Police manpower supply planning for regular duties with stochastic demands

We develop modeling strategies to alleviate the shortage of police manpower in a stochastic environment, based on flexible manpower supply planning using off-duty police officers and mutual support between police stations, along with flexible working hours and shifts. A stochastic independent assignment model (SIAM) and a stochastic mutual support model (SMSM) are constructed for manpower supply planning for regular policing duties with stochastic demands. These models are designed using mathematical programming techniques to minimize total manpower supply hours, subject to practical constraints. The SIAM is solved using CPLEX, but the SMSM is too complicated for this approach, so we develop our own heuristic algorithm to solve it efficiently. Additionally, we use the expected value of perfect information (EVPI) and the value of the stochastic solution (VSS) to evaluate the stochastic models. Numerical test results indicate that both models perform well, but the SMSM produces better manpower plans for police than the SIAM.