Two Stage Modeling-Regret and Bounding
Transcript of Two Stage Modeling-Regret and Bounding
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REGRET ANALYIS AND BOUNDINGREGRET ANALYIS AND BOUNDINGREGRET ANALYIS AND BOUNDING
Prof. Miguel Bagajewicz
CHE 4273
Prof. Miguel Bagajewicz Prof. Miguel Bagajewicz
CHE 4273 CHE 4273
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MINIMAX REGRET ANALYSISMINIMAX REGRET ANALYSIS
Motivating Example
s1High
s2Medium
s3Low Average
A 19 14 -3 10
B 16 7 4 9
C 20 8 -4 8
D 10 6 5 7
Max 20(C) 14(A) 5(D) 10(A)
-5
0
5
10
15
20
1 2 3
$ M i l l i o n
s 1 s 2 s 3
C
B D
Traditional wayMaximize Average …select A
Optimistic decision makerMaxiMax … select C
Pessimistic decision makerMaxiMmin … select D
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TwoTwo --Stage Stochastic Programming Using RegretStage Stochastic Programming Using RegretTheoryTheory
s1 s2 s3 s4 s5 ENPV Max Mind1 19.01 10.38 10.57 15.48 10.66 13.22 19.01 10.38d2 11.15 14.47 8.87 20.54 10.58 13.12 20.54 8.87d3 12.75 7.81 16.02 22.25 9.16 13.60 22.25 7.81d4 5.41 9.91 12.63 32.02 8.08 13.61 32.02 5.41d5 15.09 7.40 8.81 12.48 15.05 11.77 15.09 7.40Max 19.01 14.47 16.02 32.02 15.05 13.61 32.02 10.38
NPV
s1 s2 s3 s4 s5 Maxd1 0.00 4.09 5.45 16.54 4.39 16.54d2 7.86 0.00 7.15 11.48 4.47 11.48d3 6.26 6.66 0.00 9.77 5.89 9.77d4 13.60 4.56 3.39 0.00 6.97 13.60d5 3.92 7.07 7.21 19.54 0.00 19.54
9.77
Regret
Min
MINIMAX REGRET ANALYSISMINIMAX REGRET ANALYSIS
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SAMPLING ALGORITHMSAMPLING ALGORITHM
d=1
Generateh(s)
h=h(d)
SolveDeterministic
Model
Fix First-StageVariables
s=1
h=h(s)
SolveDeterministic
Model
Store NPV(d,s)
s
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UPPER AND LOWER BOUNDSUPPER AND LOWER BOUNDS
This is very useful because it allows nice decomposition,
That is, there is no need to solve the full stochastic problem
0
0.2
0.4
0.6
0.8
1
0.0 2.0 4.0 6.0 8.0 10.0
Risk
UpperBound
LowerBound
C
D
B
A
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UPPER AND LOWER BOUNDSUPPER AND LOWER BOUNDS
Example: Gas Commercialization in Asia
0.0
0.2
0.4
0.6
0.8
1.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
Indo-GTL
Ships: 6 & 3ENPV:4.63
Mala-GTLShips: 4 & 3ENPV:4.540
Upper EnvelopeENPV:4.921
Lower Envelope-2ENPV:4.328
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UPSIDE POTENTIAL UPSIDE POTENTIAL
0.0
0.1
0.2
0.3
0.4
0.50.6
0.7
0.8
0.9
1.0
0 1 2 3 4 5 6 7 8 9 10 Profit
Risk
E ( P r o
i t ) =
3 . 4
VaR =1.75
OV =3.075
E ( P r o
i t ) =
3 . 0
VaR =0.75
OV =0.75
Point measure for the upside
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AREA RATIOAREA RATIO
0.0
0.10.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1 2 3 4 5 6 7 8 9 10 NPV
Risk
O_Area
R_Area
Risk(x 1,NPV)
Risk(x 2,NPV)
ENPV 1ENPV 2
Comparison measure
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Utility FunctionsUtility Functions
A Risk Averse Decision Maker values more low profits than large ones
Money does not always have the same value for a company Money does not always have the same value for a company
UTILITY THEORYUTILITY THEORY
A Risk Taker values more high profits
Real Value
Utility Value
Real Value
Utility Value
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Use Utility Value instead of real profit for evaluationUse Utility Value instead of real profit for evaluation
Effect on Risk Curves Effect on Risk Curves
UTILITY THEORYUTILITY THEORY
455
555
655
755
855
955
455 555 655 755 855
Risk Averse Utility
Risk Taker's Utility
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
400 500 600 700 800 900 1000
Risk Averse View
Risk Taker's View
Original Risk Curve
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