Unformatted text preview: SCENARIO GENERATION
SCENARIO Prof. Miguel Bagajewicz
CHE 4273 SCENARIO GENERATION
Consider each parameter’s probability distribution. Discretize it.
Discretize
Option 1: pick values of
probabilities. For example, for
3 values, pick 25%, 50% and
25% probability and find the
values. Use the cumulative
curve to locate the numbers. P(θ) θ1 θ2 θ3 θ4 θ5 θ SCENARIO GENERATION
Consider each parameter’s probability distribution. Discretize it.
Discretize
Option 2: pick values
pick
(equidistantly or randomly)
and find the probability that
corresponds to them from the
area they “span”. Use the
cumulative curve for this. P(θ) θ1 θ2 θ3 θ4 θ5 θ SCENARIO GENERATION
Consider each parameter’s probability distribution. Discretize it.
Discretize
Option 3: pick equal probability
values and find parameter
values. For example, for 3
values, pick 33% and locate the
points. Use the cumulative curve
to do this. P(θ) θ1 θ2 θ3 θ4 θ5 θ FOR A LARGE NUMBER OF
SAMPLES WE USE THIS OPTION (It is the easiest and it is equivalent to the other two) SCENARIO GENERATION
Each scenario is constructed by picking
Each
one realization for each parameter. EXAMPLE:
EXAMPLE:
2 parameters (θ1, θ2). If each parameter
is discretized in three instances
(θi,low, 25%, θi,avg 50%, θi,hig 25%) SCENARIO GENERATION
Scenario
Scenario Probability Scenario Probability
θ1,low, θ2,low
6.25%
θ1,hig, θ2,low
6.25%
6.25%
6.25%
θ1,low, θ2,avg
12.5%
θ1,hig, θ2,avg
12.5%
12.5%
12.5%
θ1,low, θ2,hig
6.25%
θ1,hig, θ2,hig
6.25%
6.25%
6.25%
θ1,avg, θ2,low
12.5%
12.5%
θ1,avg, θ2,avg
25.0%
SUM OF ALL
25.0%
θ1,avg, θ2,hig
12.5%
PROBABILITIES=1
12.5% SCENARIO GENERATION
Effect of Small Number of Samples
Effect
1.2
SAMPLING 1 ACTUAL 20 Scenarios 0.8
0.6
0.4
0.2
0
75 85 95 105 115 125
1.2
SAMPLING 1 ACTUAL 0.8 500 Scenarios 0.6
0.4
0.2
0
75 85 95 105 115 125 SCENARIO GENERATION
Effect of the Number of Samples on Results (Gas in Asia)
Effect
1.0 1s
4.666 0.8 10s
4.357
100s
4.565 0.6 200s
4.678 0.4 50s
4.793 0.2 0.0
0 1 2 3 4 5 6 7 8 9 10 ...
View
Full Document
 Spring '10
 staff
 Chemical Engineering, Probability, Probability distribution, SCENARIO GENERATION, Prof. Miguel Bagajewicz

Click to edit the document details