two stage modeling-regret and bounding

8/20/2019 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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two stage modeling-regret and bounding

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