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Hillier and Lieberman: the Goferbroke Company drill-or-sell decision with a seismic survey

ToolDecision Analysis
SourceHillier, F. S., and Lieberman, G. J. (2015). Introduction to Operations Research, 10th ed. McGraw-Hill, New York. Sections 16.2–16.4, Table 16.2, Figure 16.4.
LevelUndergraduate

Problem

Goferbroke owns land that may hold oil (prior 0.25) or be dry (0.75). Drilling pays 700 if oil is found and −100 if dry (thousands of dollars); selling the land pays 90 either way. A seismic survey costing 30 gives a favourable reading with probability 0.6 if oil and 0.2 if dry. Which decision each criterion recommends, what perfect information is worth, how the survey changes the probabilities, what the survey is worth and at what prior the decision flips.

Inputs to Enter

  • Payoff table: Oil Dry / 0.25 0.75 / Drill 700 -100 / Sell 90 90 (loaded by default, unit $1,000s)
  • Likelihood table: FSS USS / Oil 0.6 0.4 / Dry 0.2 0.8; test cost 30
  • Hurwicz α 0.5
Open the Decision Analysis tool (loaded with this example)

Answers

  • Maximax Drill (700), maximin Sell (90), maximum likelihood Sell, Bayes EMV Drill 100 against Sell 90, minimax regret Drill (190 against 610)
  • EV with perfect information 242.5, EVPI = 142.5
  • P(FSS) = 0.3, P(USS) = 0.7; posteriors P(Oil | FSS) = 0.5, P(Oil | USS) = 1/7
  • FSS → Drill (EMV 300), USS → Sell (90); expected payoff with the survey 153, EVSI = 53, efficiency 53/142.5 = 37 %, net of the cost 23 → do the survey
  • Rolled-back tree: root 123 (Fig. 16.4), survey branch 123 against no-survey 100; crossover prior Drill = Sell at 190/800 = 0.2375

Notes

The tool's default inputs are this example; press Submit. With a risk tolerance R = 1,000 the exponential utility gives a certainty equivalent of 48.1 for Drill, so the risk-averse choice is Sell (hand check in the test script).

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