John Jarvis, Claudia Johnson & Liana Vetter

May 6, 2004

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

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

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

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

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

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

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

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

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

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

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

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