Documentation of SIB_130308

View the 140 variables sorted by type, module, group, module/group/name, view, Level Structure, or in a view summary.

Model Assessment Results
Model Information Number
Total Number of Variables
140
Total Number of State Variables (Level+Smooth+Delay Variables)
23
Total Number of Stocks (Stocks in Level+Smooth+Delay Variables) †
127
Total Number of Macros
0
Function Sensitivity Parameters
0
Variables with Source Information
0
Data Lookup Tables
0
Time Unit
Month
Initial Time
0
Final Time
200
Time Step
0.03125
Model Is Fully Formulated
Yes
Modeler-Defined Groups
Yes
VPM File Available
- No -

Warnings Number
Undocumented Equations
0
Equations with Embedded Data
36
Equations With Unit Errors
* *
Variables Not in Any View
0
Incompletely Defined Subscripted Variables
0
Nonmonotonic Lookup Functions
0
Cascading (Chained) Lookup Functions
0

Potential Omissions Number
Unused Variables
3
Supplementary Variables
0
Supplementary Variables Being Used
0
Overly Complex Variable Formulations (Richardson's Rule = 3)
18
Overly Complex Stock Formulations
4

Types:
L : Level (23 / 127) * SM : Smooth (0 / 0) * DE : Delay (0 / 0) * † LI : Level Initial (11) I : Initial (0)
C : Constant (44) F : Flow (24) A : Auxiliary (77) Sub: Subscripts (5) D : Data (0)
G : Game (0) T : Lookup (0 / 0) ††      
* (state variables / total stocks)
* * Feature not yet implemented.
† Total stocks do not include fixed delay variables.
†† (lookup variables / lookup tables).
 
Groups:
Control (29)
Simulation Control Parameters 		Initial Estimates (5) IRR (25) Peterborough Reconviction (0) PMS (0)
Project Timing (13) Rehab (14)
Modules:
Default (140)
Views:
System Operations (43)Analysis Sheet (50)Propensity Score Matching Measures (57)Boundaries (63)SIB (44)
Investor Finances (51) 
Search: •••    a-b    c-d    e-f    g-h    i-j    k-l    m-n    o-p    q-r    s-t    u-v    w-x    y-z    •••   

Module
Group
Type
 Variable Name and Description
Default Control F,A

Accummulating Interest from Investment (k£/Month)
Accummulating Interest from Investment[Cohorts,Interest] = IF THEN ELSE(Cohort Payment Time[Cohorts]>=Time, Limits of Unpaid Investor Returns[Cohorts,Interest]*Annual Interest Rate for Investment[Interest]/Defined Year,0)
Description: This represents the rate interest collects at the maximum rate of return based on the value by Disely et. al. (2011).
Present in 1 view: Used by:
  • Limits of Unpaid Investor Returns - This represents the payment to the investors based on a succesful project. This includes both a maximum, minimum and Bond values. This is an Author defined structure.
Default Project Timing L
Actual Cohort Closing Times (Month)
Actual Cohort Closing Times[Cohorts] = ∫ (Cohort Time[Cohorts]) dt + [0]
Description: This represents the ending time of the cohorts based on the rules of Cave et al. (2012).
Present in 2 views: Used by:
  • Cohort Active? - This turns on the flow of new incarcerations between each cohort group. The definitions are laid out in Cave's et. al. (2012) description of cohort groupings.
  • Cohort Payment Time - This represents the time at which the program is measured as a success or as a failure. RT Time and System Update Time (18 months) are added on to the accumulation time as per Cave et. al. (2012) to show the time between cohort collection finishing and the data results being collected.
  • Investment Finalization Time - This represents when the investment is finalized and ready for repayment as per the timeline in Cave et al. (2012).
  • Owner Post-Program Payments - In the event of a successful program the owner would want to assume the payments for the program. This is represented by using a switch ("Program Off?") and the value of the payments. This is an Author derived flow based on Glahn and Whistler (2011).
  • Percent Released Offenders Allowed in Program - This represents the maximum percentage of people released from prison that are allowed in the program for each cohort. This is an author defined constraint to control for entrants into the program and reduce the number of offenders allowed in the program.
  • Reconviction Termination - This represents when the reconviction counts for the project stop being collected as per Cave et. al. (2012). RT Time is (12 months) added as the time when reconvictions will be measured.
Default Project Timing L
Actual Cohort Start Times (Month)
Actual Cohort Start Times[Cohorts] = ∫ (Cohort Time Delay Rate[Cohorts]) dt + [0]
Description: This is the actual start time of the project. The time is accumulated to account for the rules set forth by Cave et al. (2012).
Present in 3 views: Used by:
  • Cohort Active? - This turns on the flow of new incarcerations between each cohort group. The definitions are laid out in Cave's et. al. (2012) description of cohort groupings.
  • Cohort initiate switch - This determines whether the cohorts have started in accordance with the rules set forth from Cave et. al. (2012) primarily that the maximum time cannot be exceeded and the cohorts must switch before if the maximum number is met or exceeded.
  • Cohort Investment switch - This represents when investors are investing in different cohorts. This is an author derived variable from Cave et al. (2012).
  • Investing - This represents the steady flow of investor funds into the system. It is an Author derived variable equivalent to the amount of the investment divided by the total duration of the project and comes from Social Finance Limited (2011).
  • program time - This represents how long the program has been operating. This is an author defined equation.
Default IRR LI,A
Actual Investor Return payments (k£/Month)
Actual Investor Return payments[Cohorts,Interest] = "Investors Cohorts Paid? Amount"[Cohorts]
Description: This represents when and how much was returned to the investors to account for payments. This is an Author defined variable.
Present in 1 view: Used by:
  • Earned Investor Return payments - This represents the amount of payment to the investors from the program reducing the amount of payment to the investors in future. This is an Author defined equation.
  • Limits of Unpaid Investor Returns - This represents the payment to the investors based on a succesful project. This includes both a maximum, minimum and Bond values. This is an Author defined structure.
Default IRR F,A

Actual Peterborough Costs (k£/Month)
= (Short Term Reconviction Costs[Peterborough])*Owner Discount Factor
Description: This represents the actual expenses for the Peterborough prison system using the costs of reconvictions found in Strickland (2010). (Reconviction cost times the number of reconvictions from Peterborough Released prisoners. This is an Author derived equation of the acutal expenses and is deflated to maintain consistent projection value.
Present in 1 view: Used by:
  • MOJ Account - This Represents the amount of money in the MOJ and BLF account. The structure of this accountto investors is pulled from Social Finance Limited (2011).
Default IRR L
Amount Available for Rehab Programs (k£)
= ∫ (Total Programs Savings Rate-MOJ Program Savings Rate-Rehabilitation Program Investment Rate) dt + [0]
Description: Amount available to repay investors as well as the amount of savings seen by the MOJ. This is an Author defined stock signifying the seperation of savings from the normal MOJ budget.
Present in 1 view: Used by:
  • MOJ Program Savings Rate - This represents the amount of savings that the MOJ sees from the Rehabilitation Program. This is an Author defined equation that allows money to be moved from a general savings account to an organizational savings account. There is no limit for the program to go to zero so that the MOJ can move money back into the general account at a later date for program funding.
Default L
Amount Investors are willing to Invest (k£)
= ∫ (-Investing) dt + [Expected Program Investment amount]
Description: This represents the amount of capital that the Investors are have set aside to invest in the program. This stock is located in both Social Finance (2011) and Glahn & Whistler (2011).
Present in 1 view: Used by:
  • Investor Balance - This represents the current balance of the investors accounts with both what they have set for investing along with the returns for a successful program. This is an Author defined performance variable that may be considered in the tests.
Default IRR L
Amount Paid for Rehab Program (k£)
= ∫ (Rehabilitation Program Investment Rate) dt + [0]
Description: This represents the amount of money paid for the program. This is an Author defined stock to measure the IRR for the MOJ.
Present in 1 view: Used by:
  • IRR MOJ - This represents the Internal Rate of Return for the owner starting after the final reconvictions are finished collecting. Both stocks used have already been discounted to the time the project started. This is an author defined variable for performance measures.
Default IRR L
Amount Saved From Programs (k£)
= ∫ (MOJ Program Savings Rate) dt + [0]
Description: This represents the amount of money saved from the program that can be used by the MOJ for anything. This stock is Author derived to from social finance limited (2011) and Glahn & Whistler (2011).
Present in 2 views: Used by:
  • IRR MOJ - This represents the Internal Rate of Return for the owner starting after the final reconvictions are finished collecting. Both stocks used have already been discounted to the time the project started. This is an author defined variable for performance measures.
  • Monthly MOJ Funded Interventions - This represents the number of people the MOJ will fund after the program is found successful. It is an Author derived based Glahn and Whistler (2011) to represent the desired expenses of the program and the desired level of expenses of the program.
Default Control C
Annual Interest Rate for Investment (Dmnl)
Annual Interest Rate for Investment[Interest] = 0.13,0.075,0.04
Description: This represents the nominal interest multiplier for each month of the project. This value comes from the Cave et. al. (2012) as the maximum return rate.
Present in 2 views: Used by:
Default Initial Estimates C
Average Prisoner Incarceration Rate for Peterborough (People/Month)
= 57.8333
Description: This represents the maximum number of people that can be placed in the prison system modelled, all other prisoners must go to a different prison system. In the Base Case Model, the prisoners are allowed to exceed the maximum capacity rate to show how many prisoners would have needed to have gone through the system if not for the program. {200 people/month tunes the model to Cave et al (2012).}
Present in 2 views: Used by:
  • New Offender Incarceration Rate - This represents the flow of first time offenders into the prison system that fit the criteria for the program as outlined in Strickland (2010). The in flow of new prisoners is the difference between the number of prisoners that can be accepted on a monthly basis and the recidivism rate of prisoners from the overall cohort. This is one of the variations from the Lyneis and Ford (2007) model
Default Rehab A
Average Time between Release and Reconviction (Month)
Average Time between Release and Reconviction[Prison Systems] = Normal Recidivism Discovery Time
Description: The average amount of time it takes to convict a resent release from the Peterborough group of a new crime. This takes Disely et al. (2012) value from the analysis and introduces a change from the programs operations.
Present in 1 view: Used by:
  • Repeat Offender Arrest Rate - This is the rate of discovery for people who recommit crimes. The flow is averaged from the backlog and the time found in Cox (2006).
Default Control LI,A
Bond Investment (k£/Month)
Bond Investment[Cohorts,maximum] = Investing*Cohort Investment switch[Cohorts]
Bond Investment[Cohorts,minimum] = Investing*Cohort Investment switch[Cohorts]
Bond Investment[Cohorts,Bond] = Investing*Cohort Investment switch[Cohorts]
Description: This represents when and how much was paid from the investors.
Present in 1 view: Used by:
  • Limits of Unpaid Investor Returns - This represents the payment to the investors based on a succesful project. This includes both a maximum, minimum and Bond values. This is an Author defined structure.
Default Project Timing LI,A
Cohort Active? (Dmnl)
Cohort Active? [Overall] = IF THEN ELSE(Actual Cohort Start Times[Overall]<Time,1,0)
Cohort Active? [Cohort 1] = IF THEN ELSE(Actual Cohort Start Times[Cohort 1]<Time,IF THEN ELSE(Actual Cohort Closing Times[Cohort 1]>=Time,1,0),0)
Cohort Active? [Cohort 2] = IF THEN ELSE(MIN(Actual Cohort Closing Times[Cohort 1],Actual Cohort Start Times[Cohort 2])<Time,IF THEN ELSE(Actual Cohort Closing Times[Cohort 2]>=Time,1,0),0)
Cohort Active? [Cohort 3] = IF THEN ELSE(MIN(Actual Cohort Closing Times[Cohort 2],Actual Cohort Start Times[Cohort 3])<Time,IF THEN ELSE(Actual Cohort Closing Times[Cohort 3]>=Time,1,0),0)
Cohort Active? [Cohort 4] = IF THEN ELSE(Actual Cohort Start Times[Cohort 4]<Time,IF THEN ELSE(Actual Cohort Closing Times[Cohort 4]>=Time,1,0),0)
Description: This turns on the flow of new incarcerations between each cohort group. The definitions are laid out in Cave's et. al. (2012) description of cohort groupings.
Present in 3 views: Used by:
  • Cohort Addition of New Offenders - This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Program Continues? - This represents whether or not the program continues after investment based on the success of the program and the investment time being met. This is an Author Defined variable in accordance with Glahn and Whistler (2011).
Default F,A

Cohort Addition of New Offenders (People/Month)
Cohort Addition of New Offenders[Cohorts,Prison Systems] = ∑((Rehabilitated Offenders Release Rate[Cohorts,Release Program!,Prison Systems,First]+Unrehabilitated Offender Release Rate[Cohorts,Release Program!,Prison Systems,First]))*"Cohort Active?"[Cohorts]
Description: This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
Present in 1 view: Used by:
  • Cohort Collection of New Offenders - This represents the accumulation of people in collected in the different cohorts for the Peterborough group based on Cave et. al. (2012).
Default L
Cohort Collection of New Offenders (People)
Cohort Collection of New Offenders[Cohorts,Prison Systems] = ∫ (Cohort Addition of New Offenders[Cohorts) dt + [Prison Systems],0]
Description: This represents the accumulation of people in collected in the different cohorts for the Peterborough group based on Cave et. al. (2012).
Present in 2 views: Used by:
  • Cohort initiate switch - This determines whether the cohorts have started in accordance with the rules set forth from Cave et. al. (2012) primarily that the maximum time cannot be exceeded and the cohorts must switch before if the maximum number is met or exceeded.
  • Cohort Time Delay Rate - This is an Author derived control to increase time according to the rules set in Cave et al. (2012).
  • Desired Program Capacity - This represents the maximum number of people that will be collected in the cohort that should get space in the program. It is an Author defined variable to slow the flow of people into programs and keep them from overrunning the financial capacity of the NGO.
  • Reconviction Fraction - This represents the rate of reconviction for people in the Peterborough group as perscribed by Cave et. al. (2012).
Default F,A

Cohort Expense Rate (k£/Month)
= Program Costs
Description: This represents how the funds are allocated. This is an author defined variable.
Present in 2 views: Used by:
Default Project Timing C,A
Cohort initiate switch (Dmnl)
Cohort initiate switch[Overall] = 1
Cohort initiate switch[Cohort 4] = IF THEN ELSE(Cohort Collection of New Offenders[Cohort 3,Peterborough]<=Max People in Cohort[Cohort 3], IF THEN ELSE(Actual Cohort Start Times[Cohort 4]+3*Max Cohort Length[Cohort 4]>Time,1,0),0)
Cohort initiate switch[Cohort 1] = IF THEN ELSE(Cohort Collection of New Offenders[Cohort 1,Peterborough]<= Max People in Cohort[Cohort 1] , IF THEN ELSE((Actual Cohort Start Times[Cohort 1]+Max Cohort Length[Cohort 1]) >Time, 1 , 0 ), 0 )
Cohort initiate switch[Cohort 2] = IF THEN ELSE(Cohort Collection of New Offenders[Cohort 2,Peterborough]<= Max People in Cohort[Cohort 2] , IF THEN ELSE((Actual Cohort Start Times[Cohort 2]+Max Cohort Length[Cohort 2]) >Time, 1 , 0 ), 0 )
Cohort initiate switch[Cohort 3] = IF THEN ELSE(Cohort Collection of New Offenders[Cohort 3,Peterborough]<= Max People in Cohort[Cohort 3] , IF THEN ELSE((Actual Cohort Start Times[Cohort 3]+Max Cohort Length[Cohort 3]) >Time, 1 , 0 ), 0 )
Description: This determines whether the cohorts have started in accordance with the rules set forth from Cave et. al. (2012) primarily that the maximum time cannot be exceeded and the cohorts must switch before if the maximum number is met or exceeded.
Present in 2 views: Used by:
  • Cohort Time - This represents the time that the cohorts are collecting people for comparison. This is determined by Cave et. al. (2012) using the Cohort initiate switch.
  • Cohort Time Delay Rate - This is an Author derived control to increase time according to the rules set in Cave et al. (2012).
Default A
Cohort Investment switch (Dmnl)
Cohort Investment switch[Cohorts] = IF THEN ELSE(Actual Cohort Start Times[Cohorts]<Time, IF THEN ELSE(Investment Finalization Time[Cohorts]>=Time, 1,0),0)
Description: This represents when investors are investing in different cohorts. This is an author derived variable from Cave et al. (2012).
Present in 3 views: Used by:
Default Project Timing C,A
Cohort Payment Time (Month)
Cohort Payment Time[Overall] = 0
Cohort Payment Time[Cohort 1] = Actual Cohort Closing Times[Cohort 1]+Time after Cohort for Reconviction Collection+Time for System Update
Cohort Payment Time[Cohort 2] = Actual Cohort Closing Times[Cohort 2]+Time after Cohort for Reconviction Collection+Time for System Update
Cohort Payment Time[Cohort 3] = Actual Cohort Closing Times[Cohort 3]+Time after Cohort for Reconviction Collection+Time for System Update
Cohort Payment Time[Cohort 4] = Actual Cohort Closing Times[Cohort 4]+Time after Cohort for Reconviction Collection+Time for System Update+ Time Program has to Pay
Description: This represents the time at which the program is measured as a success or as a failure. RT Time and System Update Time (18 months) are added on to the accumulation time as per Cave et. al. (2012) to show the time between cohort collection finishing and the data results being collected.
Present in 2 views: Used by:
  • Accummulating Interest from Investment - This represents the rate interest collects at the maximum rate of return based on the value by Disely et. al. (2011).
  • Investment Finalization Time - This represents when the investment is finalized and ready for repayment as per the timeline in Cave et al. (2012).
  • Maximum Payment Accumulation - This represents the accumulation for the maximum payment value. This is an Author defined equation to ensure investors are paid the amount they are due.
  • Payment Consideration? - This marks the time that a payment is considered in the project (Cave et. al. 2012). Payment cannot be considered before the completion of cohort collection plus the time interval for data occurence, collection and analysis.
Default Project Timing F,A

Cohort Time (Month/Month)
Cohort Time[Cohorts] = Cohort initiate switch[Cohorts]
Description: This represents the time that the cohorts are collecting people for comparison. This is determined by Cave et. al. (2012) using the Cohort initiate switch.
Present in 1 view: Used by:
Default Project Timing C,F,A

Cohort Time Delay Rate (Month/Month)
Cohort Time Delay Rate[Overall] = 0
Cohort Time Delay Rate[Cohort 1] = IF THEN ELSE(Max People in Cohort[Cohort 1]>Cohort Collection of New Offenders[Cohort 1,Peterborough],IF THEN ELSE(Latest Cohort Start Times[Cohort 1]>Time,1,0),0)*Cohort initiate switch[Cohort 1]
Cohort Time Delay Rate[Cohort 2] = IF THEN ELSE(Max People in Cohort[Cohort 2]>Cohort Collection of New Offenders[Cohort 2,Peterborough],IF THEN ELSE(Latest Cohort Start Times[Cohort 2]>Time,1,0),0)*Cohort initiate switch[Cohort 1]
Cohort Time Delay Rate[Cohort 3] = IF THEN ELSE(Max People in Cohort[Cohort 3]>Cohort Collection of New Offenders[Cohort 3,Peterborough],IF THEN ELSE(Latest Cohort Start Times[Cohort 3]>Time,1,0),0)*Cohort initiate switch[Cohort 2]
Cohort Time Delay Rate[Cohort 4] = IF THEN ELSE(Max People in Cohort[Cohort 4]>Cohort Collection of New Offenders[Cohort 4,Peterborough],IF THEN ELSE(Latest Cohort Start Times[Cohort 4]>Time,1,0),0)
Description: This is an Author derived control to increase time according to the rules set in Cave et al. (2012).
Present in 1 view: Used by:
  • Actual Cohort Start Times - This is the actual start time of the project. The time is accumulated to account for the rules set forth by Cave et al. (2012).
Default Control Sub
Cohorts
: Overall, Cohort 1, Cohort 2, Cohort 3, Cohort 4
Description: There are five (5) different groups or Cohorts in this model. The "Overall" group tracks the impact of the program on the system both before after and during. The other groups (Cohort 1-4) are listed and described as per Cave et. al. (2012).
Present in 6 views: Used by:
  • Accummulating Interest from Investment - This represents the rate interest collects at the maximum rate of return based on the value by Disely et. al. (2011).
  • Actual Cohort Closing Times - This represents the ending time of the cohorts based on the rules of Cave et al. (2012).
  • Actual Cohort Start Times - This is the actual start time of the project. The time is accumulated to account for the rules set forth by Cave et al. (2012).
  • Actual Investor Return payments - This represents when and how much was returned to the investors to account for payments. This is an Author defined variable.
  • Bond Investment - This represents when and how much was paid from the investors.
  • Cohort Active? - This turns on the flow of new incarcerations between each cohort group. The definitions are laid out in Cave's et. al. (2012) description of cohort groupings.
  • Cohort Addition of New Offenders - This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
  • Cohort Collection of New Offenders - This represents the accumulation of people in collected in the different cohorts for the Peterborough group based on Cave et. al. (2012).
  • Cohort initiate switch - This determines whether the cohorts have started in accordance with the rules set forth from Cave et. al. (2012) primarily that the maximum time cannot be exceeded and the cohorts must switch before if the maximum number is met or exceeded.
  • Cohort Investment switch - This represents when investors are investing in different cohorts. This is an author derived variable from Cave et al. (2012).
  • Cohort Payment Time - This represents the time at which the program is measured as a success or as a failure. RT Time and System Update Time (18 months) are added on to the accumulation time as per Cave et. al. (2012) to show the time between cohort collection finishing and the data results being collected.
  • Cohort Time - This represents the time that the cohorts are collecting people for comparison. This is determined by Cave et. al. (2012) using the Cohort initiate switch.
  • Cohort Time Delay Rate - This is an Author derived control to increase time according to the rules set in Cave et al. (2012).
  • Cohorts - There are five (5) different groups or Cohorts in this model. The "Overall" group tracks the impact of the program on the system both before after and during. The other groups (Cohort 1-4) are listed and described as per Cave et. al. (2012).
  • Desired Payment Value - This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
  • Desired Program Capacity - This represents the maximum number of people that will be collected in the cohort that should get space in the program. It is an Author defined variable to slow the flow of people into programs and keep them from overrunning the financial capacity of the NGO.
  • Earned Investor Return payments - This represents the amount of payment to the investors from the program reducing the amount of payment to the investors in future. This is an Author defined equation.
  • Investing - This represents the steady flow of investor funds into the system. It is an Author derived variable equivalent to the amount of the investment divided by the total duration of the project and comes from Social Finance Limited (2011).
  • Investment Finalization Time - This represents when the investment is finalized and ready for repayment as per the timeline in Cave et al. (2012).
  • Investor Earned - This represents the value of savings determined in the contracts without the limits. The Investor share value is kept anonymous to the public. according to Cave et. al. (2012) and Disely et. al. (2011). The value is determined by multiplying the number of reconvictions that should have been based on the comparison group results (Cave et. al. 2012).
  • Investor Earned Return Accumulation - This represents the accumulation of investor earnings based on Cave et. al. (2012).
  • Investors Cohorts Paid? Amount - This represents the payment rate to the investors when they are paid within their investment. This is an Author derived equation.
  • Limits of Unpaid Investor Returns - This represents the payment to the investors based on a succesful project. This includes both a maximum, minimum and Bond values. This is an Author defined structure.
  • Max Cohort Length - This represents the maximum length of an individual Cohort (1-3) or 1/3 of the maximum time for the final cumulative cohort as outlined by Cave et. al. (2012).
  • Max People in Cohort - This is the maximum number of people allowed in the cohort (Cave et. al. 2012).
  • Maximum Payment Accumulation - This represents the accumulation for the maximum payment value. This is an Author defined equation to ensure investors are paid the amount they are due.
  • Maximum Successful Program Payment Value - This represents the maximum value for payment. This is Author defined to ensure a complete payment to investors.
  • MOJ Dictated Program Capacity - This represents the percentage of people that the MOJ is willing to put through the rehabilitation program after it is proven successful. It is bound between 0 and 1. It is an Author derived from Glahn and Whistler formula bound to provide the desired people in the program with a zero value for an unsuccessful program.
  • New Offender Incarceration Rate - This represents the flow of first time offenders into the prison system that fit the criteria for the program as outlined in Strickland (2010). The in flow of new prisoners is the difference between the number of prisoners that can be accepted on a monthly basis and the recidivism rate of prisoners from the overall cohort. This is one of the variations from the Lyneis and Ford (2007) model
  • Number of Reconviction - This represents the accumulation of reconvicted people in the cohort for the comparison group as per Cave et. al. (2012)
  • Offender Release Rate - This represents the Total release rate from prison for the different prisons. This is an Author defined variable that can be used to measure performance.
  • Owner Post-Program Payments - In the event of a successful program the owner would want to assume the payments for the program. This is represented by using a switch ("Program Off?") and the value of the payments. This is an Author derived flow based on Glahn and Whistler (2011).
  • Payment Consideration? - This marks the time that a payment is considered in the project (Cave et. al. 2012). Payment cannot be considered before the completion of cohort collection plus the time interval for data occurence, collection and analysis.
  • Payment for Cohort 1 - This represents the value of the payment for Cohort 1. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 2 - This represents the payment value for Cohort 2. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 3 - This represents the payment for Cohort 3. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 4 - This represents the payment value for the entire project. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Percent Released Offenders Allowed in Program - This represents the maximum percentage of people released from prison that are allowed in the program for each cohort. This is an author defined constraint to control for entrants into the program and reduce the number of offenders allowed in the program.
  • Population in Program - This represents the number of people that are in the program at any point in time. This is an Author defined variable used to calculate the monthly program costs.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Prison Population Reduction Percent - This represents the fraction of prisoners from the peterborough population that have been reduced as a result of the program.
  • Program Continues? - This represents whether or not the program continues after investment based on the success of the program and the investment time being met. This is an Author Defined variable in accordance with Glahn and Whistler (2011).
  • Program Costs - This represents the rate of expense by the conglomerate when adding people to the program. This is an Author derived flow from the Social Finance Limited (2011).
  • program time - This represents how long the program has been operating. This is an author defined equation.
  • Rate of Offenders Coming off of Probation - This represents the rate at which people who will not be convicted leave the program.
  • Rate of Reconviction - This represents the rate of reconvicted people for the comparison group by summing the Recidivism Exclusion Rate and Recidivism Rate as per Cave et. al. (2012).
  • Reconviction Change - Percent of change between the comparison group and the Peterborough group. The equation is derived from Cave et al. (2012) explanation of the program measures.
  • Reconviction Fraction - This represents the rate of reconviction for people in the Peterborough group as perscribed by Cave et. al. (2012).
  • Reconviction Termination - This represents when the reconviction counts for the project stop being collected as per Cave et. al. (2012). RT Time is (12 months) added as the time when reconvictions will be measured.
  • Reconvictions Prevented - This represents the number of reconvictions that the program saved the government from having to go through. This is an Author derived equation.
  • Rehabilitated Offenders - This represents the people in the program that are in the program.
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
  • Repeat Offender Arrest Rate - This is the rate of discovery for people who recommit crimes. The flow is averaged from the backlog and the time found in Cox (2006).
  • Savings from Reduced Reconvictions - This represents the total savings from the reconvictions that remain short term convictions. This is an Author Derived equation.
  • Short Term Reconviction Costs - This represents the monthly cost for short term reconvictions within the Peterborough Prison System. This is an Author derived equation from Disely et al. (2011).
  • Successful Program? - This variable measures whether or not the program successfully pays out as described by Cave et. al. (2012).
  • Total Prison Population - The percentage of system use.
  • Undiscoverd Reoffenders - This represents the people that are in the program that eventually will recommit.
  • Unpaid Investor Earned Returns - This represents the accumulation of investor earnings through payment based on Cave et. al. (2012)
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default C
Conviction Cost (k£/People)
= 2.853
Description: This represents the legal costs per conviction based on the data from SEU (2002)[May also be found in Mulgan 2011].
Present in 2 views: Used by:
  • Total Cost of Incarceration - This represents the cost for each reconviction by the British government per person. It is a combination of both the legal action and the time spent in prison. This is an Author derived equation from Mulgan et al. 2012)
Default A
Cost per Participant per month (k£/(Month*People))
= Program Cost per member/Defined Year
Description: This represents the cost for one person to be in the program for one month as per Mulgan et al. (2011) page 30.
Present in 2 views: Used by:
  • Program Costs - This represents the rate of expense by the conglomerate when adding people to the program. This is an Author derived flow from the Social Finance Limited (2011).
Default L
Cummulative Investor Returns (k£)
= ∫ (Owner Success Payment) dt + [No Initial Worth]
Description: This represents the amount of money the investors have during the program cycle. This stock is pulled from Social Finance Limited (2011).
Present in 1 view: Used by:
  • Investor Balance - This represents the current balance of the investors accounts with both what they have set for investing along with the returns for a successful program. This is an Author defined performance variable that may be considered in the tests.
Default Control L
Cummulative Program Cost (k£)
= ∫ (Program Costs) dt + [No Initial Worth]
Description: This represents how much money has been paid into the program. This is an Author defined variable operating as a performance measure for total cost.
Present in 2 views:
Default Initial Estimates C
Defined Year (Month)
= 12
Description: Within this model a year is estimated at 12 months. Author defined.
Present in 4 views: Used by:
  • Accummulating Interest from Investment - This represents the rate interest collects at the maximum rate of return based on the value by Disely et. al. (2011).
  • Cost per Participant per month - This represents the cost for one person to be in the program for one month as per Mulgan et al. (2011) page 30.
  • Investor Discount Factor - This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
  • monthly cost - This represents the monthly cost of incarcerating a prisoner. Derived from Loder et al. (2010).
  • Owner Discount Factor - This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
Default Control A
Desired Payment Value (k£)
Desired Payment Value[Overall] = MIN(Limits of Unpaid Investor Returns[Overall,maximum], MAX(Unpaid Investor Earned Returns[Overall],Limits of Unpaid Investor Returns[Overall,minimum]))*"Payment Consideration?"[Overall]*"Successful Program?"[Overall]
Desired Payment Value[Cohort 1] = MIN(Limits of Unpaid Investor Returns[Cohort 1,maximum], MAX(Unpaid Investor Earned Returns[Cohort 1],Limits of Unpaid Investor Returns[Cohort 1,minimum]))*"Successful Program?"[Cohort 1]*"Payment Consideration?"[Cohort 1]*SIB?+Limits of Unpaid Investor Returns[Cohort 1,Bond]*(1-SIB?)
Desired Payment Value[Cohort 2] = MIN(Limits of Unpaid Investor Returns[Cohort 2,maximum], MAX(Unpaid Investor Earned Returns[Cohort 2],Limits of Unpaid Investor Returns[Cohort 2,minimum]))*"Successful Program?"[Cohort 2]*"Payment Consideration?"[Cohort 2]*SIB?+Limits of Unpaid Investor Returns[Cohort 2,Bond]*(1-SIB?)
Desired Payment Value[Cohort 3] = MIN(Limits of Unpaid Investor Returns[Cohort 3,maximum], MAX(Unpaid Investor Earned Returns[Cohort 3],Limits of Unpaid Investor Returns[Cohort 3,minimum]))*"Successful Program?"[Cohort 3]*"Payment Consideration?"[Cohort 3]*SIB?+Limits of Unpaid Investor Returns[Cohort 3,Bond]*(1-SIB?)
Desired Payment Value[Cohort 4] = MIN(Limits of Unpaid Investor Returns[Cohort 4,maximum], MAX(Unpaid Investor Earned Returns[Cohort 4],Limits of Unpaid Investor Returns[Cohort 4,minimum] ))*"Successful Program?"[Cohort 4]*"Payment Consideration?"[Cohort 4]*SIB?+Limits of Unpaid Investor Returns[Cohort 4,Bond]*(1-SIB?)
Description: This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
Present in 1 view: Used by:
  • Maximum Payment Accumulation - This represents the accumulation for the maximum payment value. This is an Author defined equation to ensure investors are paid the amount they are due.
Default A
Desired Program Capacity (People)
= Max People in Cohort[Cohort 4]-Cohort Collection of New Offenders[Cohort 4,Peterborough]
Description: This represents the maximum number of people that will be collected in the cohort that should get space in the program. It is an Author defined variable to slow the flow of people into programs and keep them from overrunning the financial capacity of the NGO.
Present in 1 view: Used by:
  • Percent Released Offenders Allowed in Program - This represents the maximum percentage of people released from prison that are allowed in the program for each cohort. This is an author defined constraint to control for entrants into the program and reduce the number of offenders allowed in the program.
Default IRR F,A

Earned Investor Return payments (k£/Month)
Earned Investor Return payments[Cohorts] = Actual Investor Return payments[Cohorts,maximum]
Description: This represents the amount of payment to the investors from the program reducing the amount of payment to the investors in future. This is an Author defined equation.
Present in 1 view: Used by:
Default IRR F,A

Expected Peterborough Costs (k£/Month)
= Short Term Reconviction Costs[Comparison]*Owner Discount Factor
Description: This is the expected payment rate that is allocated to MoJ for the Peterborough Prison System. this is an author derived equation set so that the MOJ receives funds under the expectation that business is operating as usual. The values are discounted from the start of the program to coinside with deflation from projection.
Present in 1 view: Used by:
  • MOJ Account - This Represents the amount of money in the MOJ and BLF account. The structure of this accountto investors is pulled from Social Finance Limited (2011).
Default LI,C
Expected Program Investment amount (k£)
= 5000
Description: This represents the minimum required investment from the investors (Stirckland 2010).
Present in 4 views: Used by:
  • Amount Investors are willing to Invest - This represents the amount of capital that the Investors are have set aside to invest in the program. This stock is located in both Social Finance (2011) and Glahn & Whistler (2011).
  • Funds Available for the Program - This represents the amount of funds remaining for the program activities. This is an Author defined stock.
  • Investment Payment per Cohort - This represents the payment amount from the investors while the cohorts are collecting as per Strickland (2010) and Mulgan et al. (2011).
Default Control C
FINAL TIME (Month)
= 200
Description: The final time for the simulation.
Not Present In Any View
Default C
Fraction for Investor share (Dmnl)
= 0.5
Description: This represents the percentage share that the investors receives of the savings (assuming a successful project). This value is not presented in the literature for confidentiality (Disely 2011). Modeler estimate.
Present in 2 views: Used by:
  • Investor Earned - This represents the value of savings determined in the contracts without the limits. The Investor share value is kept anonymous to the public. according to Cave et. al. (2012) and Disely et. al. (2011). The value is determined by multiplying the number of reconvictions that should have been based on the comparison group results (Cave et. al. 2012).
Default L
Funds Available for the Program (k£)
= ∫ (-Cohort Expense Rate) dt + [Expected Program Investment amount]
Description: This represents the amount of funds remaining for the program activities. This is an Author defined stock.
Present in 2 views: Used by:
  • Remaining Capacity for Program - This represents the estimated number of people that can be admitted into the program and is a author defined variable based on the fund available for all the cohorts.
Default Initial Estimates C
Initial First time Offender Prisoner Holding (People)
= 86.75
Description: PH stands for prison holding. This is the tuned value for the initial prisoners to meet Cave et. al. (2012) values.
Present in 2 views: Used by:
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
Default Initial Estimates C
Initial Reconvicted Prisoner Holding (People)
= 260.25
Description: This represents the initial amount of people that have been reconvicted under the program and is tuned to Cave et. al. (2012).
Present in 2 views: Used by:
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
Default Control C
INITIAL TIME (Month)
= 0
Description: The initial time for the simulation.
Not Present In Any View
Used by:
  • Time - Internally defined simulation time.
Default Initial Estimates C
Initial Undiscovered Reoffenders (People)
= 1041
Description: This represents the number of people awaiting reconviction discovery and is tuned to 555 people as per Cave et. al. (2012).
Present in 2 views: Used by:
Default IRR Sub
Interest
: maximum, minimum, Bond
Description: This represents the maximum and minimum interest that can be returned to the investor.
Present in 1 view: Used by:
  • Accummulating Interest from Investment - This represents the rate interest collects at the maximum rate of return based on the value by Disely et. al. (2011).
  • Desired Payment Value - This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
  • Earned Investor Return payments - This represents the amount of payment to the investors from the program reducing the amount of payment to the investors in future. This is an Author defined equation.
  • Interest - This represents the maximum and minimum interest that can be returned to the investor.
  • Limits of Unpaid Investor Returns - This represents the payment to the investors based on a succesful project. This includes both a maximum, minimum and Bond values. This is an Author defined structure.
Default Project Timing C,A
Interval time between Cohort completion and Payment Time (Month)
Interval time between Cohort completion and Payment Time[Overall] = 0
Interval time between Cohort completion and Payment Time[Cohort 1] = Time after Cohort for Reconviction Collection+Time for System Update+Time Program has to Pay
Interval time between Cohort completion and Payment Time[Cohort 2] = Time after Cohort for Reconviction Collection+Time for System Update+Time Program has to Pay
Interval time between Cohort completion and Payment Time[Cohort 3] = Time after Cohort for Reconviction Collection+Time for System Update+Time Program has to Pay
Interval time between Cohort completion and Payment Time[Cohort 4] = Time Program has to Pay
Description: This represents the time at which payment will be made if the program is successful. 18 months is added on to the accumulation time as per Cave et. al. (2012) shows for time between cohort collection finishing and the results being tabulated. Cohort 4 is tabulated after the Cohort 3 has been given a chance to process.
Present in 1 view: Used by:
  • Investment Finalization Time - This represents when the investment is finalized and ready for repayment as per the timeline in Cave et al. (2012).
Default IRR L
Invested Amount (k£)
= ∫ (Investment Rate) dt + [0]
Description: This represents the accumulation of investment by the investors into the program as valued at the start of the program.
Present in 2 views: Used by:
  • IRR Investor - This represents the Internal Rate of Return (IRR) for the investors after the program has stopped tracking reconvictions and continuing through the last payments. The IRR is a ratio comparison between the benefits of the investment and the amount invested. This is an Author defined variable for performance measure.
Default F,A

Investing (k£/Month)
= PULSE(Actual Cohort Start Times[Cohort 1]+1,1)*Investment Payment per Cohort+PULSE(Actual Cohort Start Times[Cohort 2]+1,1)*Investment Payment per Cohort+PULSE(Actual Cohort Start Times[Cohort 3]+1,1)*Investment Payment per Cohort
Description: This represents the steady flow of investor funds into the system. It is an Author derived variable equivalent to the amount of the investment divided by the total duration of the project and comes from Social Finance Limited (2011).
Present in 3 views: Used by:
  • Amount Investors are willing to Invest - This represents the amount of capital that the Investors are have set aside to invest in the program. This stock is located in both Social Finance (2011) and Glahn & Whistler (2011).
  • Bond Investment - This represents when and how much was paid from the investors.
  • Investment Rate - This represents the Present value of investments at the start of the project for investors by using the discount factor. This is an Author defined flow.
  • Social Impact Partnership - This represents the funds available for the One* Service (i.e. SGT and Other NGOs) to operate in the Peterborough Prison. This comes from Social Finance Limited (2011).
Default Project Timing A
Investment Finalization Time (Month)
Investment Finalization Time[Overall] = Actual Cohort Closing Times[Overall]
Investment Finalization Time[Cohort 1] = Actual Cohort Closing Times[Cohort 1]
Investment Finalization Time[Cohort 2] = Actual Cohort Closing Times[Cohort 2]
Investment Finalization Time[Cohort 3] = Actual Cohort Closing Times[Cohort 3]
Investment Finalization Time[Cohort 4] = Cohort Payment Time[Cohort 4]+Interval time between Cohort completion and Payment Time[Cohort 4]
Description: This represents when the investment is finalized and ready for repayment as per the timeline in Cave et al. (2012).
Present in 1 view: Used by:
  • Cohort Investment switch - This represents when investors are investing in different cohorts. This is an author derived variable from Cave et al. (2012).
Default A
Investment Payment per Cohort (k£/Month)
= Expected Program Investment amount/number of payments
Description: This represents the payment amount from the investors while the cohorts are collecting as per Strickland (2010) and Mulgan et al. (2011).
Present in 3 views: Used by:
  • Investing - This represents the steady flow of investor funds into the system. It is an Author derived variable equivalent to the amount of the investment divided by the total duration of the project and comes from Social Finance Limited (2011).
Default IRR F,A

Investment Rate (k£/Month)
= (Investing)*Investor Discount Factor
Description: This represents the Present value of investments at the start of the project for investors by using the discount factor. This is an Author defined flow.
Present in 1 view: Used by:
  • Invested Amount - This represents the accumulation of investment by the investors into the program as valued at the start of the program.
  • Investor Account - This represents the value of the investor account at the time of program initiation, but does not include initial funds because the discount rate represents an alternate investment option. This allows the final value of the investors account to be compared with the stock for the investment amount. This is an Author Defined stock.
Default IRR L
Investor Account (k£)
= ∫ (Investor Return Rate-Investment Rate) dt + [0]
Description: This represents the value of the investor account at the time of program initiation, but does not include initial funds because the discount rate represents an alternate investment option. This allows the final value of the investors account to be compared with the stock for the investment amount. This is an Author Defined stock.
Present in 1 view: Used by:
  • IRR Investor - This represents the Internal Rate of Return (IRR) for the investors after the program has stopped tracking reconvictions and continuing through the last payments. The IRR is a ratio comparison between the benefits of the investment and the amount invested. This is an Author defined variable for performance measure.
Default Control A
Investor Balance (k£)
= Cummulative Investor Returns+Amount Investors are willing to Invest
Description: This represents the current balance of the investors accounts with both what they have set for investing along with the returns for a successful program. This is an Author defined performance variable that may be considered in the tests.
Present in 1 view:
Default A
Investor Discount Factor (Dmnl)
= XIDZ(1,(1+Investor Discount Rate)^(program time/Defined Year),1)
Description: This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
Present in 1 view: Used by:
  • Investment Rate - This represents the Present value of investments at the start of the project for investors by using the discount factor. This is an Author defined flow.
  • Investor Return Rate - This represents the present value at the time of the initial project for payments from the owner to the investor by using the discount factor. It is author defined using the value of the payment times a discount factor from the initiation of the program.
Default IRR C
Investor Discount Rate (Dmnl)
= 0.05
Description: This represents the discount rate for investors as a representation of an alternate investment rate of return. Since the model uses an alternate investment discount rate the initial value of the investment does not need to be counted in the investor account. This is author defined using a standard discount equal or less in value than the interest rate collected on the bond.
Present in 2 views: Used by:
  • Investor Discount Factor - This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
Default A
Investor Earned (k£/Month)
Investor Earned[Cohorts] = (Savings from Reduced Reconvictions[Cohorts])*Fraction for Investor share
Description: This represents the value of savings determined in the contracts without the limits. The Investor share value is kept anonymous to the public. according to Cave et. al. (2012) and Disely et. al. (2011). The value is determined by multiplying the number of reconvictions that should have been based on the comparison group results (Cave et. al. 2012).
Present in 1 view: Used by:
Default IRR F,A

Investor Earned Return Accumulation (k£/Month)
Investor Earned Return Accumulation[Cohorts] = Investor Earned[Cohorts]*Cohort Investment switch[Cohorts]
Description: This represents the accumulation of investor earnings based on Cave et. al. (2012).
Present in 1 view: Used by:
Default IRR F,A

Investor Return Rate (k£/Month)
= Owner Success Payment*Investor Discount Factor
Description: This represents the present value at the time of the initial project for payments from the owner to the investor by using the discount factor. It is author defined using the value of the payment times a discount factor from the initiation of the program.
Present in 1 view: Used by:
  • Investor Account - This represents the value of the investor account at the time of program initiation, but does not include initial funds because the discount rate represents an alternate investment option. This allows the final value of the investors account to be compared with the stock for the investment amount. This is an Author Defined stock.
Default A
Investors Cohorts Paid? Amount (k£/Month)
Investors Cohorts Paid? Amount [Cohorts] = Owner Success Payment*"Payment Consideration?"[Cohorts]
Description: This represents the payment rate to the investors when they are paid within their investment. This is an Author derived equation.
Present in 2 views: Used by:
  • Actual Investor Return payments - This represents when and how much was returned to the investors to account for payments. This is an Author defined variable.
Default IRR A
IRR Investor (Dmnl)
= ZIDZ(Investor Account,Invested Amount)
Description: This represents the Internal Rate of Return (IRR) for the investors after the program has stopped tracking reconvictions and continuing through the last payments. The IRR is a ratio comparison between the benefits of the investment and the amount invested. This is an Author defined variable for performance measure.
Present in 2 views:
Default IRR A
IRR MOJ (Dmnl)
= ZIDZ(Amount Saved From Programs,Amount Paid for Rehab Program)
Description: This represents the Internal Rate of Return for the owner starting after the final reconvictions are finished collecting. Both stocks used have already been discounted to the time the project started. This is an author defined variable for performance measures.
Present in 2 views:
Default Project Timing C
Latest Cohort Start Times (Month)
Latest Cohort Start Times[Cohorts] = -0.5,20,44,68,20
Description: This represents the lateset time for a cohort to start (Cave et al. 2012).
Present in 1 view: Used by:
  • Cohort Time Delay Rate - This is an Author derived control to increase time according to the rules set in Cave et al. (2012).
Default Control L
Limits of Unpaid Investor Returns (k£)
Limits of Unpaid Investor Returns[Cohorts,Interest] = ∫ (Accummulating Interest from Investment[Cohorts) dt + [Interest]+Bond Investment[Cohorts,Interest]-Actual Investor Return payments[Cohorts,Interest],No Initial Worth]
Description: This represents the payment to the investors based on a succesful project. This includes both a maximum, minimum and Bond values. This is an Author defined structure.
Present in 1 view: Used by:
  • Accummulating Interest from Investment - This represents the rate interest collects at the maximum rate of return based on the value by Disely et. al. (2011).
  • Desired Payment Value - This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
Default Control C,A
Max Cohort Length (Month)
Max Cohort Length[Overall] = 0
Max Cohort Length[Cohort 1] = Standard Cohort Length
Max Cohort Length[Cohort 2] = Standard Cohort Length
Max Cohort Length[Cohort 3] = Standard Cohort Length
Max Cohort Length[Cohort 4] = Max Cohort Length[Cohort 1]+Max Cohort Length[Cohort 2]+Max Cohort Length[Cohort 3]
Description: This represents the maximum length of an individual Cohort (1-3) or 1/3 of the maximum time for the final cumulative cohort as outlined by Cave et. al. (2012).
Present in 2 views: Used by:
  • Cohort initiate switch - This determines whether the cohorts have started in accordance with the rules set forth from Cave et. al. (2012) primarily that the maximum time cannot be exceeded and the cohorts must switch before if the maximum number is met or exceeded.
  • Max Cohort Length - This represents the maximum length of an individual Cohort (1-3) or 1/3 of the maximum time for the final cumulative cohort as outlined by Cave et. al. (2012).
Default Control C,A
Max People in Cohort (People)
Max People in Cohort[Overall] = 1e+015
Max People in Cohort[Cohort 1] = Standard People in Cohort
Max People in Cohort[Cohort 2] = Standard People in Cohort
Max People in Cohort[Cohort 3] = Standard People in Cohort
Max People in Cohort[Cohort 4] = Max People in Cohort[Cohort 1]+Max People in Cohort[Cohort 2]+Max People in Cohort[Cohort 3]
Description: This is the maximum number of people allowed in the cohort (Cave et. al. 2012).
Present in 3 views: Used by:
  • Cohort initiate switch - This determines whether the cohorts have started in accordance with the rules set forth from Cave et. al. (2012) primarily that the maximum time cannot be exceeded and the cohorts must switch before if the maximum number is met or exceeded.
  • Cohort Time Delay Rate - This is an Author derived control to increase time according to the rules set in Cave et al. (2012).
  • Desired Program Capacity - This represents the maximum number of people that will be collected in the cohort that should get space in the program. It is an Author defined variable to slow the flow of people into programs and keep them from overrunning the financial capacity of the NGO.
  • Max People in Cohort - This is the maximum number of people allowed in the cohort (Cave et. al. 2012).
Default F,A

Maximum Payment Accumulation (k£/Month)
Maximum Payment Accumulation[Cohorts] = IF THEN ELSE(Cohort Payment Time[Cohorts]<Time,IF THEN ELSE(Desired Payment Value[Cohorts]>Maximum Successful Program Payment Value[Cohorts],Desired Payment Value[Cohorts]-Maximum Successful Program Payment Value[Cohorts],0)/TIME STEP,0)
Description: This represents the accumulation for the maximum payment value. This is an Author defined equation to ensure investors are paid the amount they are due.
Present in 1 view: Used by:
Default L
Maximum Successful Program Payment Value (k£)
Maximum Successful Program Payment Value[Cohorts] = ∫ (Maximum Payment Accumulation[Cohorts]) dt + [0]
Description: This represents the maximum value for payment. This is Author defined to ensure a complete payment to investors.
Present in 2 views: Used by:
  • Maximum Payment Accumulation - This represents the accumulation for the maximum payment value. This is an Author defined equation to ensure investors are paid the amount they are due.
  • Payment for Cohort 1 - This represents the value of the payment for Cohort 1. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 2 - This represents the payment value for Cohort 2. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 3 - This represents the payment for Cohort 3. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 4 - This represents the payment value for the entire project. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
Default Control C
Minimum Change in Reconvictions (Dmnl)
Minimum Change in Reconvictions[Cohorts] = 1,0.1,0.1,0.1,0.075
Description: This represents the minimum change in reconvictions for the program to be considered a success (Strickland 2010, Mulgan et al. 2011, Cave et al. 2012).
Present in 2 views: Used by:
  • Successful Program? - This variable measures whether or not the program successfully pays out as described by Cave et. al. (2012).
Default IRR L
MOJ Account (k£)
= ∫ (Expected Peterborough Costs-Actual Peterborough Costs-Total Programs Savings Rate) dt + [0]
Description: This Represents the amount of money in the MOJ and BLF account. The structure of this accountto investors is pulled from Social Finance Limited (2011).
Present in 1 view: Used by:
  • Total Programs Savings Rate - This represents the rate of total savings from the program. This is an Author defined equation that represents the decaying time value of money as it moves from the MOJ spending account into a savings account.
Default A
MOJ Dictated Program Capacity (Dmnl)
= MIN(MAX(Monthly MOJ Funded Interventions/∑(Offender Release Rate[Overall,Peterborough,Offense!]),0),1)*"Successful Program?"[Cohort 4]
Description: This represents the percentage of people that the MOJ is willing to put through the rehabilitation program after it is proven successful. It is bound between 0 and 1. It is an Author derived from Glahn and Whistler formula bound to provide the desired people in the program with a zero value for an unsuccessful program.
Present in 1 view: Used by:
  • Percent Released Offenders Allowed in Program - This represents the maximum percentage of people released from prison that are allowed in the program for each cohort. This is an author defined constraint to control for entrants into the program and reduce the number of offenders allowed in the program.
Default IRR C
MOJ Discount Rate (Dmnl)
= 0.03
Description: This represents the discount rate for investors as a representation of an alternate investment rate of return. Since the model uses an alternate investment discount rate the initial value of the investment does not need to be counted in the investor account. This is an author defined value that can be set at the consumer price index (CPI).
Present in 2 views: Used by:
  • Owner Discount Factor - This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
Default IRR F,A

MOJ Program Savings Rate (k£/Month)
= Amount Available for Rehab Programs/Time for System Update*Owner Discount Factor
Description: This represents the amount of savings that the MOJ sees from the Rehabilitation Program. This is an Author defined equation that allows money to be moved from a general savings account to an organizational savings account. There is no limit for the program to go to zero so that the MOJ can move money back into the general account at a later date for program funding.
Present in 1 view: Used by:
  • Amount Available for Rehab Programs - Amount available to repay investors as well as the amount of savings seen by the MOJ. This is an Author defined stock signifying the seperation of savings from the normal MOJ budget.
  • Amount Saved From Programs - This represents the amount of money saved from the program that can be used by the MOJ for anything. This stock is Author derived to from social finance limited (2011) and Glahn & Whistler (2011).
Default A
monthly cost (k£/Month/People)
= Yearly Cost of Incarceration/Defined Year
Description: This represents the monthly cost of incarcerating a prisoner. Derived from Loder et al. (2010).
Present in 1 view: Used by:
  • Total Cost of Incarceration - This represents the cost for each reconviction by the British government per person. It is a combination of both the legal action and the time spent in prison. This is an Author derived equation from Mulgan et al. 2012)
Default A
Monthly MOJ Funded Interventions (People/Month)
= MAX(Post-Program-Savings-Reinvestment Percent per month*Amount Saved From Programs/Program Cost per member,Program Payments from SIP/Program Cost per member)
Description: This represents the number of people the MOJ will fund after the program is found successful. It is an Author derived based Glahn and Whistler (2011) to represent the desired expenses of the program and the desired level of expenses of the program.
Present in 2 views: Used by:
  • MOJ Dictated Program Capacity - This represents the percentage of people that the MOJ is willing to put through the rehabilitation program after it is proven successful. It is bound between 0 and 1. It is an Author derived from Glahn and Whistler formula bound to provide the desired people in the program with a zero value for an unsuccessful program.
Default Rehab F,A

New Offender Incarceration Rate (People/Month)
New Offender Incarceration Rate[Overall,Peterborough] = Average Prisoner Incarceration Rate for Peterborough*Offender Multiplier between Prison Systems[Peterborough]
New Offender Incarceration Rate[Overall,Comparison] = Offender Multiplier between Prison Systems[Comparison]*New Offender Incarceration Rate[Overall,Peterborough]
Description: This represents the flow of first time offenders into the prison system that fit the criteria for the program as outlined in Strickland (2010). The in flow of new prisoners is the difference between the number of prisoners that can be accepted on a monthly basis and the recidivism rate of prisoners from the overall cohort. This is one of the variations from the Lyneis and Ford (2007) model
Present in 1 view: Used by:
  • New Offender Incarceration Rate - This represents the flow of first time offenders into the prison system that fit the criteria for the program as outlined in Strickland (2010). The in flow of new prisoners is the difference between the number of prisoners that can be accepted on a monthly basis and the recidivism rate of prisoners from the overall cohort. This is one of the variations from the Lyneis and Ford (2007) model
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
Default LI,C
No Initial Worth (k£)
= 0
Description: This represents the initial value for any stock that has no starting value. Use the uses tree to see what values do not have an initial value.Author defined.
Present in 5 views: Used by:
  • Cummulative Investor Returns - This represents the amount of money the investors have during the program cycle. This stock is pulled from Social Finance Limited (2011).
  • Cummulative Program Cost - This represents how much money has been paid into the program. This is an Author defined variable operating as a performance measure for total cost.
  • Limits of Unpaid Investor Returns - This represents the payment to the investors based on a succesful project. This includes both a maximum, minimum and Bond values. This is an Author defined structure.
  • One Service - The amount of built up capital that the conglomerate of NGOs have in their system. This is representative of the Social Finance Limited (2011).
  • Social Impact Partnership - This represents the funds available for the One* Service (i.e. SGT and Other NGOs) to operate in the Peterborough Prison. This comes from Social Finance Limited (2011).
  • Unpaid Investor Earned Returns - This represents the accumulation of investor earnings through payment based on Cave et. al. (2012)
Default Rehab C
Normal Recidivism Discovery Time (Month)
= 6
Description: The average amount of time it takes to convict a resent release from the comparison group of a new crime. This is taken from an approximation of Cave et. al. (2012) analysis. It is an approximation because the units used were days in Cave et. al. (2012), but the units in the model are months. (3.7= 110/30)
Present in 2 views: Used by:
  • Average Time between Release and Reconviction - The average amount of time it takes to convict a resent release from the Peterborough group of a new crime. This takes Disely et al. (2012) value from the analysis and introduces a change from the programs operations.
Default Control C
Normal Recidivism Fraction (Dmnl)
= 0.75
Description: The normal quality of the system without having the project in play. Value pulled from Strickland (2010), Loder et al. (2010), and Mulgan et. al. (2011).
Present in 2 views: Used by:
  • Program Recidivism Fraction - This represents the estimated quality of the program in terms of the number of satisfactory outcomes divided by unsatisfactory outcomes . The change in recidivism is subtracted because of its representation in Loder et. al. (2010) and Mulgan et. al. (2011). This relates to the Mission portion of the Balanced Scorecard for the conglomerate of NGOs.
  • Rehabilitated Offender Percent - This variable represents the fraction of rehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
  • Unrehabilitated Offender Percent - This variable represents the fraction of unrehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
Default C
number of payments (Month)
= 3
Description: This represents the number of payments that are made by the investors. The number is derived based on the number of primary cohorts identified in both Disely et al. (2012) and Cave et al. (2012). There are three primary (the fourth is an overall grouping).
Present in 1 view: Used by:
  • Investment Payment per Cohort - This represents the payment amount from the investors while the cohorts are collecting as per Strickland (2010) and Mulgan et al. (2011).
Default L
Number of Reconviction (People)
Number of Reconviction[Cohorts,Prison Systems] = ∫ (Rate of Reconviction[Cohorts) dt + [Prison Systems],0]
Description: This represents the accumulation of reconvicted people in the cohort for the comparison group as per Cave et. al. (2012)
Present in 1 view: Used by:
  • Reconviction Fraction - This represents the rate of reconviction for people in the Peterborough group as perscribed by Cave et. al. (2012).
Default Control LI,C
Offender Multiplier between Prison Systems (Dmnl)
Offender Multiplier between Prison Systems[Prison Systems] = 1,10
Description: This represents the ratio of people needed in each grouping to have an appropriate power level in accordance with Cave et. al. (2012)
Present in 5 views: Used by:
  • New Offender Incarceration Rate - This represents the flow of first time offenders into the prison system that fit the criteria for the program as outlined in Strickland (2010). The in flow of new prisoners is the difference between the number of prisoners that can be accepted on a monthly basis and the recidivism rate of prisoners from the overall cohort. This is one of the variations from the Lyneis and Ford (2007) model
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Prison Population Reduction Percent - This represents the fraction of prisoners from the peterborough population that have been reduced as a result of the program.
  • Reconvictions Prevented - This represents the number of reconvictions that the program saved the government from having to go through. This is an Author derived equation.
  • Short Term Reconviction Costs - This represents the monthly cost for short term reconvictions within the Peterborough Prison System. This is an Author derived equation from Disely et al. (2011).
  • Undiscoverd Reoffenders - This represents the people that are in the program that eventually will recommit.
Default Rehab A
Offender Release Rate (People/Month)
Offender Release Rate[Cohorts,Prison Systems,First] = "Prison Holding-First Offence"[Cohorts,Prison Systems]/Time spent in prison for a Conviction
Offender Release Rate[Cohorts,Prison Systems,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Prison Systems]/Time spent in prison for a Conviction
Description: This represents the Total release rate from prison for the different prisons. This is an Author defined variable that can be used to measure performance.
Present in 3 views: Used by:
  • MOJ Dictated Program Capacity - This represents the percentage of people that the MOJ is willing to put through the rehabilitation program after it is proven successful. It is bound between 0 and 1. It is an Author derived from Glahn and Whistler formula bound to provide the desired people in the program with a zero value for an unsuccessful program.
Default Control C
Offenders' Willing to enter program Fraction (Dmnl)
= 0.7
Description: This represents the percentage of prisoners that elect to go through the program and can be changed to tune for different levels of participation between 0 and 1. Disely et. al. (2012) note a 70% acceptance. The program off represents the Financial Measure of the BSC in providing funds for prisoners to go through the program.
Present in 2 views: Used by:
  • Program's Acceptance Fraction - This represents the percentage of prisoners of the allowable population that do elect to go through the program and are able. Disely et. al. (2012) note a 70% willingness and the program allowance is an Author derived equation.
Default Rehab Sub
Offense
: First, Repeat
Description: This seperates out the first time Offenders from the Repeat Offenders.
Present in 4 views: Used by:
  • Cohort Addition of New Offenders - This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
  • MOJ Dictated Program Capacity - This represents the percentage of people that the MOJ is willing to put through the rehabilitation program after it is proven successful. It is bound between 0 and 1. It is an Author derived from Glahn and Whistler formula bound to provide the desired people in the program with a zero value for an unsuccessful program.
  • Offense - This seperates out the first time Offenders from the Repeat Offenders.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Rehabilitated Offenders - This represents the people in the program that are in the program.
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
  • Undiscoverd Reoffenders - This represents the people that are in the program that eventually will recommit.
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default Control L
One Service (k£)
= ∫ (Program Payments from SIP-Program Costs) dt + [No Initial Worth]
Description: The amount of built up capital that the conglomerate of NGOs have in their system. This is representative of the Social Finance Limited (2011).
Present in 1 view:
Default IRR A
Owner Discount Factor (Dmnl)
= XIDZ(1,(1+MOJ Discount Rate)^(program time/Defined Year),1)
Description: This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
Present in 1 view: Used by:
  • Actual Peterborough Costs - This represents the actual expenses for the Peterborough prison system using the costs of reconvictions found in Strickland (2010). (Reconviction cost times the number of reconvictions from Peterborough Released prisoners. This is an Author derived equation of the acutal expenses and is deflated to maintain consistent projection value.
  • Expected Peterborough Costs - This is the expected payment rate that is allocated to MoJ for the Peterborough Prison System. this is an author derived equation set so that the MOJ receives funds under the expectation that business is operating as usual. The values are discounted from the start of the program to coinside with deflation from projection.
  • MOJ Program Savings Rate - This represents the amount of savings that the MOJ sees from the Rehabilitation Program. This is an Author defined equation that allows money to be moved from a general savings account to an organizational savings account. There is no limit for the program to go to zero so that the MOJ can move money back into the general account at a later date for program funding.
  • Rehabilitation Program Investment Rate - This represents the rate at which money is spent on the program including, payments to investors and payments to the SPV when the MOJ takes over. This is an Author defined equation using a discount from the start of the program as a form of projection.
  • Total Programs Savings Rate - This represents the rate of total savings from the program. This is an Author defined equation that represents the decaying time value of money as it moves from the MOJ spending account into a savings account.
Default A
Owner Post-Program Payments (k£/Month)
= IF THEN ELSE( Actual Cohort Closing Times[Cohort 4]<Time, Program Payments from SIP*("Successful Program?"[Cohort 4]),0)
Description: In the event of a successful program the owner would want to assume the payments for the program. This is represented by using a switch ("Program Off?") and the value of the payments. This is an Author derived flow based on Glahn and Whistler (2011).
Present in 2 views: Used by:
  • Rehabilitation Program Investment Rate - This represents the rate at which money is spent on the program including, payments to investors and payments to the SPV when the MOJ takes over. This is an Author defined equation using a discount from the start of the program as a form of projection.
  • Social Impact Partnership - This represents the funds available for the One* Service (i.e. SGT and Other NGOs) to operate in the Peterborough Prison. This comes from Social Finance Limited (2011).
Default F,A

Owner Success Payment (k£/Month)
= (Payment for Cohort 1+Payment for Cohort 2+Payment for Cohort 3+Payment for Cohort 4)/Time Program has to Pay
Description: This represents when and how much the investors are paid. This relationship is made from the Social Finance Limited (2011).
Present in 3 views: Used by:
  • Cummulative Investor Returns - This represents the amount of money the investors have during the program cycle. This stock is pulled from Social Finance Limited (2011).
  • Investor Return Rate - This represents the present value at the time of the initial project for payments from the owner to the investor by using the discount factor. It is author defined using the value of the payment times a discount factor from the initiation of the program.
  • Investors Cohorts Paid? Amount - This represents the payment rate to the investors when they are paid within their investment. This is an Author derived equation.
  • Rehabilitation Program Investment Rate - This represents the rate at which money is spent on the program including, payments to investors and payments to the SPV when the MOJ takes over. This is an Author defined equation using a discount from the start of the program as a form of projection.
Default C,A
Payment Consideration? (Dmnl)
Payment Consideration? [Overall] = 1
Payment Consideration? [Cohort 1] = IF THEN ELSE(Cohort Payment Time[Cohort 1]<=Time,IF THEN ELSE(Cohort Payment Time[Cohort 1]+Time Program has to Pay>=Time,1,0),0)
Payment Consideration? [Cohort 2] = IF THEN ELSE(Cohort Payment Time[Cohort 2]<=Time,IF THEN ELSE(Cohort Payment Time[Cohort 2]+Time Program has to Pay>=Time,1,0),0)
Payment Consideration? [Cohort 3] = IF THEN ELSE(Cohort Payment Time[Cohort 3]<=Time,IF THEN ELSE(Cohort Payment Time[Cohort 3]+Time Program has to Pay>=Time,1,0),0)
Payment Consideration? [Cohort 4] = IF THEN ELSE(Cohort Payment Time[Cohort 1]<=Time,IF THEN ELSE(Cohort Payment Time[Cohort 4]+Time Program has to Pay>=Time,1,0),0)
Description: This marks the time that a payment is considered in the project (Cave et. al. 2012). Payment cannot be considered before the completion of cohort collection plus the time interval for data occurence, collection and analysis.
Present in 3 views: Used by:
  • Desired Payment Value - This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
  • Investors Cohorts Paid? Amount - This represents the payment rate to the investors when they are paid within their investment. This is an Author derived equation.
  • Payment for Cohort 1 - This represents the value of the payment for Cohort 1. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 2 - This represents the payment value for Cohort 2. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 3 - This represents the payment for Cohort 3. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
  • Payment for Cohort 4 - This represents the payment value for the entire project. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
Default A
Payment for Cohort 1 (k£)
= Maximum Successful Program Payment Value[Cohort 1]*"Payment Consideration?"[Cohort 1]
Description: This represents the value of the payment for Cohort 1. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
Present in 1 view: Used by:
  • Owner Success Payment - This represents when and how much the investors are paid. This relationship is made from the Social Finance Limited (2011).
Default A
Payment for Cohort 2 (k£)
= Maximum Successful Program Payment Value[Cohort 2]*"Payment Consideration?"[Cohort 2]
Description: This represents the payment value for Cohort 2. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
Present in 1 view: Used by:
  • Owner Success Payment - This represents when and how much the investors are paid. This relationship is made from the Social Finance Limited (2011).
Default A
Payment for Cohort 3 (k£)
= Maximum Successful Program Payment Value[Cohort 3]*"Payment Consideration?"[Cohort 3]
Description: This represents the payment for Cohort 3. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
Present in 1 view: Used by:
  • Owner Success Payment - This represents when and how much the investors are paid. This relationship is made from the Social Finance Limited (2011).
Default A
Payment for Cohort 4 (k£)
= Maximum Successful Program Payment Value[Cohort 4]*"Payment Consideration?"[Cohort 4]
Description: This represents the payment value for the entire project. Author defined from Mulgan et al. (2011) and Cave et al. (2012).
Present in 1 view: Used by:
  • Owner Success Payment - This represents when and how much the investors are paid. This relationship is made from the Social Finance Limited (2011).
Default A
Percent Released Offenders Allowed in Program (Dmnl)
= MAX(MIN(max(Remaining Capacity for Program,0)/Desired Program Capacity,1),IF THEN ELSE(Actual Cohort Closing Times[Cohort 4]<Time,MOJ Dictated Program Capacity,0))
Description: This represents the maximum percentage of people released from prison that are allowed in the program for each cohort. This is an author defined constraint to control for entrants into the program and reduce the number of offenders allowed in the program.
Present in 2 views: Used by:
  • Program's Acceptance Fraction - This represents the percentage of prisoners of the allowable population that do elect to go through the program and are able. Disely et. al. (2012) note a 70% willingness and the program allowance is an Author derived equation.
Default A
Population in Program (People)
Population in Program[Cohorts] = Rehabilitated Offenders[Cohorts,Peterborough,SIB]+Undiscoverd Reoffenders[Cohorts,Peterborough,SIB]
Description: This represents the number of people that are in the program at any point in time. This is an Author defined variable used to calculate the monthly program costs.
Present in 1 view: Used by:
  • Program Costs - This represents the rate of expense by the conglomerate when adding people to the program. This is an Author derived flow from the Social Finance Limited (2011).
Default Control C
Post-Program-Savings-Reinvestment Percent per month (Dmnl/Month)
= 0.000833333
Description: This represents the percentage of savings that is reinvested into a working program. This is an author defined variable meant to drive the investment of savings into the program when the SIB is complete. The structure associated with this is based on the relationship outlined in Glahn and Whistler (2011).
Present in 2 views: Used by:
  • Monthly MOJ Funded Interventions - This represents the number of people the MOJ will fund after the program is found successful. It is an Author derived based Glahn and Whistler (2011) to represent the desired expenses of the program and the desired level of expenses of the program.
Default Rehab L
Prison Holding-First Offence (People)
Prison Holding-First Offence [Overall,Prison Systems] = ∫ (New Offender Incarceration Rate[Overall) dt + [Prison Systems]-∑(Rehabilitated Offenders Release Rate[Overall,Release Program!,Prison Systems,First])-SUM(Unrehabilitated Offender Release Rate[Overall,Release Program!,Prison Systems,First]),Initial First time Offender Prisoner Holding*Offender Multiplier between Prison Systems[Prison Systems]]
Prison Holding-First Offence [Cohort 1,Prison Systems] = ∫ ((New Offender Incarceration Rate[Overall) dt + [Prison Systems]*"Cohort Active?"[Cohort 1]-∑(Rehabilitated Offenders Release Rate[Cohort 1,Release Program!,Prison Systems,First])-SUM(Unrehabilitated Offender Release Rate[Cohort 1,Release Program!,Prison Systems,First]))-(1-"Cohort Active?"[Cohort 1])*"Prison Holding-First Offence"[Cohort 1,Prison Systems]/TIME STEP,0]
Prison Holding-First Offence [Cohort 2,Prison Systems] = ∫ ((New Offender Incarceration Rate[Overall) dt + [Prison Systems]*"Cohort Active?"[Cohort 2]-∑(Rehabilitated Offenders Release Rate[Cohort 2,Release Program!,Prison Systems,First])-SUM(Unrehabilitated Offender Release Rate[Cohort 2,Release Program!,Prison Systems,First]))+(1-"Cohort Active?"[Cohort 1])*"Prison Holding-First Offence"[Cohort 1,Prison Systems]/TIME STEP-(1-"Cohort Active?"[Cohort 2])*"Prison Holding-First Offence"[Cohort 2,Prison Systems]/TIME STEP,0]
Prison Holding-First Offence [Cohort 3,Prison Systems] = ∫ ((New Offender Incarceration Rate[Overall) dt + [Prison Systems]*"Cohort Active?"[Cohort 3]-∑(Rehabilitated Offenders Release Rate[Cohort 3,Release Program!,Prison Systems,First])-SUM(Unrehabilitated Offender Release Rate[Cohort 3,Release Program!,Prison Systems,First]))+(1-"Cohort Active?"[Cohort 2])*"Prison Holding-First Offence"[Cohort 2,Prison Systems]/TIME STEP-(1-"Cohort Active?"[Cohort 3])*"Prison Holding-First Offence"[Cohort 3,Prison Systems]/TIME STEP,0]
Prison Holding-First Offence [Cohort 4,Prison Systems] = ∫ ((New Offender Incarceration Rate[Overall) dt + [Prison Systems]*"Cohort Active?"[Cohort 4]-∑(Rehabilitated Offenders Release Rate[Cohort 4,Release Program!,Prison Systems,First])-SUM(Unrehabilitated Offender Release Rate[Cohort 4,Release Program!,Prison Systems,First])),0]
Description: This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
Present in 2 views: Used by:
  • Offender Release Rate - This represents the Total release rate from prison for the different prisons. This is an Author defined variable that can be used to measure performance.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
  • Total Prison Population - The percentage of system use.
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default Rehab L
Prison Holding-Repeat Offence (People)
Prison Holding-Repeat Offence [Overall,Prison Systems] = ∫ (∑(Repeat Offender Arrest Rate[Overall) dt + [Prison Systems,Release Program!]-Rehabilitated Offenders Release Rate[Overall,Release Program!,Prison Systems,Repeat]-Unrehabilitated Offender Release Rate[Overall,Release Program!,Prison Systems,Repeat]),Initial Reconvicted Prisoner Holding*Offender Multiplier between Prison Systems[Prison Systems]]
Prison Holding-Repeat Offence [Cohort 1,Prison Systems] = ∫ (∑(Repeat Offender Arrest Rate[Cohort 1) dt + [Prison Systems,Release Program!])-SUM(Rehabilitated Offenders Release Rate[Cohort 1,Release Program!,Prison Systems,Repeat]+Unrehabilitated Offender Release Rate[Cohort 1,Release Program!,Prison Systems,Repeat]),0]
Prison Holding-Repeat Offence [Cohort 2,Prison Systems] = ∫ (∑(Repeat Offender Arrest Rate[Cohort 2) dt + [Prison Systems,Release Program!])-SUM(Rehabilitated Offenders Release Rate[Cohort 2,Release Program!,Prison Systems,Repeat]+Unrehabilitated Offender Release Rate[Cohort 2,Release Program!,Prison Systems,Repeat]),0]
Prison Holding-Repeat Offence [Cohort 3,Prison Systems] = ∫ (∑(Repeat Offender Arrest Rate[Cohort 3) dt + [Prison Systems,Release Program!])-SUM(Rehabilitated Offenders Release Rate[Cohort 3,Release Program!,Prison Systems,Repeat]+Unrehabilitated Offender Release Rate[Cohort 3,Release Program!,Prison Systems,Repeat]),0]
Prison Holding-Repeat Offence [Cohort 4,Prison Systems] = ∫ (∑(Repeat Offender Arrest Rate[Cohort 4) dt + [Prison Systems,Release Program!])-SUM(Rehabilitated Offenders Release Rate[Cohort 4,Release Program!,Prison Systems,Repeat]+Unrehabilitated Offender Release Rate[Cohort 4,Release Program!,Prison Systems,Repeat]),0]
Description: This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
Present in 2 views: Used by:
  • Offender Release Rate - This represents the Total release rate from prison for the different prisons. This is an Author defined variable that can be used to measure performance.
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
  • Total Prison Population - The percentage of system use.
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default A
Prison Population Reduction Percent (Dmnl)
= (Total Prison Population[Overall,Comparison]/Offender Multiplier between Prison Systems[Comparison]-Total Prison Population[Overall,Peterborough]/Offender Multiplier between Prison Systems[Peterborough])/(Total Prison Population[Overall,Comparison]/Offender Multiplier between Prison Systems[Comparison])*100
Description: This represents the fraction of prisoners from the peterborough population that have been reduced as a result of the program.
Present in 2 views:
Default Control Sub
Prison Systems
: Peterborough, Comparison
Description: This array represents the difference between the prisoners in the Peterborough system and those in the comparison group as defined by Cave et. al. (2012).
Present in 6 views: Used by:
  • Actual Peterborough Costs - This represents the actual expenses for the Peterborough prison system using the costs of reconvictions found in Strickland (2010). (Reconviction cost times the number of reconvictions from Peterborough Released prisoners. This is an Author derived equation of the acutal expenses and is deflated to maintain consistent projection value.
  • Cohort Addition of New Offenders - This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
  • Cohort Collection of New Offenders - This represents the accumulation of people in collected in the different cohorts for the Peterborough group based on Cave et. al. (2012).
  • Cohort initiate switch - This determines whether the cohorts have started in accordance with the rules set forth from Cave et. al. (2012) primarily that the maximum time cannot be exceeded and the cohorts must switch before if the maximum number is met or exceeded.
  • Cohort Time Delay Rate - This is an Author derived control to increase time according to the rules set in Cave et al. (2012).
  • Desired Program Capacity - This represents the maximum number of people that will be collected in the cohort that should get space in the program. It is an Author defined variable to slow the flow of people into programs and keep them from overrunning the financial capacity of the NGO.
  • Expected Peterborough Costs - This is the expected payment rate that is allocated to MoJ for the Peterborough Prison System. this is an author derived equation set so that the MOJ receives funds under the expectation that business is operating as usual. The values are discounted from the start of the program to coinside with deflation from projection.
  • MOJ Dictated Program Capacity - This represents the percentage of people that the MOJ is willing to put through the rehabilitation program after it is proven successful. It is bound between 0 and 1. It is an Author derived from Glahn and Whistler formula bound to provide the desired people in the program with a zero value for an unsuccessful program.
  • New Offender Incarceration Rate - This represents the flow of first time offenders into the prison system that fit the criteria for the program as outlined in Strickland (2010). The in flow of new prisoners is the difference between the number of prisoners that can be accepted on a monthly basis and the recidivism rate of prisoners from the overall cohort. This is one of the variations from the Lyneis and Ford (2007) model
  • Number of Reconviction - This represents the accumulation of reconvicted people in the cohort for the comparison group as per Cave et. al. (2012)
  • Offender Release Rate - This represents the Total release rate from prison for the different prisons. This is an Author defined variable that can be used to measure performance.
  • Population in Program - This represents the number of people that are in the program at any point in time. This is an Author defined variable used to calculate the monthly program costs.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Prison Population Reduction Percent - This represents the fraction of prisoners from the peterborough population that have been reduced as a result of the program.
  • Prison Systems - This array represents the difference between the prisoners in the Peterborough system and those in the comparison group as defined by Cave et. al. (2012).
  • Rate of Offenders Coming off of Probation - This represents the rate at which people who will not be convicted leave the program.
  • Rate of Reconviction - This represents the rate of reconvicted people for the comparison group by summing the Recidivism Exclusion Rate and Recidivism Rate as per Cave et. al. (2012).
  • Reconviction Change - Percent of change between the comparison group and the Peterborough group. The equation is derived from Cave et al. (2012) explanation of the program measures.
  • Reconviction Fraction - This represents the rate of reconviction for people in the Peterborough group as perscribed by Cave et. al. (2012).
  • Reconvictions Prevented - This represents the number of reconvictions that the program saved the government from having to go through. This is an Author derived equation.
  • Rehabilitated Offender Percent - This variable represents the fraction of rehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
  • Rehabilitated Offenders - This represents the people in the program that are in the program.
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
  • Repeat Offender Arrest Rate - This is the rate of discovery for people who recommit crimes. The flow is averaged from the backlog and the time found in Cox (2006).
  • Short Term Reconviction Costs - This represents the monthly cost for short term reconvictions within the Peterborough Prison System. This is an Author derived equation from Disely et al. (2011).
  • Total Prison Population - The percentage of system use.
  • Undiscoverd Reoffenders - This represents the people that are in the program that eventually will recommit.
  • Unrehabilitated Offender Percent - This variable represents the fraction of unrehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default C
Probationary Period Length (Month)
= 12
Description: This represents how long the program lasts (Mulgan et al. 2011, Cave et al. 2012).
Present in 3 views: Used by:
Default A
Program Continues? (Dmnl)
= MAX("Cohort Active?"[Cohort 4], "Successful Program?"[Cohort 4])
Description: This represents whether or not the program continues after investment based on the success of the program and the investment time being met. This is an Author Defined variable in accordance with Glahn and Whistler (2011).
Present in 3 views: Used by:
  • Program Recidivism Fraction - This represents the estimated quality of the program in terms of the number of satisfactory outcomes divided by unsatisfactory outcomes . The change in recidivism is subtracted because of its representation in Loder et. al. (2010) and Mulgan et. al. (2011). This relates to the Mission portion of the Balanced Scorecard for the conglomerate of NGOs.
  • Program's Acceptance Fraction - This represents the percentage of prisoners of the allowable population that do elect to go through the program and are able. Disely et. al. (2012) note a 70% willingness and the program allowance is an Author derived equation.
Default C
Program Cost per member (k£/People)
= 1.5
Description: This represents the number of people that can still be added to the program and can be found in Mulgan et al. (2011)
Present in 3 views: Used by:
  • Cost per Participant per month - This represents the cost for one person to be in the program for one month as per Mulgan et al. (2011) page 30.
  • Monthly MOJ Funded Interventions - This represents the number of people the MOJ will fund after the program is found successful. It is an Author derived based Glahn and Whistler (2011) to represent the desired expenses of the program and the desired level of expenses of the program.
  • Remaining Capacity for Program - This represents the estimated number of people that can be admitted into the program and is a author defined variable based on the fund available for all the cohorts.
Default F,A

Program Costs (k£/Month)
= Population in Program[Overall]*Cost per Participant per month
Description: This represents the rate of expense by the conglomerate when adding people to the program. This is an Author derived flow from the Social Finance Limited (2011).
Present in 2 views: Used by:
  • Cohort Expense Rate - This represents how the funds are allocated. This is an author defined variable.
  • Cummulative Program Cost - This represents how much money has been paid into the program. This is an Author defined variable operating as a performance measure for total cost.
  • One Service - The amount of built up capital that the conglomerate of NGOs have in their system. This is representative of the Social Finance Limited (2011).
  • Program Payments from SIP - The amount that SIP pays the conglomerate per month. This is based on the expected budgeted expenses and the lacking funds of the NGOs. This flow represents the flow from One* Service to the conglomerate of NGOs in Social Finance Limited (2011).
Default F,A

Program Payments from SIP (k£/Month)
= Program Costs
Description: The amount that SIP pays the conglomerate per month. This is based on the expected budgeted expenses and the lacking funds of the NGOs. This flow represents the flow from One* Service to the conglomerate of NGOs in Social Finance Limited (2011).
Present in 2 views: Used by:
  • Monthly MOJ Funded Interventions - This represents the number of people the MOJ will fund after the program is found successful. It is an Author derived based Glahn and Whistler (2011) to represent the desired expenses of the program and the desired level of expenses of the program.
  • One Service - The amount of built up capital that the conglomerate of NGOs have in their system. This is representative of the Social Finance Limited (2011).
  • Owner Post-Program Payments - In the event of a successful program the owner would want to assume the payments for the program. This is represented by using a switch ("Program Off?") and the value of the payments. This is an Author derived flow based on Glahn and Whistler (2011).
  • Social Impact Partnership - This represents the funds available for the One* Service (i.e. SGT and Other NGOs) to operate in the Peterborough Prison. This comes from Social Finance Limited (2011).
Default Control A
Program Recidivism Fraction (Dmnl)
= Normal Recidivism Fraction-Recidivism Change Fraction*Normal Recidivism Fraction*Program Continues?
Description: This represents the estimated quality of the program in terms of the number of satisfactory outcomes divided by unsatisfactory outcomes . The change in recidivism is subtracted because of its representation in Loder et. al. (2010) and Mulgan et. al. (2011). This relates to the Mission portion of the Balanced Scorecard for the conglomerate of NGOs.
Present in 1 view: Used by:
  • Rehabilitated Offender Percent - This variable represents the fraction of rehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
  • Unrehabilitated Offender Percent - This variable represents the fraction of unrehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
Default Rehab C,A
Program Switch (Dmnl)
Program Switch[Peterborough] = IF THEN ELSE( Time>=20,1,0)
Program Switch[Comparison] = 0
Description: This is an on/off switch to control whether or not the project is in operation. Author defined.
Present in 2 views: Used by:
  • Rehabilitated Offender Percent - This variable represents the fraction of rehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
  • Unrehabilitated Offender Percent - This variable represents the fraction of unrehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
Default IRR A
program time (Month)
= Time-Actual Cohort Start Times[Cohort 4]
Description: This represents how long the program has been operating. This is an author defined equation.
Present in 1 view: Used by:
  • Investor Discount Factor - This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
  • Owner Discount Factor - This represents the factor by which investors discount future benefits and costs as they occurr based on a fixed discount rate. This is an author defined equation based on an equation to calculate a discount factor.
Default Control C,A
Program's Acceptance Fraction (Dmnl)
Program's Acceptance Fraction[Peterborough] = MIN(Percent Released Offenders Allowed in Program,Offenders' Willing to enter program Fraction)*Program Continues?
Program's Acceptance Fraction[Comparison] = 0
Description: This represents the percentage of prisoners of the allowable population that do elect to go through the program and are able. Disely et. al. (2012) note a 70% willingness and the program allowance is an Author derived equation.
Present in 1 view: Used by:
  • Rehabilitated Offender Percent - This variable represents the fraction of rehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
  • Unrehabilitated Offender Percent - This variable represents the fraction of unrehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
Default Control LI,A
Rate of Offenders Coming off of Probation (People/Month)
Rate of Offenders Coming off of Probation[Cohorts,Prison Systems,Release Program] = Rehabilitated Offenders[Cohorts,Prison Systems,Release Program]/Probationary Period Length
Description: This represents the rate at which people who will not be convicted leave the program.
Present in 1 view: Used by:
Default F,A

Rate of Reconviction (People/Month)
Rate of Reconviction[Cohorts,Prison Systems] = ∑(Repeat Offender Arrest Rate[Cohorts,Prison Systems,Release Program!])*Reconviction Termination[Cohorts]
Description: This represents the rate of reconvicted people for the comparison group by summing the Recidivism Exclusion Rate and Recidivism Rate as per Cave et. al. (2012).
Present in 2 views: Used by:
  • Number of Reconviction - This represents the accumulation of reconvicted people in the cohort for the comparison group as per Cave et. al. (2012)
  • Reconvictions Prevented - This represents the number of reconvictions that the program saved the government from having to go through. This is an Author derived equation.
Default Control C
Recidivism Change Fraction (Dmnl)
= 0.3
Description: This represents the change in recidivism that occurs from the program. Based on Mulgan et. al. (2011) and Loder et. al. (2010) average recidivism change is 20%.
Present in 2 views: Used by:
  • Program Recidivism Fraction - This represents the estimated quality of the program in terms of the number of satisfactory outcomes divided by unsatisfactory outcomes . The change in recidivism is subtracted because of its representation in Loder et. al. (2010) and Mulgan et. al. (2011). This relates to the Mission portion of the Balanced Scorecard for the conglomerate of NGOs.
Default A
Reconviction Change (Dmnl)
Reconviction Change[Cohorts] = 1-XIDZ(Reconviction Fraction[Cohorts,Peterborough],Reconviction Fraction[Cohorts,Comparison],1)
Description: Percent of change between the comparison group and the Peterborough group. The equation is derived from Cave et al. (2012) explanation of the program measures.
Present in 2 views: Used by:
  • Successful Program? - This variable measures whether or not the program successfully pays out as described by Cave et. al. (2012).
Default A
Reconviction Fraction (Dmnl)
Reconviction Fraction[Cohorts,Prison Systems] = ZIDZ(Number of Reconviction[Cohorts,Prison Systems],Cohort Collection of New Offenders[Cohorts,Prison Systems])
Description: This represents the rate of reconviction for people in the Peterborough group as perscribed by Cave et. al. (2012).
Present in 2 views: Used by:
  • Reconviction Change - Percent of change between the comparison group and the Peterborough group. The equation is derived from Cave et al. (2012) explanation of the program measures.
Default Project Timing A
Reconviction Termination (Dmnl)
Reconviction Termination[Cohorts] = IF THEN ELSE(Actual Cohort Closing Times[Cohorts]+Time after Cohort for Reconviction Collection<Time,0,1)
Description: This represents when the reconviction counts for the project stop being collected as per Cave et. al. (2012). RT Time is (12 months) added as the time when reconvictions will be measured.
Present in 3 views: Used by:
  • Rate of Reconviction - This represents the rate of reconvicted people for the comparison group by summing the Recidivism Exclusion Rate and Recidivism Rate as per Cave et. al. (2012).
Default A
Reconvictions Prevented (People/Month)
Reconvictions Prevented[Cohorts] = Rate of Reconviction[Cohorts,Comparison]/Offender Multiplier between Prison Systems[Comparison]-Rate of Reconviction[Cohorts,Peterborough]/Offender Multiplier between Prison Systems[Peterborough]
Description: This represents the number of reconvictions that the program saved the government from having to go through. This is an Author derived equation.
Present in 1 view: Used by:
Default A
Rehabilitated Offender Percent (Dmnl)
Rehabilitated Offender Percent[Prison Systems,SIB,Offense,Cohorts] = Program's Acceptance Fraction[Prison Systems]*(1-Program Recidivism Fraction)*Program Switch[Prison Systems]
Rehabilitated Offender Percent[Prison Systems,Normal,Offense,Cohorts] = (1-Program's Acceptance Fraction[Prison Systems])*(1-Normal Recidivism Fraction)*Program Switch[Prison Systems]+(1-Normal Recidivism Fraction)*(1-Program Switch[Prison Systems])
Description: This variable represents the fraction of rehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
Present in 1 view: Used by:
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
Default Rehab L
Rehabilitated Offenders (People)
Rehabilitated Offenders[Cohorts,Prison Systems,Release Program] = ∫ (∑(Rehabilitated Offenders Release Rate[Cohorts) dt + [Release Program,Prison Systems,Offense!])-Rate of Offenders Coming off of Probation[Cohorts,Prison Systems,Release Program],0]
Description: This represents the people in the program that are in the program.
Present in 2 views: Used by:
  • Population in Program - This represents the number of people that are in the program at any point in time. This is an Author defined variable used to calculate the monthly program costs.
  • Rate of Offenders Coming off of Probation - This represents the rate at which people who will not be convicted leave the program.
Default Rehab LI,F,A

Rehabilitated Offenders Release Rate (People/Month)
Rehabilitated Offenders Release Rate[Cohorts,Normal,Comparison,First] = "Prison Holding-First Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Comparison,Normal,First,Cohorts]
Rehabilitated Offenders Release Rate[Cohorts,SIB,Comparison,First] = "Prison Holding-First Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Comparison,SIB,First,Cohorts]
Rehabilitated Offenders Release Rate[Cohorts,SIB,Peterborough,First] = "Prison Holding-First Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Peterborough,SIB,First,Cohorts ]
Rehabilitated Offenders Release Rate[Cohorts,Normal,Peterborough,First] = "Prison Holding-First Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*(Rehabilitated Offender Percent[Peterborough,Normal,First,Cohorts ])
Rehabilitated Offenders Release Rate[Cohorts,Normal,Comparison,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Comparison,Normal,Repeat,Cohorts ]
Rehabilitated Offenders Release Rate[Cohorts,SIB,Comparison,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Comparison,SIB,Repeat,Cohorts]
Rehabilitated Offenders Release Rate[Cohorts,SIB,Peterborough,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Peterborough,SIB,Repeat,Cohorts ]
Rehabilitated Offenders Release Rate[Cohorts,Normal,Peterborough,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Peterborough,Normal,Repeat,Cohorts ]
Description: This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
Present in 3 views: Used by:
  • Cohort Addition of New Offenders - This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Rehabilitated Offenders - This represents the people in the program that are in the program.
Default IRR F,A

Rehabilitation Program Investment Rate (k£/Month)
= (Owner Success Payment+Owner Post-Program Payments)*Owner Discount Factor
Description: This represents the rate at which money is spent on the program including, payments to investors and payments to the SPV when the MOJ takes over. This is an Author defined equation using a discount from the start of the program as a form of projection.
Present in 1 view: Used by:
  • Amount Available for Rehab Programs - Amount available to repay investors as well as the amount of savings seen by the MOJ. This is an Author defined stock signifying the seperation of savings from the normal MOJ budget.
  • Amount Paid for Rehab Program - This represents the amount of money paid for the program. This is an Author defined stock to measure the IRR for the MOJ.
Default Rehab Sub
Release Program
: Normal, SIB
Description: These array distinguishes between the normal release program and the program funded by the SIB.
Present in 5 views: Used by:
  • Cohort Addition of New Offenders - This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
  • Population in Program - This represents the number of people that are in the program at any point in time. This is an Author defined variable used to calculate the monthly program costs.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Rate of Offenders Coming off of Probation - This represents the rate at which people who will not be convicted leave the program.
  • Rate of Reconviction - This represents the rate of reconvicted people for the comparison group by summing the Recidivism Exclusion Rate and Recidivism Rate as per Cave et. al. (2012).
  • Rehabilitated Offenders - This represents the people in the program that are in the program.
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
  • Release Program - These array distinguishes between the normal release program and the program funded by the SIB.
  • Repeat Offender Arrest Rate - This is the rate of discovery for people who recommit crimes. The flow is averaged from the backlog and the time found in Cox (2006).
  • Short Term Reconviction Costs - This represents the monthly cost for short term reconvictions within the Peterborough Prison System. This is an Author derived equation from Disely et al. (2011).
  • Undiscoverd Reoffenders - This represents the people that are in the program that eventually will recommit.
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default A
Remaining Capacity for Program (People)
= Funds Available for the Program/Program Cost per member
Description: This represents the estimated number of people that can be admitted into the program and is a author defined variable based on the fund available for all the cohorts.
Present in 1 view: Used by:
  • Percent Released Offenders Allowed in Program - This represents the maximum percentage of people released from prison that are allowed in the program for each cohort. This is an author defined constraint to control for entrants into the program and reduce the number of offenders allowed in the program.
Default Rehab LI,F,A

Repeat Offender Arrest Rate (People/Month)
Repeat Offender Arrest Rate[Cohorts,Prison Systems,Release Program] = (Undiscoverd Reoffenders[Cohorts,Prison Systems,Release Program])/Average Time between Release and Reconviction[Prison Systems]
Description: This is the rate of discovery for people who recommit crimes. The flow is averaged from the backlog and the time found in Cox (2006).
Present in 3 views: Used by:
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Rate of Reconviction - This represents the rate of reconvicted people for the comparison group by summing the Recidivism Exclusion Rate and Recidivism Rate as per Cave et. al. (2012).
  • Short Term Reconviction Costs - This represents the monthly cost for short term reconvictions within the Peterborough Prison System. This is an Author derived equation from Disely et al. (2011).
  • Undiscoverd Reoffenders - This represents the people that are in the program that eventually will recommit.
Default Control C
SAVEPER (Month [0,?])
= 1
Description: The frequency with which output is stored.
Not Present In Any View
Default A
Savings from Reduced Reconvictions (k£/Month)
Savings from Reduced Reconvictions[Cohorts] = Total Cost of Incarceration *(Reconvictions Prevented[Cohorts])
Description: This represents the total savings from the reconvictions that remain short term convictions. This is an Author Derived equation.
Present in 1 view: Used by:
  • Investor Earned - This represents the value of savings determined in the contracts without the limits. The Investor share value is kept anonymous to the public. according to Cave et. al. (2012) and Disely et. al. (2011). The value is determined by multiplying the number of reconvictions that should have been based on the comparison group results (Cave et. al. 2012).
Default IRR A
Short Term Reconviction Costs (k£/Month)
Short Term Reconviction Costs[Prison Systems] = ∑(Repeat Offender Arrest Rate[Overall,Prison Systems,Release Program!])*Total Cost of Incarceration/Offender Multiplier between Prison Systems[Prison Systems]
Description: This represents the monthly cost for short term reconvictions within the Peterborough Prison System. This is an Author derived equation from Disely et al. (2011).
Present in 1 view: Used by:
  • Actual Peterborough Costs - This represents the actual expenses for the Peterborough prison system using the costs of reconvictions found in Strickland (2010). (Reconviction cost times the number of reconvictions from Peterborough Released prisoners. This is an Author derived equation of the acutal expenses and is deflated to maintain consistent projection value.
  • Expected Peterborough Costs - This is the expected payment rate that is allocated to MoJ for the Peterborough Prison System. this is an author derived equation set so that the MOJ receives funds under the expectation that business is operating as usual. The values are discounted from the start of the program to coinside with deflation from projection.
Default Control C
SIB? (Dmnl)
= 1
Description: This switch represents whether or not the program is operating as a SIB. 1= SIB, 0=Bond. This is an Author defined value to test the change in risk and value from different projects.
Present in 3 views: Used by:
  • Desired Payment Value - This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
Default Control L
Social Impact Partnership (k£)
= ∫ (Investing+Owner Post-Program Payments-Program Payments from SIP) dt + [No Initial Worth]
Description: This represents the funds available for the One* Service (i.e. SGT and Other NGOs) to operate in the Peterborough Prison. This comes from Social Finance Limited (2011).
Present in 1 view:
Default C
Standard Cohort Length (Month)
= 24
Description: This is the standard time length of a cohort based on Cave et al. (2012).
Present in 2 views: Used by:
  • Max Cohort Length - This represents the maximum length of an individual Cohort (1-3) or 1/3 of the maximum time for the final cumulative cohort as outlined by Cave et. al. (2012).
Default C
Standard People in Cohort (People)
= 1000
Description: This is an Author defined variable based on information provided in Cave et al. (2012).
Present in 1 view: Used by:
  • Max People in Cohort - This is the maximum number of people allowed in the cohort (Cave et. al. 2012).
Default A
Successful Program? (Dmnl)
Successful Program? [Overall] = IF THEN ELSE(Reconviction Change[Overall]>=Minimum Change in Reconvictions[Overall],1,0)
Successful Program? [Cohort 1] = IF THEN ELSE(Reconviction Change[Cohort 1]>=Minimum Change in Reconvictions[Cohort 1],1,0)
Successful Program? [Cohort 2] = IF THEN ELSE(Reconviction Change[Cohort 2]>=Minimum Change in Reconvictions[Cohort 2],1,0)
Successful Program? [Cohort 3] = IF THEN ELSE(Reconviction Change[Cohort 3]>=Minimum Change in Reconvictions[Cohort 3],1,0)
Successful Program? [Cohort 4] = IF THEN ELSE(Reconviction Change[Cohort 4]>=Minimum Change in Reconvictions[Cohort 4],1,0)
Description: This variable measures whether or not the program successfully pays out as described by Cave et. al. (2012).
Present in 3 views: Used by:
  • Desired Payment Value - This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
  • MOJ Dictated Program Capacity - This represents the percentage of people that the MOJ is willing to put through the rehabilitation program after it is proven successful. It is bound between 0 and 1. It is an Author derived from Glahn and Whistler formula bound to provide the desired people in the program with a zero value for an unsuccessful program.
  • Owner Post-Program Payments - In the event of a successful program the owner would want to assume the payments for the program. This is represented by using a switch ("Program Off?") and the value of the payments. This is an Author derived flow based on Glahn and Whistler (2011).
  • Program Continues? - This represents whether or not the program continues after investment based on the success of the program and the investment time being met. This is an Author Defined variable in accordance with Glahn and Whistler (2011).
Default Project Timing C
Time after Cohort for Reconviction Collection (Month)
= 12
Description: RT stands for Reconviction Tally and represents the time from when cohort collection ends and the reconviction collection ends. It is set at 12 months as per Cave et. al. (2012)
Present in 2 views: Used by:
  • Cohort Payment Time - This represents the time at which the program is measured as a success or as a failure. RT Time and System Update Time (18 months) are added on to the accumulation time as per Cave et. al. (2012) to show the time between cohort collection finishing and the data results being collected.
  • Interval time between Cohort completion and Payment Time - This represents the time at which payment will be made if the program is successful. 18 months is added on to the accumulation time as per Cave et. al. (2012) shows for time between cohort collection finishing and the results being tabulated. Cohort 4 is tabulated after the Cohort 3 has been given a chance to process.
  • Reconviction Termination - This represents when the reconviction counts for the project stop being collected as per Cave et. al. (2012). RT Time is (12 months) added as the time when reconvictions will be measured.
Default Project Timing C
Time for System Update (Month)
= 6
Description: This represents the time taken for systems to update any information change in the system. This includes both the recording of reconvictions and Budget surpluses. This value is pulled from Cave et.al. (2012)
Present in 3 views: Used by:
  • Cohort Payment Time - This represents the time at which the program is measured as a success or as a failure. RT Time and System Update Time (18 months) are added on to the accumulation time as per Cave et. al. (2012) to show the time between cohort collection finishing and the data results being collected.
  • Interval time between Cohort completion and Payment Time - This represents the time at which payment will be made if the program is successful. 18 months is added on to the accumulation time as per Cave et. al. (2012) shows for time between cohort collection finishing and the results being tabulated. Cohort 4 is tabulated after the Cohort 3 has been given a chance to process.
  • MOJ Program Savings Rate - This represents the amount of savings that the MOJ sees from the Rehabilitation Program. This is an Author defined equation that allows money to be moved from a general savings account to an organizational savings account. There is no limit for the program to go to zero so that the MOJ can move money back into the general account at a later date for program funding.
  • Total Programs Savings Rate - This represents the rate of total savings from the program. This is an Author defined equation that represents the decaying time value of money as it moves from the MOJ spending account into a savings account.
Default C
Time Program has to Pay (Month)
= 3
Description: The time interval between the final collection of data and the time that payments are made to the investors of Social Impact Partnership. This is an Author defined variable since the payment timing and methods are confidential.
Present in 3 views: Used by:
  • Cohort Payment Time - This represents the time at which the program is measured as a success or as a failure. RT Time and System Update Time (18 months) are added on to the accumulation time as per Cave et. al. (2012) to show the time between cohort collection finishing and the data results being collected.
  • Interval time between Cohort completion and Payment Time - This represents the time at which payment will be made if the program is successful. 18 months is added on to the accumulation time as per Cave et. al. (2012) shows for time between cohort collection finishing and the results being tabulated. Cohort 4 is tabulated after the Cohort 3 has been given a chance to process.
  • Owner Success Payment - This represents when and how much the investors are paid. This relationship is made from the Social Finance Limited (2011).
  • Payment Consideration? - This marks the time that a payment is considered in the project (Cave et. al. 2012). Payment cannot be considered before the completion of cohort collection plus the time interval for data occurence, collection and analysis.
Default Control C
Time spent in prison for a Conviction (Month)
= 1.5
Description: The average time a short-term offender remains in prison per visit according to Cave et. al. (2012). {1.5= 43/30
Present in 4 views: Used by:
  • Offender Release Rate - This represents the Total release rate from prison for the different prisons. This is an Author defined variable that can be used to measure performance.
  • Rehabilitated Offenders Release Rate - This represents the rate of inmates that are released from the system and are properly rehabilitated. Combined with the flow "Program Unrehabilitated Rate" this variable represents the flow of people out of the prison through the rehabilitation program. The structure aligns with Ford and Lyneis (2007).
  • Total Cost of Incarceration - This represents the cost for each reconviction by the British government per person. It is a combination of both the legal action and the time spent in prison. This is an Author derived equation from Mulgan et al. 2012)
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default Control LI,C
TIME STEP (Month [0,?])
= 0.03125
Description: The time step for the simulation.
Present in 2 views: Used by:
  • Maximum Payment Accumulation - This represents the accumulation for the maximum payment value. This is an Author defined equation to ensure investors are paid the amount they are due.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
Default A
Total Cost of Incarceration (k£/People)
= monthly cost*Time spent in prison for a Conviction+Conviction Cost
Description: This represents the cost for each reconviction by the British government per person. It is a combination of both the legal action and the time spent in prison. This is an Author derived equation from Mulgan et al. 2012)
Present in 3 views: Used by:
  • Savings from Reduced Reconvictions - This represents the total savings from the reconvictions that remain short term convictions. This is an Author Derived equation.
  • Short Term Reconviction Costs - This represents the monthly cost for short term reconvictions within the Peterborough Prison System. This is an Author derived equation from Disely et al. (2011).
Default A
Total Prison Population (People)
Total Prison Population[Cohorts,Prison Systems] = "Prison Holding-First Offence"[Cohorts,Prison Systems]+"Prison Holding-Repeat Offence"[Cohorts,Prison Systems]
Description: The percentage of system use.
Present in 2 views: Used by:
Default IRR F,A

Total Programs Savings Rate (k£/Month)
= MOJ Account/Time for System Update*Owner Discount Factor
Description: This represents the rate of total savings from the program. This is an Author defined equation that represents the decaying time value of money as it moves from the MOJ spending account into a savings account.
Present in 1 view: Used by:
  • Amount Available for Rehab Programs - Amount available to repay investors as well as the amount of savings seen by the MOJ. This is an Author defined stock signifying the seperation of savings from the normal MOJ budget.
  • MOJ Account - This Represents the amount of money in the MOJ and BLF account. The structure of this accountto investors is pulled from Social Finance Limited (2011).
Default Rehab L
Undiscoverd Reoffenders (People)
Undiscoverd Reoffenders[Overall,Prison Systems,Normal] = ∫ (∑(Unrehabilitated Offender Release Rate[Overall) dt + [Normal,Prison Systems,Offense!])-Repeat Offender Arrest Rate[Overall,Prison Systems,Normal],Initial Undiscovered Reoffenders*Offender Multiplier between Prison Systems[Prison Systems]]
Undiscoverd Reoffenders[Cohorts,Prison Systems,SIB] = ∫ (∑(Unrehabilitated Offender Release Rate[Cohorts) dt + [SIB,Prison Systems,Offense!])-Repeat Offender Arrest Rate[Cohorts,Prison Systems,SIB],0]
Undiscoverd Reoffenders[Cohort 1,Prison Systems,Normal] = ∫ (∑(Unrehabilitated Offender Release Rate[Cohort 1) dt + [Normal,Prison Systems,Offense!])-Repeat Offender Arrest Rate[Cohort 1,Prison Systems,Normal],0]
Undiscoverd Reoffenders[Cohort 2,Prison Systems,Normal] = ∫ (∑(Unrehabilitated Offender Release Rate[Cohort 2) dt + [Normal,Prison Systems,Offense!])-Repeat Offender Arrest Rate[Cohort 2,Prison Systems,Normal],0]
Undiscoverd Reoffenders[Cohort 3,Prison Systems,Normal] = ∫ (∑(Unrehabilitated Offender Release Rate[Cohort 3) dt + [Normal,Prison Systems,Offense!])-Repeat Offender Arrest Rate[Cohort 3,Prison Systems,Normal],0]
Undiscoverd Reoffenders[Cohort 4,Prison Systems,Normal] = ∫ (∑(Unrehabilitated Offender Release Rate[Cohort 4) dt + [Normal,Prison Systems,Offense!])-Repeat Offender Arrest Rate[Cohort 4,Prison Systems,Normal],0]
Description: This represents the people that are in the program that eventually will recommit.
Present in 2 views: Used by:
  • Population in Program - This represents the number of people that are in the program at any point in time. This is an Author defined variable used to calculate the monthly program costs.
  • Repeat Offender Arrest Rate - This is the rate of discovery for people who recommit crimes. The flow is averaged from the backlog and the time found in Cox (2006).
Default IRR L
Unpaid Investor Earned Returns (k£)
Unpaid Investor Earned Returns[Cohorts] = ∫ (Investor Earned Return Accumulation[Cohorts]-Earned Investor Return payments[Cohorts]) dt + [No Initial Worth]
Description: This represents the accumulation of investor earnings through payment based on Cave et. al. (2012)
Present in 1 view: Used by:
  • Desired Payment Value - This represents the value of the payments to investors based on the information provided by Cave et. al. (2012). The value for a successful payment is the "Investor Earned" if it is between the maximum and minimum return values, or the values of the maximum (if the IE is greater) or minimum (if smaller) return. Cohort 4 is only viable if an investment oportunity was missed by any of the Cohorts not meeting their hurdle value.
Default A
Unrehabilitated Offender Percent (Dmnl)
Unrehabilitated Offender Percent[Prison Systems,SIB,Offense,Cohorts] = Program's Acceptance Fraction[Prison Systems]*(Program Recidivism Fraction)*Program Switch[Prison Systems]
Unrehabilitated Offender Percent[Prison Systems,Normal,Offense,Cohorts] = (1-Program's Acceptance Fraction[Prison Systems])*(Normal Recidivism Fraction)*Program Switch[Prison Systems]+(Normal Recidivism Fraction)*(1-Program Switch[Prison Systems])
Description: This variable represents the fraction of unrehabilitated prisoners being released from prison based on release program and offense. This is an Author derived variable.
Present in 1 view: Used by:
  • Unrehabilitated Offender Release Rate - This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Default Rehab LI,F,A

Unrehabilitated Offender Release Rate (People/Month)
Unrehabilitated Offender Release Rate[Cohorts,Normal,Comparison,First] = "Prison Holding-First Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*(Unrehabilitated Offender Percent[Comparison,Normal,First,Cohorts])
Unrehabilitated Offender Release Rate[Cohorts,Normal,Peterborough,First] = "Prison Holding-First Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Peterborough,Normal,First,Cohorts ]
Unrehabilitated Offender Release Rate[Cohorts,SIB,Peterborough,First] = "Prison Holding-First Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Peterborough,SIB,First,Cohorts ]
Unrehabilitated Offender Release Rate[Cohorts,SIB,Comparison,First] = "Prison Holding-First Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Comparison,SIB,First,Cohorts]
Unrehabilitated Offender Release Rate[Cohorts,Normal,Comparison,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Comparison,Normal,Repeat,Cohorts ]
Unrehabilitated Offender Release Rate[Cohorts,Normal,Peterborough,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Peterborough,Normal,Repeat, Cohorts]
Unrehabilitated Offender Release Rate[Cohorts,SIB,Peterborough,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Peterborough,SIB,Repeat,Cohorts ]
Unrehabilitated Offender Release Rate[Cohorts,SIB,Comparison,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Comparison,SIB,Repeat,Cohorts ]
Description: This represents the flow of inmates that were in the program, but not fully rehabilitated and will perform unsatisfactorily to the point that they will require recidivism. This variable along with the flow of "Program Rehabilitation Rate" are equal to the total release of prisoners from the system using the rehabilitation program. This aligns with the structure from Ford and Lyneis (2007).
Present in 3 views: Used by:
  • Cohort Addition of New Offenders - This represents the rate people enter the Peterborough Cohorts as per Cave et. al. (2012) study.
  • Prison Holding-First Offence - This represents the amount of first time offenders in prison holding after their first conviction.{70 people tunes the model to Cave et al (2012).} Similar to Ford and Lyneis (2008).
  • Prison Holding-Repeat Offence - This represents the stock of reconvicted persons in prison at any point in time during the life of the measures.{168.75 people tunes the model toCave et al (2012).} Similar in structure to Ford and Lyneis (2008).
  • Undiscoverd Reoffenders - This represents the people that are in the program that eventually will recommit.
Default Control C
Yearly Cost of Incarceration (k£/People)
= 39
Description: This represents the annum cost for each incarceration by the British government per person that is in prison as per Loder et. al. (2010).
Present in 2 views: Used by:
  • monthly cost - This represents the monthly cost of incarcerating a prisoner. Derived from Loder et al. (2010).

List of 4 Overly Complex Stock Formulations

Module
Group
Type
 Variable (4)
Default Rehab L Prison Holding-First Offence (People)
Default Rehab L Prison Holding-Repeat Offence (People)
Default Rehab L Rehabilitated Offenders (People)
Default Rehab L Undiscoverd Reoffenders (People)

Formulation Complexity Summary (Violations of Richardson's Rule)

Module
Group
Type
 Variable
Complexity Score
Default Control F,A Accummulating Interest from Investment (k£/Month)
4
Default Rehab LI,F,A Unrehabilitated Offender Release Rate (People/Month)
4
Default A Unrehabilitated Offender Percent (Dmnl)
4
Default Rehab L Undiscoverd Reoffenders (People)
4
Default F,A Maximum Payment Accumulation (k£/Month)
4
Default A Monthly MOJ Funded Interventions (People/Month)
4
Default Project Timing C,A Cohort initiate switch (Dmnl)
4
Default Project Timing C,A Cohort Payment Time (Month)
4
Default Project Timing C,F,A Cohort Time Delay Rate (Month/Month)
4
Default Control L Limits of Unpaid Investor Returns (k£)
4
Default A Rehabilitated Offender Percent (Dmnl)
4
Default Rehab LI,F,A Rehabilitated Offenders Release Rate (People/Month)
4
Default Control L Social Impact Partnership (k£)
4
Default A Percent Released Offenders Allowed in Program (Dmnl)
4
Default F,A Owner Success Payment (k£/Month)
5
Default Rehab L Prison Holding-Repeat Offence (People)
5
Default Control A Desired Payment Value (k£)
5
Default Rehab L Prison Holding-First Offence (People)
8

List of 36 Equations with Embedded Data

Module
Group
Type
 Variable (36)
Default Control F,A Accummulating Interest from Investment (k£/Month)
Default Project Timing L Actual Cohort Closing Times (Month)
Default Project Timing L Actual Cohort Start Times (Month)
Default IRR L Amount Available for Rehab Programs (k£)
Default IRR L Amount Paid for Rehab Program (k£)
Default IRR L Amount Saved From Programs (k£)
Default Project Timing LI,A Cohort Active? (Dmnl)
Default L Cohort Collection of New Offenders (People)
Default Project Timing C,A Cohort initiate switch (Dmnl)
Default A Cohort Investment switch (Dmnl)
Default Project Timing C,F,A Cohort Time Delay Rate (Month/Month)
Default Control A Desired Payment Value (k£)
Default IRR L Invested Amount (k£)
Default F,A Investing (k£/Month)
Default IRR L Investor Account (k£)
Default A Investor Discount Factor (Dmnl)
Default F,A Maximum Payment Accumulation (k£/Month)
Default L Maximum Successful Program Payment Value (k£)
Default IRR L MOJ Account (k£)
Default A MOJ Dictated Program Capacity (Dmnl)
Default L Number of Reconviction (People)
Default IRR A Owner Discount Factor (Dmnl)
Default A Owner Post-Program Payments (k£/Month)
Default C,A Payment Consideration? (Dmnl)
Default A Percent Released Offenders Allowed in Program (Dmnl)
Default Rehab L Prison Holding-First Offence (People)
Default Rehab L Prison Holding-Repeat Offence (People)
Default A Prison Population Reduction Percent (Dmnl)
Default Rehab C,A Program Switch (Dmnl)
Default A Reconviction Change (Dmnl)
Default Project Timing A Reconviction Termination (Dmnl)
Default A Rehabilitated Offender Percent (Dmnl)
Default Rehab L Rehabilitated Offenders (People)
Default A Successful Program? (Dmnl)
Default Rehab L Undiscoverd Reoffenders (People)
Default A Unrehabilitated Offender Percent (Dmnl)

List of 23 State Variables

Module
Group
Type
 Variable
Default Project Timing L Actual Cohort Closing Times (Month)
Default Project Timing L Actual Cohort Start Times (Month)
Default IRR L Amount Available for Rehab Programs (k£)
Default L Amount Investors are willing to Invest (k£)
Default IRR L Amount Paid for Rehab Program (k£)
Default IRR L Amount Saved From Programs (k£)
Default L Cohort Collection of New Offenders (People)
Default L Cummulative Investor Returns (k£)
Default Control L Cummulative Program Cost (k£)
Default L Funds Available for the Program (k£)
Default IRR L Invested Amount (k£)
Default IRR L Investor Account (k£)
Default Control L Limits of Unpaid Investor Returns (k£)
Default L Maximum Successful Program Payment Value (k£)
Default IRR L MOJ Account (k£)
Default L Number of Reconviction (People)
Default Control L One Service (k£)
Default Rehab L Prison Holding-First Offence (People)
Default Rehab L Prison Holding-Repeat Offence (People)
Default Rehab L Rehabilitated Offenders (People)
Default Control L Social Impact Partnership (k£)
Default Rehab L Undiscoverd Reoffenders (People)
Default IRR L Unpaid Investor Earned Returns (k£)

List of 3 Unused Variables

Module
Group
Type
 Unused Variable (3)
Default IRR A IRR Investor (Dmnl)
Default IRR A IRR MOJ (Dmnl)
Default A Prison Population Reduction Percent (Dmnl)

List of 6 Views and Their 141 Variables*

 
System Operations
Analysis Sheet
Propensity Score Matching Measures
Boundaries
SIB
Investor Finances
  
Total: 43 50 57 63 44 51 :Total
Accummulating Interest from Investment (in 1 view)     X       Accummulating Interest from Investment (in 1 view)
Actual Cohort Closing Times (in 2 views)       X X   Actual Cohort Closing Times (in 2 views)
Actual Cohort Start Times (in 3 views)       X X X Actual Cohort Start Times (in 3 views)
Actual Investor Return payments (in 1 view)     X       Actual Investor Return payments (in 1 view)
Actual Peterborough Costs (in 1 view)           X Actual Peterborough Costs (in 1 view)
Amount Available for Rehab Programs (in 1 view)           X Amount Available for Rehab Programs (in 1 view)
Amount Investors are willing to Invest (in 1 view)         X   Amount Investors are willing to Invest (in 1 view)
Amount Paid for Rehab Program (in 1 view)           X Amount Paid for Rehab Program (in 1 view)
Amount Saved From Programs (in 2 views)       X   X Amount Saved From Programs (in 2 views)
Annual Interest Rate for Investment (in 2 views)   X X       Annual Interest Rate for Investment (in 2 views)
Average Prisoner Incarceration Rate for Peterborough (in 2 views) X X         Average Prisoner Incarceration Rate for Peterborough (in 2 views)
Average Time between Release and Reconviction (in 1 view) X           Average Time between Release and Reconviction (in 1 view)
Bond Investment (in 1 view)     X       Bond Investment (in 1 view)
Cohort Active? (in 3 views) X   X X     Cohort Active? (in 3 views)
Cohort Addition of New Offenders (in 1 view)     X       Cohort Addition of New Offenders (in 1 view)
Cohort Collection of New Offenders (in 2 views)     X X     Cohort Collection of New Offenders (in 2 views)
Cohort Expense Rate (in 2 views)     X X     Cohort Expense Rate (in 2 views)
Cohort initiate switch (in 2 views) X     X     Cohort initiate switch (in 2 views)
Cohort Investment switch (in 3 views)     X X   X Cohort Investment switch (in 3 views)
Cohort Payment Time (in 2 views)     X X     Cohort Payment Time (in 2 views)
Cohort Time (in 1 view)       X     Cohort Time (in 1 view)
Cohort Time Delay Rate (in 1 view)       X     Cohort Time Delay Rate (in 1 view)
Cohorts (in 6 views) X X X X X X Cohorts (in 6 views)
Conviction Cost (in 2 views)   X X       Conviction Cost (in 2 views)
Cost per Participant per month (in 2 views)       X X   Cost per Participant per month (in 2 views)
Cummulative Investor Returns (in 1 view)         X   Cummulative Investor Returns (in 1 view)
Cummulative Program Cost (in 2 views)   X     X   Cummulative Program Cost (in 2 views)
Defined Year (in 4 views)   X X   X X Defined Year (in 4 views)
Desired Payment Value (in 1 view)     X       Desired Payment Value (in 1 view)
Desired Program Capacity (in 1 view)       X     Desired Program Capacity (in 1 view)
Earned Investor Return payments (in 1 view)     X       Earned Investor Return payments (in 1 view)
Expected Peterborough Costs (in 1 view)           X Expected Peterborough Costs (in 1 view)
Expected Program Investment amount (in 4 views)   X X X X   Expected Program Investment amount (in 4 views)
FINAL TIME (in 0 views)             FINAL TIME (in 0 views)
Fraction for Investor share (in 2 views)   X X       Fraction for Investor share (in 2 views)
Funds Available for the Program (in 2 views)     X X     Funds Available for the Program (in 2 views)
Initial First time Offender Prisoner Holding (in 2 views) X X         Initial First time Offender Prisoner Holding (in 2 views)
Initial Reconvicted Prisoner Holding (in 2 views) X X         Initial Reconvicted Prisoner Holding (in 2 views)
INITIAL TIME (in 0 views)             INITIAL TIME (in 0 views)
Initial Undiscovered Reoffenders (in 2 views) X X         Initial Undiscovered Reoffenders (in 2 views)
Interest (in 1 view)     X       Interest (in 1 view)
Interval time between Cohort completion and Payment Time (in 1 view)       X     Interval time between Cohort completion and Payment Time (in 1 view)
Invested Amount (in 2 views)   X       X Invested Amount (in 2 views)
Investing (in 3 views)     X   X X Investing (in 3 views)
Investment Finalization Time (in 1 view)       X     Investment Finalization Time (in 1 view)
Investment Payment per Cohort (in 3 views)   X   X X   Investment Payment per Cohort (in 3 views)
Investment Rate (in 1 view)           X Investment Rate (in 1 view)
Investor Account (in 1 view)           X Investor Account (in 1 view)
Investor Balance (in 1 view)         X   Investor Balance (in 1 view)
Investor Discount Factor (in 1 view)           X Investor Discount Factor (in 1 view)
Investor Discount Rate (in 2 views)   X       X Investor Discount Rate (in 2 views)
Investor Earned (in 1 view)     X       Investor Earned (in 1 view)
Investor Earned Return Accumulation (in 1 view)     X       Investor Earned Return Accumulation (in 1 view)
Investor Return Rate (in 1 view)           X Investor Return Rate (in 1 view)
Investors Cohorts Paid? Amount (in 2 views)     X X     Investors Cohorts Paid? Amount (in 2 views)
IRR Investor (in 2 views)   X       X IRR Investor (in 2 views)
IRR MOJ (in 2 views)   X       X IRR MOJ (in 2 views)
Latest Cohort Start Times (in 1 view)       X     Latest Cohort Start Times (in 1 view)
Limits of Unpaid Investor Returns (in 1 view)     X       Limits of Unpaid Investor Returns (in 1 view)
Max Cohort Length (in 2 views)   X   X     Max Cohort Length (in 2 views)
Max People in Cohort (in 3 views)   X   X X   Max People in Cohort (in 3 views)
Maximum Payment Accumulation (in 1 view)     X       Maximum Payment Accumulation (in 1 view)
Maximum Successful Program Payment Value (in 2 views)     X   X   Maximum Successful Program Payment Value (in 2 views)
Minimum Change in Reconvictions (in 2 views)   X X       Minimum Change in Reconvictions (in 2 views)
MOJ Account (in 1 view)           X MOJ Account (in 1 view)
MOJ Dictated Program Capacity (in 1 view)       X     MOJ Dictated Program Capacity (in 1 view)
MOJ Discount Rate (in 2 views)   X       X MOJ Discount Rate (in 2 views)
MOJ Program Savings Rate (in 1 view)           X MOJ Program Savings Rate (in 1 view)
monthly cost (in 1 view)     X       monthly cost (in 1 view)
Monthly MOJ Funded Interventions (in 2 views)   X   X     Monthly MOJ Funded Interventions (in 2 views)
New Offender Incarceration Rate (in 1 view) X           New Offender Incarceration Rate (in 1 view)
No Initial Worth (in 5 views) X X X   X X No Initial Worth (in 5 views)
Normal Recidivism Discovery Time (in 2 views) X X         Normal Recidivism Discovery Time (in 2 views)
Normal Recidivism Fraction (in 2 views) X X         Normal Recidivism Fraction (in 2 views)
number of payments (in 1 view)       X     number of payments (in 1 view)
Number of Reconviction (in 1 view)     X       Number of Reconviction (in 1 view)
Offender Multiplier between Prison Systems (in 5 views) X X X X   X Offender Multiplier between Prison Systems (in 5 views)
Offender Release Rate (in 3 views) X X   X     Offender Release Rate (in 3 views)
Offenders' Willing to enter program Fraction (in 2 views) X X         Offenders' Willing to enter program Fraction (in 2 views)
Offense (in 4 views) X   X X X   Offense (in 4 views)
One Service (in 1 view)         X   One Service (in 1 view)
Owner Discount Factor (in 1 view)           X Owner Discount Factor (in 1 view)
Owner Post-Program Payments (in 2 views)         X X Owner Post-Program Payments (in 2 views)
Owner Success Payment (in 3 views)     X   X X Owner Success Payment (in 3 views)
Payment Consideration? (in 3 views)     X X X   Payment Consideration? (in 3 views)
Payment for Cohort 1 (in 1 view)         X   Payment for Cohort 1 (in 1 view)
Payment for Cohort 2 (in 1 view)         X   Payment for Cohort 2 (in 1 view)
Payment for Cohort 3 (in 1 view)         X   Payment for Cohort 3 (in 1 view)
Payment for Cohort 4 (in 1 view)         X   Payment for Cohort 4 (in 1 view)
Percent Released Offenders Allowed in Program (in 2 views) X     X     Percent Released Offenders Allowed in Program (in 2 views)
Population in Program (in 1 view)         X   Population in Program (in 1 view)
Post-Program-Savings-Reinvestment Percent per month (in 2 views)   X   X     Post-Program-Savings-Reinvestment Percent per month (in 2 views)
Prison Holding-First Offence (in 2 views) X     X     Prison Holding-First Offence (in 2 views)
Prison Holding-Repeat Offence (in 2 views) X     X     Prison Holding-Repeat Offence (in 2 views)
Prison Population Reduction Percent (in 2 views)   X   X     Prison Population Reduction Percent (in 2 views)
Prison Systems (in 6 views) X X X X X X Prison Systems (in 6 views)
Probationary Period Length (in 3 views) X X     X   Probationary Period Length (in 3 views)
Program Continues? (in 3 views) X     X X   Program Continues? (in 3 views)
Program Cost per member (in 3 views)   X   X X   Program Cost per member (in 3 views)
Program Costs (in 2 views)       X X   Program Costs (in 2 views)
Program Payments from SIP (in 2 views)       X X   Program Payments from SIP (in 2 views)
Program Recidivism Fraction (in 1 view) X           Program Recidivism Fraction (in 1 view)
Program Switch (in 2 views) X       X   Program Switch (in 2 views)
program time (in 1 view)           X program time (in 1 view)
Program's Acceptance Fraction (in 1 view) X           Program's Acceptance Fraction (in 1 view)
Rate of Offenders Coming off of Probation (in 1 view) X           Rate of Offenders Coming off of Probation (in 1 view)
Rate of Reconviction (in 2 views)     X     X Rate of Reconviction (in 2 views)
Recidivism Change Fraction (in 2 views) X X         Recidivism Change Fraction (in 2 views)
Reconviction Change (in 2 views)   X X       Reconviction Change (in 2 views)
Reconviction Fraction (in 2 views)   X X       Reconviction Fraction (in 2 views)
Reconviction Termination (in 3 views)     X X   X Reconviction Termination (in 3 views)
Reconvictions Prevented (in 1 view)     X       Reconvictions Prevented (in 1 view)
Rehabilitated Offender Percent (in 1 view) X           Rehabilitated Offender Percent (in 1 view)
Rehabilitated Offenders (in 2 views) X       X   Rehabilitated Offenders (in 2 views)
Rehabilitated Offenders Release Rate (in 3 views) X   X X     Rehabilitated Offenders Release Rate (in 3 views)
Rehabilitation Program Investment Rate (in 1 view)           X Rehabilitation Program Investment Rate (in 1 view)
Release Program (in 5 views) X   X X X X Release Program (in 5 views)
Remaining Capacity for Program (in 1 view)       X     Remaining Capacity for Program (in 1 view)
Repeat Offender Arrest Rate (in 3 views) X   X     X Repeat Offender Arrest Rate (in 3 views)
SAVEPER (in 0 views)             SAVEPER (in 0 views)
Savings from Reduced Reconvictions (in 1 view)     X       Savings from Reduced Reconvictions (in 1 view)
Short Term Reconviction Costs (in 1 view)           X Short Term Reconviction Costs (in 1 view)
SIB? (in 3 views)   X X   X   SIB? (in 3 views)
Social Impact Partnership (in 1 view)         X   Social Impact Partnership (in 1 view)
Standard Cohort Length (in 2 views)   X   X     Standard Cohort Length (in 2 views)
Standard People in Cohort (in 1 view)       X     Standard People in Cohort (in 1 view)
Successful Program? (in 3 views)     X X X   Successful Program? (in 3 views)
Time (in 5 views) X   X X X X Time (in 5 views)
Time after Cohort for Reconviction Collection (in 2 views)   X   X     Time after Cohort for Reconviction Collection (in 2 views)
Time for System Update (in 3 views)   X   X   X Time for System Update (in 3 views)
Time Program has to Pay (in 3 views)   X   X X   Time Program has to Pay (in 3 views)
Time spent in prison for a Conviction (in 4 views) X X X X     Time spent in prison for a Conviction (in 4 views)
TIME STEP (in 2 views) X   X       TIME STEP (in 2 views)
Total Cost of Incarceration (in 3 views) X   X     X Total Cost of Incarceration (in 3 views)
Total Prison Population (in 2 views)   X   X     Total Prison Population (in 2 views)
Total Programs Savings Rate (in 1 view)           X Total Programs Savings Rate (in 1 view)
Undiscoverd Reoffenders (in 2 views) X       X   Undiscoverd Reoffenders (in 2 views)
Unpaid Investor Earned Returns (in 1 view)     X       Unpaid Investor Earned Returns (in 1 view)
Unrehabilitated Offender Percent (in 1 view) X           Unrehabilitated Offender Percent (in 1 view)
Unrehabilitated Offender Release Rate (in 3 views) X   X X     Unrehabilitated Offender Release Rate (in 3 views)
Yearly Cost of Incarceration (in 2 views)   X X       Yearly Cost of Incarceration (in 2 views)
Total: 43 50 57 63 44 51 :Total
 
System Operations
Analysis Sheet
Propensity Score Matching Measures
Boundaries
SIB
Investor Finances
  

* Includes Time, if used in a view. Excludes variables not present in any view.

Level Structure †

Actual Cohort Closing Times[Cohorts] = ∫ (Cohort Time[Cohorts]) dt + [0]
    Cohort Time[Cohorts] = Cohort initiate switch[Cohorts]
    Cohorts : Overall, Cohort 1, Cohort 2, Cohort 3, Cohort 4

Actual Cohort Start Times[Cohorts] = ∫ (Cohort Time Delay Rate[Cohorts]) dt + [0]
    Cohort Time Delay Rate[Cohort 4] = IF THEN ELSE(Max People in Cohort[Cohort 4]>Cohort Collection of New Offenders[Cohort 4,Peterborough],IF THEN ELSE(Latest Cohort Start Times[Cohort 4]>Time,1,0),0)

Amount Available for Rehab Programs = ∫ (Total Programs Savings Rate-MOJ Program Savings Rate-Rehabilitation Program Investment Rate) dt + [0]
    MOJ Program Savings Rate = Amount Available for Rehab Programs/Time for System Update*Owner Discount Factor
    Rehabilitation Program Investment Rate = (Owner Success Payment+Owner Post-Program Payments)*Owner Discount Factor
    Total Programs Savings Rate = MOJ Account/Time for System Update*Owner Discount Factor

Amount Investors are willing to Invest = ∫ (-Investing) dt + [Expected Program Investment amount]
Expected Program Investment amount = 5000
    Investing = PULSE(Actual Cohort Start Times[Cohort 1]+1,1)*Investment Payment per Cohort+PULSE(Actual Cohort Start Times[Cohort 2]+1,1)*Investment Payment per Cohort+PULSE(Actual Cohort Start Times[Cohort 3]+1,1)*Investment Payment per Cohort

Amount Paid for Rehab Program = ∫ (Rehabilitation Program Investment Rate) dt + [0]

Amount Saved From Programs = ∫ (MOJ Program Savings Rate) dt + [0]

Cohort Collection of New Offenders[Cohorts,Prison Systems] = ∫ (Cohort Addition of New Offenders[Cohorts) dt + [Prison Systems],0]
Prison Systems : Peterborough, Comparison
    Cohort Addition of New Offenders[Cohorts,Prison Systems] = ∑((Rehabilitated Offenders Release Rate[Cohorts,Release Program!,Prison Systems,First]+Unrehabilitated Offender Release Rate[Cohorts,Release Program!,Prison Systems,First]))*"Cohort Active?"[Cohorts]

Cummulative Investor Returns = ∫ (Owner Success Payment) dt + [No Initial Worth]
No Initial Worth = 0
    Owner Success Payment = (Payment for Cohort 1+Payment for Cohort 2+Payment for Cohort 3+Payment for Cohort 4)/Time Program has to Pay

Cummulative Program Cost = ∫ (Program Costs) dt + [No Initial Worth]
    Program Costs = Population in Program[Overall]*Cost per Participant per month

Funds Available for the Program = ∫ (-Cohort Expense Rate) dt + [Expected Program Investment amount]
    Cohort Expense Rate = Program Costs

Invested Amount = ∫ (Investment Rate) dt + [0]
    Investment Rate = (Investing)*Investor Discount Factor

Investor Account = ∫ (Investor Return Rate-Investment Rate) dt + [0]
    Investor Return Rate = Owner Success Payment*Investor Discount Factor

Limits of Unpaid Investor Returns[Cohorts,Interest] = ∫ (Accummulating Interest from Investment[Cohorts) dt + [Interest]+Bond Investment[Cohorts,Interest]-Actual Investor Return payments[Cohorts,Interest],No Initial Worth]
Interest : maximum, minimum, Bond
    Accummulating Interest from Investment[Cohorts,Interest] = IF THEN ELSE(Cohort Payment Time[Cohorts]>=Time, Limits of Unpaid Investor Returns[Cohorts,Interest]*Annual Interest Rate for Investment[Interest]/Defined Year,0)
    Actual Investor Return payments[Cohorts,Interest] = "Investors Cohorts Paid? Amount"[Cohorts]
    Bond Investment[Cohorts,Bond] = Investing*Cohort Investment switch[Cohorts]

Maximum Successful Program Payment Value[Cohorts] = ∫ (Maximum Payment Accumulation[Cohorts]) dt + [0]
    Maximum Payment Accumulation[Cohorts] = IF THEN ELSE(Cohort Payment Time[Cohorts]<Time,IF THEN ELSE(Desired Payment Value[Cohorts]>Maximum Successful Program Payment Value[Cohorts],Desired Payment Value[Cohorts]-Maximum Successful Program Payment Value[Cohorts],0)/TIME STEP,0)

MOJ Account = ∫ (Expected Peterborough Costs-Actual Peterborough Costs-Total Programs Savings Rate) dt + [0]
    Actual Peterborough Costs = (Short Term Reconviction Costs[Peterborough])*Owner Discount Factor
    Expected Peterborough Costs = Short Term Reconviction Costs[Comparison]*Owner Discount Factor

Number of Reconviction[Cohorts,Prison Systems] = ∫ (Rate of Reconviction[Cohorts) dt + [Prison Systems],0]
    Rate of Reconviction[Cohorts,Prison Systems] = ∑(Repeat Offender Arrest Rate[Cohorts,Prison Systems,Release Program!])*Reconviction Termination[Cohorts]

One Service = ∫ (Program Payments from SIP-Program Costs) dt + [No Initial Worth]
    Program Payments from SIP = Program Costs

Prison Holding-First Offence [Cohort 4,Prison Systems] = ∫ ((New Offender Incarceration Rate[Overall) dt + [Prison Systems]*"Cohort Active?"[Cohort 4]-∑(Rehabilitated Offenders Release Rate[Cohort 4,Release Program!,Prison Systems,First])-SUM(Unrehabilitated Offender Release Rate[Cohort 4,Release Program!,Prison Systems,First])),0]
Release Program : Normal, SIB
    Cohort Active? [Cohort 4] = IF THEN ELSE(Actual Cohort Start Times[Cohort 4]<Time,IF THEN ELSE(Actual Cohort Closing Times[Cohort 4]>=Time,1,0),0)
    New Offender Incarceration Rate[Overall,Comparison] = Offender Multiplier between Prison Systems[Comparison]*New Offender Incarceration Rate[Overall,Peterborough]
    Rehabilitated Offenders Release Rate[Cohorts,Normal,Peterborough,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Peterborough]/Time spent in prison for a Conviction*Rehabilitated Offender Percent[Peterborough,Normal,Repeat,Cohorts ]
    Unrehabilitated Offender Release Rate[Cohorts,SIB,Comparison,Repeat] = "Prison Holding-Repeat Offence"[Cohorts,Comparison]/Time spent in prison for a Conviction*Unrehabilitated Offender Percent[Comparison,SIB,Repeat,Cohorts ]

Prison Holding-Repeat Offence [Cohort 4,Prison Systems] = ∫ (∑(Repeat Offender Arrest Rate[Cohort 4) dt + [Prison Systems,Release Program!])-SUM(Rehabilitated Offenders Release Rate[Cohort 4,Release Program!,Prison Systems,Repeat]+Unrehabilitated Offender Release Rate[Cohort 4,Release Program!,Prison Systems,Repeat]),0]
    Repeat Offender Arrest Rate[Cohorts,Prison Systems,Release Program] = (Undiscoverd Reoffenders[Cohorts,Prison Systems,Release Program])/Average Time between Release and Reconviction[Prison Systems]

Rehabilitated Offenders[Cohorts,Prison Systems,Release Program] = ∫ (∑(Rehabilitated Offenders Release Rate[Cohorts) dt + [Release Program,Prison Systems,Offense!])-Rate of Offenders Coming off of Probation[Cohorts,Prison Systems,Release Program],0]
    Offense : First, Repeat
    Rate of Offenders Coming off of Probation[Cohorts,Prison Systems,Release Program] = Rehabilitated Offenders[Cohorts,Prison Systems,Release Program]/Probationary Period Length

Social Impact Partnership = ∫ (Investing+Owner Post-Program Payments-Program Payments from SIP) dt + [No Initial Worth]
    "Owner Post-Program Payments" = IF THEN ELSE( Actual Cohort Closing Times[Cohort 4]<Time, Program Payments from SIP*("Successful Program?"[Cohort 4]),0)

Undiscoverd Reoffenders[Cohort 4,Prison Systems,Normal] = ∫ (∑(Unrehabilitated Offender Release Rate[Cohort 4) dt + [Normal,Prison Systems,Offense!])-Repeat Offender Arrest Rate[Cohort 4,Prison Systems,Normal],0]

Unpaid Investor Earned Returns[Cohorts] = ∫ (Investor Earned Return Accumulation[Cohorts]-Earned Investor Return payments[Cohorts]) dt + [No Initial Worth]
    Earned Investor Return payments[Cohorts] = Actual Investor Return payments[Cohorts,maximum]
    Investor Earned Return Accumulation[Cohorts] = Investor Earned[Cohorts]*Cohort Investment switch[Cohorts]

†  Level Structure Report still under development.

Source file: SIB_130308.mdl (3/8/13 - 1:53 AM)
Report Created on 3/8/13 - 1:56 AM
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