{ From user Fred, Model Benefit_cost_analysi at 9-Apr-2016 3:34:02 PM, encoding="ascii" }
SoftwareVersion 4.7.0


{ System Variables with non-default values: }
Time := [0]
Description Time: Dynamic simulation periods are specified in Time's definition. This is usually a list of numbers or labels, typically in some unit of time (days, weeks, months, etc.).  Use the “Dynamic()” function in your variables to perform dynamic simulation.
NumberWidth := 7
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{!-40203|Attribute CloudPlayerStyles}
Attribute Reference

Attribute Prev_attribute
Title: Prev_attribute



Model Benefit_cost_analysi
Title: Benefit-cost analysis of toxic emissions
Description: This model demonstrates a risk/benefit analysis, in this case regarding the benefits of reducing the emissions of a (fictitious) air pollutant "TXC".   ~
~
Among other things it illustrates~
  * A user-interface form giving easy access to key assumptions and results, including~
   - A list of key assumptions, including probability distributions, and two pulldown menus, "Emissions reduction" and "Statistical value of a life"~
   - Results, including comparison of Benefits and costs, Net benefits, and "Importance of uncertainties" showing sensitivity of net benefits to each uncertain input. ~
  * Double click on "Model details" to see an influence diagram showing the model structure, ~
    - A Decision "Emissions reduction" (0% to 95%)~
    - Several uncertain inputs shown as ovals~
    - Intermediate variables, such as Reduced concentration and Benefits of lives saved.
Author: Max Henrion 2 Oct 1982 updated 10 Oct 2006
Date: Wed, Aug 03, 2005 11:56 AM
SaveAuthor: Fred
SaveDate: Sat, Apr 9, 2016 3:34 PM
DefaultSize: 48,24
DiagState: 2,22,-12,1109,475,17
WindState: 2,371,9,697,578
DiagramColor: 52428,52428,52428
FontStyle: Arial, 15
FileInfo: 0,Model Benefit_cost_analysi,2,2,0,0,C:\rep\Work new repo\Changes to wiki\Bug regression test script\16265.ana
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Module Model_details
Title: Model details
Description: Influence diagram showing key elements of the model.
Author: Max Henrion
Date: Sun, Aug 18, 1991 10:40 PM
SaveAuthor: fredb
SaveDate: Wed, Sep 10, 1997 2:28 PM
DefaultSize: 48,20
NodeLocation: 72,576,1
NodeSize: 60,24
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DiagramColor: 52428,52428,52428
FontStyle: Arial, 15
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Att__CloakDefn: 0
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Variable Benefits_of_lives_sa
Title: Benefits of lives saved
Units: $/year
Description: Benefits from lives saved, calculated as the change in mortality rates, the size of population exposed and the statistical "value of a life"/
Definition: (Current_mortality_ra - Reduced_mortality_ra) * Pop_exp * Stat_value_of_life
NodeLocation: 416,280,1
NodeSize: 56,24
ValueState: 2,300,303,529,361,1,MEAN
NodeColor: 1,49155,65535
ReformVal: [Reduction,Stat_value_of_life]
NumberFormat: 1,D,7,2,0,1

Objective Net_benefits
Title: Net benefits
Units: $/yr
Description: Total cost to society, calculated as the difference between the value of the lives saved, and the cost of the Emissions Reduction required to save those lives.
Definition: Benefits_of_lives_sa - Control_costs
NodeLocation: 416,120,1
NodeSize: 56,24
ValueState: 2,617,4,748,711,1,MIDM
Aliases: FormNode Net_benefits1
NodeColor: 65535,19661,38773
GraphSetup: ProbIndex:[0.05,0.25,0.5,0.75,0.95]~
StatsLabels:['Min','Median','Mean','Max','Std. Dev.']~
StatsSelect:[1,1,1,1,1,0,0,0]~
IncludeZZero:0~
IncludeYZero:1~
IncludeXZero:0~
Yintervals:0~
Xintervals:0~
Zmaximum:1~
Zminimum:1~
Ymaximum:260M~
Yminimum:80M~
Xmaximum:1~
Xminimum:0~
ShowKey:1~
FrameAuto:1~
Depth:70~
Tilt:0~
Rotation:0~
Scales:1~
Mesh:1~
Ticks:1~
Frame:1~
LineStyle:10~
BarOverlap:0~
SymbolSize:6~
CdfSteps:1~
CdfResol:5~
DistSteps:1~
DistResol:20~
GraphTool:0
FontStyle: Arial, 8
ReformVal: [Reduction,Stat_value_of_life,Undefined,Undefined,Undefined,2]
NumberFormat: 1,D,4,2,0,1
Att__CloakDefn: 0
{!40000|Att_XRole: Reduction}
{!40000|Att_ColorRole: Run}

Decision Reduction
Title: Emissions~
Reduction
Description: Decision on the percentage reduction of emissions of TXC by installing emissions control technology on the plant.  ~
~
Choose emissions reduction level of interest, or choose "All" to compare effects of different levels.
Definition: Choice(Self,0,1)
NodeLocation: 80,48,1
NodeSize: 56,24
WindState: 2,102,90,529,486
Aliases: FormNode Emissions_reduction
NodeColor: 1,65535,32766
NumberFormat: 1,%,7,0,0,0
Domain: [0,0.1,0.3,0.5,0.7,0.8,0.9,0.95]
{!40300|DomainExpr: Discrete(0%,10%,30%,50%,70%,80%,90%,95%,type:'number')}
{!40200|Att_ChoiceIndexes: Keyword Self}

Chance Pop_exp
Title: Population~
Exposed
Units: people
Description: The size of the population exposed to TXC.
Definition: Normal(30M, 3M)
NodeLocation: 416,192,1
NodeSize: 56,24
ValueState: 2,619,4,738,694,1,PDFP
Aliases: FormNode Population_exposed
NodeColor: 1,65535,65535
GraphSetup: {!40000|Att_AreaFill Graph_KDE_Valdim:1}~
{!40000|Att_ContLineStyle Graph_KDE_Valdim:1}~
GraphTool:0~
DistResol:50~
DistSteps:0~
CdfResol:5~
CdfSteps:1~
SymbolSize:6~
BarOverlap:0~
LineStyle:10~
Frame:1~
Grid:1~
Ticks:1~
Mesh:1~
Scales:1~
Rotation:45~
Tilt:0~
Depth:70~
FrameAuto:1~
ShowKey:1~
Xminimum:15M~
Xmaximum:45M~
Yminimum:0~
Ymaximum:140n~
Zminimum:1~
Zmaximum:1~
Xintervals:0~
Yintervals:0~
IncludeXZero:0~
IncludeYZero:0~
IncludeZZero:0~
StatsSelect:[1,1,1,1,1,0,0,0]~
StatsLabels:['Min','Median','Mean','Max','Std. Dev.']~
ProbIndex:[0.05,0.25,0.5,0.75,0.95]
FontStyle: Arial, 8

Chance H_damage_factor
Title: Health Damage Factor
Units: d/yr/ug/m^3
Description: The slope of the dose-response function for TXC, expressing the increase in mortality rate per unit increase in atmospheric concentration of TXC, assuming concentration is above the threshold level, in deaths per eyear per microgram per cubic meter.
Definition: Lognormal( 0.3u, 1.7 )
NodeLocation: 152,280,1
NodeSize: 56,24
WindState: 2,102,90,474,300
ValueState: 2,617,4,745,698,1,PDFP
Aliases: FormNode Health_damage_factor
NodeColor: 1,65535,65535
GraphSetup: {!40000|Att_AreaFill Graph_KDE_Valdim:1}~
ProbIndex:[0.05,0.25,0.5,0.75,0.95]~
StatsLabels:['Min','Median','Mean','Max','Std. Dev.']~
StatsSelect:[1,1,1,1,1,0,0,0]~
IncludeZZero:0~
IncludeYZero:0~
IncludeXZero:0~
Yintervals:0~
Xintervals:0~
Zmaximum:1~
Zminimum:1~
Ymaximum:3M~
Yminimum:0~
Xmaximum:1.8u~
Xminimum:-200n~
ShowKey:1~
FrameAuto:1~
Depth:70~
Tilt:0~
Rotation:45~
Scales:1~
Mesh:1~
Ticks:1~
Grid:1~
Frame:1~
LineStyle:1~
BarOverlap:0~
SymbolSize:6~
CdfSteps:1~
CdfResol:5~
DistSteps:0~
DistResol:50~
GraphTool:0

Variable Reduced_concentratio
Title: Reduced concentration
Units: ug/m^3
Description: The average atmospheric concentration of TXC assuming reduced emissions, in micrograms per cubic meter.
Definition: Base_concentration*(1 - Reduction)
NodeLocation: 80,192,1
NodeSize: 56,24
NodeColor: 1,49155,65535

Variable Current_mortality_ra
Title: Current mortality rate
Units: /yr
Description: Current annual mortality rate from exposure to current level of TXC.~
~
This is zero if the concentration is less than the threshold,~
otherwise it's the Health Damage Factor time the amount that the Concentration is above the Threshold.
Definition: IF Base_concentration < Threshhold THEN  0~
ELSE H_damage_factor * (Base_concentration - Threshhold)
NodeLocation: 232,360,1
NodeSize: 56,24
WindState: 2,238,233,476,224
NodeColor: 1,49155,65535

Chance Threshhold
Title: Threshold
Units: ug/m^3
Description: The Threshold atmospheric concentration of TXC below which TXC has no effect.
Definition: Uniform(0,10)
NodeLocation: 288,280,1
NodeSize: 56,24
ValueState: 2,619,1,749,714,1,PDFP
Aliases: FormNode Threshold
NodeColor: 1,65535,65535
GraphSetup: {!40000|Att_AreaFill Graph_Pdf_Valdim:1}~
{!40000|Att_ContLineStyle Graph_KDE_Valdim:1}~
{!40400|Sys_PdfSmoothMethod:0}~
DistSteps:1~
DistResol:100

Chance Base_concentration
Title: Base concentration
Units: ug/m^3
Description: The current concentration of TXC in micrograms per cubic meter, with current emissions, i.e. with no control to reduce emissions.
Definition: Lognormal(10, 1.5)
NodeLocation: 80,360,1
NodeSize: 56,24
WindState: 2,375,65,476,224
ValueState: 2,618,2,748,712,1,PDFP
Aliases: FormNode Base_conc_1458942721
NodeColor: 1,65535,65535
GraphSetup: {!40000|Att_GraphValueRange Base_concentration:|1:1,,0,,,,,0,40,0}~
{!40000|Att_ContLineStyle Graph_KDE_Valdim:1}~
{!40000|Att_AreaFill Graph_KDE_Valdim:1}
{!40200|Att_GraphSetupSlices: [3,1,DensityIndex,1]}

Variable Control_costs
Title: Control~
Costs
Units: $/yr
Description: Annualized cost of emissions control technology.~
~
This is modeled as a exponential function (using the Logten(1-Reduction) function),~
to reflect the fact that as emissions reduction increases, the cost of additional reduction increases.
Definition: -Cost_control_factor*Logten(1 - Reduction)/Logten(2)
NodeLocation: 224,120,1
NodeSize: 56,24
WindState: 2,208,223,476,323
ValueState: 2,261,338,416,303,1,MIDM
NodeColor: 1,49155,65535

Decision Stat_value_of_life
Title: Statistical Value of a Life
Units: $/d
Description: Dollar investment deemed appropriate to avert a statistical death from TXC exposure.
Definition: Choice(Self,2,1)
NodeLocation: 416,360,1
NodeSize: 56,24
WindState: 2,364,78,550,405
ValueState: 1,72,82,416,303,1,PDFP
Aliases: FormNode Statistical_value_o1
NodeColor: 1,65535,32766
NumberFormat: 1,D,7,2,0,1
Domain: [1M,3M,10M]
{!40300|DomainExpr: Discrete(1M,3M,10M,type:'number')}
{!40200|Att_ChoiceIndexes: Keyword Self}

Variable Reduced_mortality_ra
Title: Reduced mortality rate
Units: /year
Description: Current annual mortality rate from exposure to reduced level of TXC.~
~
This is zero if the  reduced concentration is less than the threshold,~
otherwise it's the Health Damage Factor time the amount that the Reduced concentration is above the Threshold.
Definition: IF Reduced_concentratio < Threshhold THEN  0~
ELSE H_damage_factor * (Reduced_concentratio - Threshhold)
NodeLocation: 224,192,1
NodeSize: 56,24
WindState: 2,37,439,495,272
ValueState: 2,216,226,416,303,1,MEAN

Chance Cost_control_factor
Title: Cost control factor
Units: $
Description: Cost to reduce emissions by a factor of 2.
Definition: Lognormal(30M, 1.5)
NodeLocation: 224,48,1
NodeSize: 56,24
WindState: 2,617,5,476,224
ValueState: 2,1197,371,416,303,0,STAT
Aliases: FormNode Cost_control_factor1

Text Te1458943354
NodeLocation: 788,208,-1
NodeSize: 292,200
NodeInfo: 1,0,0,1,1,1,0,,0,,0

Close Model_details

Module Uncert_analy
Title: Analysis
Description: This module performs uncertainty analysis of TXC, particularly to examine the relative importance of uncertain inputs in terms of their contribution to uncertainty in total cost.
Author: henrion
Date: Wed, Jul 18, 1990 4:47 PM
SaveAuthor: Max's
SaveDate: Thu, Aug 23, 1990 10:25 AM
DefaultSize: 44,20
NodeLocation: 216,576,1
NodeSize: 56,24
DiagState: 2,418,285,1108,447,3
NodeColor: 39321,39325,65535
FontStyle: Arial, 15
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Variable Evpi
Title: Value of  Information
Units: $/yr
Description: This node demonstrates how to perform "Value of Information" calculations, which can be useful in determining if it's worthwhile to invest in collecting further information on uncertainties.~
~
Value of Information is defined as the difference in expected cost between the decision that minimizes expected cost with current info and the optimal decision given additional information.~
~
In this case, the additional information is perfect (100% accurate) information on which Emissions Reductions strategy will actually be the most cost effective.~
~
(Min(Mean(Cost),Reduction)-Mean(Min(Cost,Reduction)))
Definition: Min(Mean(Net_benefits), Reduction) ~
- Mean(Min(Net_benefits, Reduction))
NodeLocation: 208,184,1
NodeSize: 56,24
NodeInfo: 1,1,1,1,1,1,0,,0,,0
ValueState: 2,40,50,416,303,0,MIDM
NodeFont: Geneva, 12
NumberFormat: 1,D,4,2,0,0

Variable Optimal_reduction
Title: Optimal reduction
Description: The level of emissions reduction that will maximize expected value  of net benefits.
Definition: Argmax(Mean(Net_benefits), Reduction)
NodeLocation: 208,40,1
NodeSize: 56,24
NodeInfo: 1,1,1,1,1,1,0,,0,,0
WindState: 2,88,98,629,516
ValueState: 2,620,4,368,263,1,MIDM
Aliases: FormNode Emissions_reduction1
NodeFont: Geneva, 12
NumberFormat: 1,D,4,2,0,0

Variable Importance_of_uncert
Title: Importance of uncertainties to net benefits
Description: This node demonstrates Analytica's "Importance" function.  Note how the relative importance of the variables changes with Emissions Reduction.~
~
Importance calculates the relative contribution of the uncertainty in each of the uncertain inputs to the uncertainty in the value of "Total Cost".~
The Rankcorrel function computes the rank-order correlation (see the User Guide for more info) of each input to "Total Cost", and then the Abs function computes the absolute values of those results, yielding positive relative importances.~
~
This node was created by selecting the Total Cost node with the edit tool, and then selecting "Make Importance" from the Object menu.
Definition: Abs( RankCorrel( Uncertain_inputs, Net_benefits ) )
NodeLocation: 208,112,1
NodeSize: 56,32
NodeInfo: 1,1,1,1,1,1,0,,0,,0
WindState: 2,102,89,676,540
ValueState: 2,616,5,509,429,1,MIDM
Aliases: FormNode Importance1458943496
GraphSetup: {!40000|Att_CatLineStyle Graph_Primary_Valdim:9}~
{!40000|Flip:8}
ReformVal: [Uncertain_inputs,Null]
NumberFormat: 2,%,4,2,0,0,4,0,$,0,"ABBREV",0,,,0,0
{!40000|Att_ResultSliceState: [Reduction,5,Uncertain_inputs,1]}
{!40000|Att_XRole: Uncertain_inputs}
{!40000|Att_YRole: Self}
{!40600|Att_ClusterIndex: Reduction}

Variable Uncertain_inputs
Title: Uncertain inputs
Description: A table of all the uncertain inputs to the "Total Cost" node.~
This node acts as as the input to "Total Cost Importance", and was created automatically when that node was created.
Definition: [Pop_exp,H_damage_factor,Threshhold,Base_concentration,Cost_control_factor]
NodeLocation: 80,112,1
NodeSize: 56,32
NodeInfo: 1,1,1,1,1,1,0,,0,,0
WindState: 2,575,103,590,433

Variable Benefits_and_costs
Title: Benefits and costs
Definition: [Benefits_of_lives_sa, Control_costs, Net_benefits]
IndexVals: ['Benefits of lives saved','Control~
Costs','Net benefits']
NodeLocation: 80,40,1
NodeSize: 56,24
NodeInfo: 1,1,1,1,1,1,0,,0,,0
ValueState: 2,361,3,389,444,1,MEAN
Aliases: FormNode Benefits_and_costs1
GraphSetup: {!40000|Att_GraphValueRange Benefits_and_costs:1,,,,,,5}~
ShowKey:1~
{!40000|Att_GraphIndexRange Reduction:1,0,0,1,,,5,0,0.95,0}
ReformVal: [Reduction,Self]
NumberFormat: 1,D,5,2,0,1

Text Te1458943662
NodeLocation: 680,208,-1
NodeSize: 400,200
NodeInfo: 1,0,0,1,1,1,0,,0,,0

Close Uncert_analy

FormNode Emissions_reduction
Title: Emissions~
Reduction
Definition: 0
NodeLocation: 216,192,1
NodeSize: 200,16
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 1,65535,32766
Original: Reduction

FormNode Population_exposed
Title: Population~
Exposed
Definition: 0
NodeLocation: 216,155,1
NodeSize: 200,12
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 1,49155,65535
Original: Pop_exp

FormNode Threshold
Title: Threshold
Definition: 0
NodeLocation: 216,76,1
NodeSize: 200,12
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 1,49155,65535
Original: Threshhold

FormNode Base_conc_1458942721
Title: Base~
Concentration
Definition: 0
NodeLocation: 216,52,1
NodeSize: 200,12
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 1,49155,65535
Original: Base_concentration

FormNode Statistical_value_o1
Title: Statistical Value of a Life
Definition: 0
NodeLocation: 216,220,1
NodeSize: 200,12
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 1,49155,65535
Original: Stat_value_of_life

Text Te1
Description: Input assumptions
NodeLocation: 212,128,-1
NodeSize: 204,120
NodeInfo: 1,0,0,1,1,1,1,,0,
NodeFont: Arial Black, 15

Text Te2
Description: Results
NodeLocation: 212,332,-1
NodeSize: 204,76
NodeInfo: 1,0,0,1,1,1,1,,0,,0
NodeFont: Arial Black,15

FormNode Net_benefits1
Title: Net benefits
Definition: 1
NodeLocation: 216,325,1
NodeSize: 200,13
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 65535,19661,38773
Original: Net_benefits

FormNode Benefits_and_costs1
Title: Benefits and costs
Definition: 1
NodeLocation: 216,296,1
NodeSize: 200,16
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
Original: Benefits_and_costs

FormNode Emissions_reduction1
Title: Emissions reduction to max exp value
Definition: 1
NodeLocation: 216,384,1
NodeSize: 200,16
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 19661,42599,65535
NodeFont: Geneva, 12
Original: Optimal_reduction

FormNode Health_damage_factor
Title: Health Damage Factor
Definition: 0
NodeLocation: 216,100,1
NodeSize: 200,12
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
NodeColor: 1,65535,65535
Original: H_damage_factor

FormNode Cost_control_factor1
Title: Cost control factor
Definition: 0
NodeLocation: 216,124,1
NodeSize: 200,12
NodeInfo: 1,0,0,1,0,0,0,78,0,,,
Original: Cost_control_factor

Text FRame1
NodeLocation: 752,208,-1
NodeSize: 328,200
NodeInfo: 1,0,0,1,1,1,0,,0,,0

FormNode Importance1458943496
Title: Importance of uncertainties to net benefits
Definition: 1
NodeLocation: 216,352,1
NodeSize: 200,15
NodeInfo: 1,,,,,,0,78,,,,
Original: Importance_of_uncert

Close Benefit_cost_analysi