For the decision tree

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For the decision tree in Figure 12.13, assume Chance Events E and F are independent.

a. Draw the appropriate decision tree and calculate the EVPI for Chance Event E only.

b. Draw the appropriate decision tree and calculate the EVPI for Chance Event F only.

c. Draw the appropriate decision tree and calculate the EVPI for both Chance Events E and F: that is, perfect information for both E and F is available before a decision is made

The Correct Answer and Explanation is :

To determine the Expected Value of Perfect Information (EVPI) for Chance Events E and F in the decision tree, we follow these steps:

a. EVPI for Chance Event E Only

  1. Expected Monetary Value (EMV) without Perfect Information:
  • Decision A:
    • Outcomes:
    • 0.1 probability of 20
    • 0.2 probability of 10
    • 0.6 probability of 0
    • 0.1 probability of -10
    • EMV(A) = (0.1 × 20) + (0.2 × 10) + (0.6 × 0) + (0.1 × -10) = 2 + 2 + 0 – 1 = 3
  • Decision B:
    • Outcomes:
    • 0.7 probability of 5
    • 0.3 probability of 1
    • EMV(B) = (0.7 × 5) + (0.3 × 1) = 3.5 + 0.3 = 3.8
  • Optimal decision without perfect information: Decision B with EMV = 3.8
  1. Expected Value with Perfect Information about E (EVwPI):
  • With perfect information on E, choose the decision with the highest payoff for each outcome of E.
  • If E = 20:
    • Choose A (since 20 > 5)
  • If E = 10:
    • Choose A (since 10 > 5)
  • If E = 0:
    • Choose B (since 5 > 0)
  • If E = -10:
    • Choose B (since 5 > -10)
  • EVwPI = (0.1 × 20) + (0.2 × 10) + (0.6 × 5) + (0.1 × 5) = 2 + 2 + 3 + 0.5 = 7.5
  1. EVPI for E:
  • EVPI(E) = EVwPI – EMV(B) = 7.5 – 3.8 = 3.7

b. EVPI for Chance Event F Only

  1. Expected Monetary Value (EMV) without Perfect Information:
  • As calculated above, EMV(A) = 3 and EMV(B) = 3.8
  • Optimal decision without perfect information: Decision B with EMV = 3.8
  1. Expected Value with Perfect Information about F (EVwPI):
  • With perfect information on F, choose the decision with the highest payoff for each outcome of F.
  • If F = 5:
    • Choose B (since 5 > 20, 10, 0, -10)
  • If F = 1:
    • Choose B (since 1 > 20, 10, 0, -10)
  • EVwPI = (0.7 × 5) + (0.3 × 1) = 3.5 + 0.3 = 3.8
  1. EVPI for F:
  • EVPI(F) = EVwPI – EMV(B) = 3.8 – 3.8 = 0

c. EVPI for Both Chance Events E and F

  1. Expected Value with Perfect Information about Both E and F (EVwPI):
  • With perfect information on both E and F, choose the decision with the highest payoff for each combination of E and F outcomes.
  • Combinations:
    • E = 20, F = 5: Choose A (20 > 5)
    • E = 20, F = 1: Choose A (20 > 1)
    • E = 10, F = 5: Choose A (10 > 5)
    • E = 10, F = 1: Choose A (10 > 1)
    • E = 0, F = 5: Choose B (5 > 0)
    • E = 0, F = 1: Choose B (5 > 0)
    • E = -10, F = 5: Choose B (5 > -10)
    • E = -10, F = 1: Choose B (5 > -10)
  • Probabilities:
    • P(E = 20) = 0.1
    • P(E = 10) = 0.2
    • P(E = 0) = 0.6
    • P(E = -10) = 0.1
    • P(F = 5) = 0.7
    • P(F = 1) = 0.3
  • Joint Probabilities (since E and F are independent):
    • P(E = 20 and F = 5) = 0.1 × 0.7 = 0.07
    • P

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