Demand estimation with failure and capacity constraints: An application to prisons

A stochastic model for projecting demand for a population-driven, input–output facility that incorporates demographic changes, facility returns representing ‘failures’, and capacity constraints is proposed and demonstrated. The model is applied to the problem of prison population projection. The approach models the flow of inmates through the prison system, exploits the differences in the incarceration hazard rates of individuals in the general population and those who have been incarcerated previously, and explicitly considers the impact of constrained prison capacity on release policy and future admissions. First-time arrivals to prison are modeled as a Poisson process arising from the general population; recidivist arrivals are modeled using a failure model, where the reincarceration hazard rate is a function of age and race. The model is demonstrated for the State of North Carolina. The effect of limited prison capacity on the average time served is shown. Further, the results demonstrate that an early release policy will generate an increase in prison admissions through the return to prison of former inmates. The implications for current ‘get tough’ sentencing policy initiatives relative to the prison crowding problem, the length of stay for offenders not included in the new policies, and the recursive effect of these policies on the input–output dynamics are considered. The results suggest the tradeoffs that exist between early release policies and capacity limitations.