis confirm the validity of the proposed algorithms.