Petroleum Industry Management

1
Petroleum Industry Management

• Cliff Bowmen
• Scott Fulton
• Gary Reynolds
• Mike Wells

2
Introduction

• Provide consulting to a petroleum company
• Advise on how to meet demands
• Motor oil
• Diesel oil
• Gasoline
• They have three plants
• Plants also output waste (paraffin)

3
Production Specifications from Each Barrel of
Crude Oil

• Factory 1
• 20 gallons motor oil
• 10 gallons diesel oil
• 5 gallons gasoline
• 3 gallons paraffin
• Factory 2
• 4 gallons motor oil
• 14 gallons diesel oil
• 5 gallons gasoline
• 5 gallons paraffin

• Factory 2
• 4 gallons motor oil
• 5 gallons diesel oil
• 12 gallons gasoline
• 2 gallons paraffin

4
System of Equations

• 20 x 4 y 4 z 5000
• 10 x 14 y 5 z 8500
• 5 x 5 y 12 z 10000

5
Barrels Needed to Meet Demand

• Conclusions
• 49 barrels needed for factory 1
• 331 barrels needed for factory 2
• 675 barrels needed for factory 3
• 1055 total barrels of oil needed to meet the
  demand
• This is an example of a unique solution

6
When Demand is Doubled

• Conclusions
• 98 barrels needed for factory 1
• 663 barrels needed for factory 2
• 1350 barrels needed for factory 3
• 2111 total barrels of oil needed to meet the
  demand
• When demand doubles the barrels of oil needed to
  meet it also doubles
• To be expected due to the fact that we have
  simply applied a scalar multiple

7
Acquiring a New Distributor

• Conclusions
• 13 barrels needed for factory 1
• 188 barrels needed for factory 2
• 250 barrels needed for factory 3
• 451 total barrels of oil needed to meet the
  demand of the new distributor
• Also an example of both a unique and consistent
  solution

8
Demand for both Distributors

• Conclusions
• 61 barrels needed for factory 1
• 519 barrels needed for factory 2
• 925 barrels needed for factory 3
• 1505 total barrels of oil needed to meet the
  demand
• Originally 1055, New Acquisition 451
• 1055 451 1506
• They add up correctly (not including rounding
  errors)

9
Sensitivity and Robustness

• Constants are rarely ever exactly equal to their
  stated value
• We measured averages over a period of time
• Now we will explore small changes

10
Sensitivity Analysis

• We select any three coefficient one at a time
• For each case, we note what effect this has on
  the solution, as a percentage change
• If there is little change then the system is
  deemed robust

11
Sensitivity Analysis

• In all three cases a 3 change in one coefficient
  causes less than a 3 change in the resulting
  product
• We can conclude that the system is robust

12
Plant Off-Line

• Factory 3 is shut down by the EPA temporarily
  for excessive emissions into the atmosphere
• Demand does not change
• Our new same system of equations

13
Factory 3 Off-Line

• Corresponding System of Linear Equations
• 1 x  0 
• 1 y 0 
• 0 1 

• Conclusions
• System of Equations cannot be solved
• Inconsistent system
• A surplus of one product would have to be
  produced to meet the demand of all three products

14
Overdetermined System

• The previous was an example of an overdetermined
  system of equations
• More equations than unknowns
• The overdetermined case occurs when the system
  has been overconstrained
• The number of equations outnumbers the number of
  the unknowns

15
Adding a Fourth Plant

• CEO is considering buying another plant,
  identical to the third, and use it permanently
• Our system of equations for all 4 on-line

16
New Production

• Conclusions
• 49 barrels needed for factory 1
• 331 barrels needed for factory 2
• No equation of this system has a form zero
  nonzero Therefore, the system is consistent.
• The system has infinitely many solutions
  (underdetermined)
• x1 195/4
• x2 1325/4
• x3 -1 x4675
• x4 arbitrary
• Adding the fourth plant has increased flexibility
  and thus robustness

17
Supplying Paraffin
Here we have chosen factories 3 and 4 to produce
equally
18
Shutting Down Plant 1

• Conclusions
• Equation 3 cannot be solved with the current
  demand, therefore, the system has no solution
  (i.e. the system is inconsistent).

19
With only Plants 2 and 3

• Conclusions
• Equation 3 cannot be solved, therefore, the
  system has no solution (i.e. the system is
  inconsistent).

20
Demands that Can be Met

• Applying any integer values x and y to this
  system of linear equations would give possible
  demand to be met with just factories 2 and 3
• Example x 100, y 200
• 4(100) 4(200) 400 800 1200 gallons motor
  oil
• 14(100) 5(200) 1400 1000 2400 gallons
  diesel oil
• 5(100) 12(200) 500 2400 2900 gallons
  gasoline