Forecasting using Discrete Event Simulation for the NZ Prison Population Dr Jason (Qingsheng) Wang Mr Ross Edney Ministry of Justice

2 Prison Population Projections The prison population in NZ has grown steadily over the last decade The prisoner population is the end result of a chain of complex causal factors Serious crime, apprehensions, investigations, prosecutions and court cases which can involve variable periods of remand are precursors to imprisonment The opportunity cost of excess prison beds is high The costs of bed shortages is also high due in part to risks to staff and prisoner safety Several years of planning is required to build a prison so accurate forecasts are important

3 Discrete Event Simulation (DES) DES treats each prisoner entering the prison system separately and assigns the time that will be spent in prison so there is an entry date and exit date The technique “releases” prisoners from the virtual prison system when they have served their sentence DES can support multiple inflows A forecast track for the prisoner population can be derived by using the inflow and stay-time data

4 Remand Prison Population DES Model and Its Direct Drivers Remand prisoner inflows/arrivals Time spend on remand

5 Sentenced Prison Population DES Model and Its Direct Drivers Sentenced prisoner inflows/arrivals Given sentence for each arrived prisoners Proportion of sentence served

6 Determining Forecast Assumptions Historic data is employed to derive key input assumptions Time series and expert opinion is used to form a view of the likely direction of key driver variables Experts provide independent input on the impact of new policy that may affect, for example, custodial sentences and their length during the forecast horizon

Forecast, Sentenced Inflow

Forecast, Proportion Served

Forecast, Male Sentenced

Forecast, Male Remand

Forecast Performance, Including EI after New Sentences

12 DES Monte-Carlo Model, Confidence Intervals, and Capacity Planning Buffer Instead of using fixed mean values, the distributional DES model will feed the direct drivers with distributional values. Monte Carlo simulation will generate the population/muster probability distribution so to identify peak demand and risks over the planning horizon Policy simulation: this approach can be applied in policy changes with distributional impact

13 Sentenced Distributional DES Model

14 Remand Monthly Inflow and Distribution Using normal distribution of Holt-Winters model residuals and prediction errors

15 Time on Remand Distributions Annual empirical distributions

16 Remand Muster Monte-Carlo, Male

17 Muster Distribution Normality Test Cross-Section Distributions, Remand

18 Standardised Monte-Carlo, Remand

19 Standardised Monte-Carlo’s Distributions, Remand

20 Standardised Monte-Carlo Distribution, Sentenced

21 Forecast Confidence Intervals with Normal Distribution and Empirical Distribution

22 Volatility Buffer Calculation Assuming Normal Distributions

23 End Thank you

24 Jarque-Bera Test, Remand

25 Sentenced Distributional DES Model Inflows and Distributions

26 Sentenced Distributional DES Model Given Sentence Distributions

27 Sentenced Distributional DES Model Proportion Served Distributions

28 Proportion Served Distributions

29 Sentenced Muster Monte-Carlo, Male

30 Jarque-Bera Test, Sentenced Male