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John Jarvis, Claudia Johnson & Liana Vetter
May 6, 2004
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Description of Problem
• Quest’s current gas marketing– Oneok is sole purchaser
• 85% guaranteed monthly• The remainder sold daily
– Pipeline serves as middleman
• Goal of the project– Analyze the market trends and forecasting
accuracy of Quest– Determine what percentage is optimal to
guarantee on contract– Create optimization model Quest can use
monthly
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Variables Considered
• Two different sale points– R&H: large and unstable
– Housel: small and unstable
• Historical data – Forecasted daily production by sale point (2004)
– Actual daily production by sale point (2004)
– Daily NYMEX prices (2002-2004)
• Limits to set– Maximum days and amount in debt
– Bounds on percentage to guarantee
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Limits to Set
• Maximum days and amount in debt– Set limit of 2 days in debt based on 2004 data
– Set limit of 10% of production in debt
– Conservative limits to minimize risk in case of unexpected changes in production
• Bounds on percentage to guarantee– Set upper limit as 95%, highest Quest has used
– Set lower limit as 30% to protect against sharp decrease in production
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Market 2002-2004Market Variability
0
1
2
-0.38 -0.13 -0.03 0.02 0.07 0.16 0.26
Percent Market Change
Fre
qu
en
cy
Falling
Rising
Probability Average percent changeFalling 0.44 -0.055751Rising 0.56 0.096644
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R&H Production 2004
RH Probability Average relative errorOver 0.51 1.073852Equal 0.27 1Under 0.22 0.900982
R&H Production Variability
0
2
4
6
8
10
0.57 0.83 0.9 0.95 0.98 1.01 1.04 1.07 1.1 1.14 1.17
Relative Error on Forecast
Fre
qu
en
cy
Under
Equal
Over
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Non-Stochastic Model• In 5-day test case, user provides data:
• Model returns output:
• Revenue: $1,002
Day 1 2 3 4 5 Production 130 90 80 110 100 Daily price $1.50 $3.00 $1.75 $2.10 $1.00 Monthly price $2.00
Day 1 2 3 4 5 Monthly guarantee 90 90 90 90 90 Daily sales 40 0 0 20 0 Total sales 130 90 90 110 90 Debt 0 0 10 10 0
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Stochastic Model• Benefits of stochastic modeling
– Incorporates uncertainty using probabilities of different scenarios– Calculates expected revenue based on market forecasts– Approximates actual production from forecast given
• Example case– User provides data:
– Model returns output:
– Expected revenue: $1,039
Probability market rises 0.8 Probability market falls 0.2 Price at beginning of month 2 Forecasted daily production 100
Monthly guarantee 30 Approximate daily sales 71 Expected Production 102
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Stochastic Model with Regret• Regret – difference between optimal revenue and actual
revenue• Benefits of regret
– Solution does well in rising and falling market– Less sensitive to predicted probabilities
• Example case– User provided data:
– Model returns output:
– Expected revenue: $1,037
Probability market rises 0.8 Probability market falls 0.2 Price at beginning of month 2 Forecasted daily production 100
Monthly guarantee 39 Approximate daily sales 63 Expected Production 102
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Sensitivity Analysis• Optimal monthly guarantee varies little when expected
production data changes
• Model is more sensitive to changes in market data
R&H Market Sensivility
0
500
1000
1500
2000
2500
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability of Rising Market
Op
tim
al
Mo
nth
ly
Gu
ara
nte
e
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Problems and Limitations
• Problems encountered– Limited historical data
– Multiple daily gas prices (strip price used)
– Large variability of the gas market
– Difference in production records from meter inconsistency
• Limitations of the solution – Dependant on the market which is unpredictable
– Stochastic variables are based on limited data
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Analysis and Recommendation
• 50-55% should be guaranteed monthly if no market predictions added from Quest
• Consequences of guaranteeing 50-55%– $18,000 additional revenue from January – March
2004 for R&H– $2,400 additional revenue from January – March
2004 for Housel
• Regret model yields less additional profit than stochastic model but provides more consistency between months
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Interface
• Questions asked by interface– Probability the market will rise– Sale point– Month to forecast, days in month– Expected initial NYMEX price– Forecasted daily production– Expected beginning debt
• Results of interface– Creates data file for AMPL– Data file can be run with regret model to resolve
each month