Two Stage Modeling-Sampling

# Two Stage Modeling-Sampling - SCENARIO GENERATION SCENARIO...

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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 ...
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