Oil Drilling Problem

CHAPTER 12: VALUE OF INFORMATION

INTRODUCTION

 information can help us make better decisions

 information alternatives

- consult experts

- perform math/stat analyses

- conduct surveys

- read books, journals, or articles

 DA offers methodology to assess the value of information

Illustrative Example: Wildcat Oil Drilling Problem

Reference:

Raiffa, Howard, Decision Analysis: Introductory Lectures on Choice under Uncertainty, Addison-Wesley, Reading, Massachusetts, 1968, pp. 34-36, pp. 47-50

Part I: (pp. 34-36)

 The drilling cost is fixed at $70k.

 Profit data :

State Profit ($k) Dry 0 Wet 120 Soaking 270  Cost to determine the seismic structure is $10k 2

 Joint and marginal probabilities.

Seismic Outcome State No Structure Open Closed Marginal Structure Structure Probability Dry .3 .15 .05 .5 Wet .09 .12 .09 .3 Soaking .02 .08 .1 .2 Marginal probability .41 .35 .24 1.0

 Draw the influence diagram and decision tree.

 What is the best strategy without the seismic test?

 What is the optimal strategy with the seismic test?

 What is the expected value of seismic information?

Wildcat Oil, Part I

Seismic Green Structure Oil

Drill? Blue

Seismic Blue Test? Profit

Drilling Cost 3

Seismic Structure Oil Drill?

Seismic None Dry Test? Yes Profit Yes Open Wet a No Profit Closed Soaking Profit

Dry [-80] Oil .732 -80 Yes [-40.5] Wet [40] Drill_ .220 40 None [-10] Soaking [190] .410 .049 190 Oil No [-10]

Dry [-80] Oil .429 -80 Yes [22.9] Wet [40] Seismic_Structure Drill_ .343 40 Yes [22.5] Open [22.9] Soaking [190] .350 .229 190 Oil Seismic_Test_ No [-10] [22.5] Dry [-80] Oil .208 -80 Yes [77.5] Wet [40] Drill_ .375 40 Closed [77.5] Soaking [190] .240 .417 190 Oil No [-10]

Dry [-70] Oil .500 -70 Yes [20] Wet [50] Drill_ .300 50 No [20] Soaking [200] .200 200 Oil No [0] 4

Cummulative Distribution Function (Part I)

Seismic_Test_:

-75 -50 -25 0 25 50 75 100 125 150 175 200

Part II. Perfect Information:

EXPECTED VALUE OF PERFECT INFORMATION, EVPI

 perfect information is always correct

 EVPI allows us to put an upper bound on how much we would pay for any information

Wildcat Oil, Part II (Perfect Information)

Blue Drill? Profit

Drilling Cost 5

Drill_ Yes [-70] Dry [0] -70 .500 No [0] 0 Oil Drill_ Yes [50] [55] Wet [50] 50 .300 No [0] 0 Drill_ Yes [200] Soaking [200] 200 .200 No [0] 0

Part III: (p. 47)

 The drilling cost is uncertain.

State Probability Drilling Cost ($k) Low 0.2 40 Medium 0.7 50 High 0.1 70

 What is the new expected value? Why might an expert have given an analyst the previous value of $70k?

 Draw the new influence diagram and decision tree.

Wildcat Oil, Part III (Uncertain Drilling Cost)

Seismic Green Structure Oil

Drill? Blue

Drilling Cost 6

Seismic Drilling Structure Oil Cost Drill?

Seismic None Dry Low Test? Yes Profit Yes Open Wet Medium a No Profit Closed Soaking HIgh Profit

Low [-50] Drilling_Cost .200 -50 Dry [-60] Medium [-60] .732 .700 -60 HIgh [-80] .100 -80 Low [70] Oil Drilling_Cost .200 70 Yes [-20.5] Wet [60] Medium [60] Drill_ .220 .700 60 None [-10] HIgh [40] .410 .100 40 Low [220] Drilling_Cost .200 220 Soaking [210] Medium [210] Seismic_Structure .049 .700 210 Yes [34.3] HIgh [190] .100 190 Oil No [-10]

Oil Yes [42.9] Drill_ Open [42.9] Oil .350 Seismic_Test_ No [-10] [40] Oil Yes [97.5] Drill_ Closed [97.5] Oil .240 No [-10]

Low [-40] Drilling_Cost .200 -40 Dry [-50] Medium [-50] .500 .700 -50 HIgh [-70] .100 -70 Low [80] Oil Drilling_Cost .200 80 Yes [40] Wet [70] Medium [70] Drill_ .300 .700 70 No [40] HIgh [50] .100 50 Low [230] Drilling_Cost .200 230 Soaking [220] Medium [220] .200 .700 220 HIgh [200] .100 200 Oil No [0] 7

Cummulative Distribution Function

Seism ic_Test_:

-50 0 50 100 150 200

 Next, we do a Rainbow Diagram on the cost of the Seismic Test

42.5 e

u 42.0 l a V

41.5 e t c e p x

41.0 E

0 1 2 3 4 5 6 7 8 9 10 11

Seismic_Test_

 How do we interpret the Rainbow Diagram?

 What is the expected value with perfect information on oil? 8

 How did I change the decision tree? What changes did I have to make to the influence diagram?

Seismic Drilling Structure Oil Cost Drill?

Seismic None Dry Low Test? Yes Profit Yes Open Wet Medium a No Profit Closed Soaking HIgh Profit

Seismic_Structure Yes [55]

Drilling_Cost Yes [-50] Drill_ Dry [0] Drilling_Cost .500 No [0]

Seismic_Test_ Drilling_Cost [65] Yes [70] Oil Drill_ No [65] Wet [70] Drilling_Cost .300 No [0]

Drilling_Cost Yes [220] Drill_ Soaking [220] Drilling_Cost .200 No [0]

EV of PI[Oil]= $65k - $40k = $25k

 What is the expected value with perfect information on drilling cost? $40k

 How do I modify the ID and DT? 9

EV of PI[Drilling Cost]=$40k - $40k = 0

 What is the expected value with perfect information on both oil and drilling cost? $65k

 How do I modify the ID and DT?

Seismic Drilling Structure Cost Oil Drill?

Seismic None Low Dry Test? Yes Yes Open Medium Wet Profit a No Closed HIgh Soaking Profit

EV of PI[Oil & Drilling Cost]= $65k - $40k = $25k

Part IV: The first seismic test accurately discloses the true seismic structure. A less expensive test ($3k) will indicate the subsurface structure, but will be wrong part of the time. What is the EVPI of the imperfect test?

 Here’s the probability data.

State\Test “No “Open “Closed Structure” Structure” Structure” No Structure 0.9 0.1 0.0 Open 0.2 0.7 0.1 Structure Closed 0.1 0.3 0.6 Structure

 Explain the data. What type of distribution is it?

 Draw the influence diagram and the decision tree. 10

Wildcat Oil, Part IV (Second Seismic Test)

Green Seismic Green Structure Estimated Oil Seismic Structure Drill? Blue

Drilling Cost

 Here’s how we enter the likelihood data:

NS Estimated_Seismic_Structure 0.9 None OS 0.1 CS 0 NS Seismic_Structure Estimated_Seismic_Structure 0.2 Open OS 0.7 CS 0.1 NS Estimated_Seismic_Structure 0.1 Closed OS 0.3 CS 0.6

Seismic Drilling Estimated Structure Oil Cost Seismic Drill? Seismic Structure Test? NS None Dry Low Yes Profit Yes OS Open Wet Medium a No Profit CS Closed Soaking HIgh Profit

No a 11

Drilling_Cost Dry [-53] .732 Oil Drilling_Cost None [-13.5] Wet [67] .797 .220 Drilling_Cost Soaking [217] .049 Drilling_Cost Dry [-53] .429 Seismic_Structure Oil Drilling_Cost Yes [2.21] Open [49.9] Wet [67] Drill_ .151 .343 NS [2.21] Drilling_Cost .463 Soaking [217] .229 Drilling_Cost Dry [-53] Estimated_Seismic_Structure .208 Yes [37] Oil Drilling_Cost Closed [105] Wet [67] Seismic_Test_ .052 .375 [40] Drilling_Cost Soaking [217] .417 Seismic_Structure No [-3]

Seismic_Structure Yes [53.6] Drill_ OS [53.6] Seismic_Structure .358 No [-3]

Seismic_Structure Yes [93.8] Drill_ CS [93.8] Seismic_Structure .179 No [-3]

Seismic_Structure Yes [40] Drill_ No [40] Seismic_Structure No [0]

Seismic_Test_:

-50 0 50 100 150 200 12

 Next, we do a Rainbow Diagram on the cost of the Imperfect Seismic Test

42 e u l 40 a V

e 38 t c e p x

0 0 .5 1 1.5 2 2 .5 3 3.5 4

Seism ic_ Tes t_

 How do we interpret these results?

Part V. Here is another decision tree that gives the same answers for the three alternatives. This tree uses GET and PAY to assign values to each node.

 What are the benefits of this approach?

WILDCAT OIL DRILLING PROBLEM

Drilling Amount Drill Costs of Oil Low Dry Drilling_Costs Revenues Yes Med Wet None Drilling_Costs Revenues a No Test High Soaking Drilling_Costs Revenues Seismic No Structure Test Core Sample Open a Test Closed Exp Seismic No Test Exp Seismic Open a Test Closed 13

CASE SUMMARIES

Case Uncertainties Expected Optimal Decision Policy Value ($k) I.A. Basic problem Oil 20 Drill with fixed drilling cost I.B. Problem 1A plus Oil 22.5 Seismic Test: Yes seismic test Seismic Structure SS = None: Don't Drill SS= Open/Closed: Drill II. Perfect Information Oil 55 Dry: Don't Drill on Oil Wet/Soaking: Drill III.A. Basic problem Oil 40 Drill with uncertain drilling Drilling Cost cost III.B. Problem III.A. Oil 34.3 SS = None: Don't Drill plus seismic test Drilling Cost SS= Open/Closed: Drill Seismic Structure III. C. Perfect Oil 65 Dry: Don't Drill Information on Oil Drilling Cost Wet/Soaking: Drill Seismic Structure III. D. Perfect Oil 40 Drill Information on Drilling Drilling Cost Cost Seismic Structure III. D. Perfect Oil 65 Dry: Don't Drill Information on Oil and Drilling Cost Wet/Soaking: Drill Drilling Cost Seismic Structure IV. Estimated Seismic Oil 37 Drill Structure Drilling Cost Seismic Structure Estimated Seismic Structure

QUESTIONS: 14

1. What caused the seismic test to part of the optimal policy strategy in Problem I and not in Problem III?

2. What is the value of sample information for the above cases?

IMPORTANT DISTINCTION

 Expected value with and expected value of

- EV with PI[X] = Expected Value with PI on random variable X

- EV of PI[X] = Expected value of PI on random variable X compared to the EV without PI on X

- EV with SI[X] = Expected Value with SI on random variable X

- EV of SI[X] = Expected value of SI on random variable X compared to the EV without SI on X

 Both EV of PI and EV of SI are relative to our current state of information

VALUE OF INFORMATION PRINCIPLES

 INFORMATION HAS VALUE ONLY IF IT CHANGES THE OPTIMAL DECISION POLICY

 YOU CAN NEVER BE WORSE OFF WITH MORE (FREE) INFORMATION; BUT, ADDITIONAL INFORMATION MAY HAVE NO VALUE.

 THE EXPECTED VALUE OF PERFECT INFORMATION PROVIDES AN UPPER BOUND ON THE AMOUNT YOU SHOULD PAY FOR INFORMATION 15

CONCLUDING NOTE

 Our final decision problem had four uncertainties

- seismic structure

- estimated seismic structure

- drilling

 Which nodes directly impact the value node?

 Which nodes represent information that is probabilistically dependent with the nodes that impact the value node?

 Which nodes provide imperfect information about oil?

 Which nodes provide imperfect information about seismic structure?

 Value of Information should be calculated for ALL combinations of uncertain nodes.

- Not possible for very large problems