Use the following decision tree, but update the probabilities as follows Probabi
ID: 3375416 • Letter: U
Question
Use the following decision tree, but update the probabilities as follows Probability of Small Demand 11% Probability of Medium Demand 35% Probability of Large Demand- remaining probability What is the expected value with perfect information (in millions)? $1.0* $1.3 Do nothing Medium demand (.5) Large demand (.1) Expand $1.3 $1.5 $1.6 $1.8 $0.7 $1.5 $1.0 $1.6 $1.6 $1.5 $1.7 ($0.9) $1.4 $1.0 $1.0 $1.1 $0.9 Do nothing Expand Build Do nothing Other use #1 Other use #2 Small demand (.4) Expand Medium demand (.5) Large demand (.1) Do nothing Subcontract Build Do nothing Other use #1 Other use #2 Small demand (.4) Medium demand (.5) Do nothing Other use #1 Other use #2 *Net present value in millions $2.4Explanation / Answer
Solution
A. Decision: Build
Small demand, max pay-off decision: Other use # 1 with pay-off = 1.4 and probability 0.11
Medium demand, max pay-off decision: Other use # 1 with pay-off = 1.1 and probability 0.35
Large demand, only option with pay-off = 2.4 and probability 0.54
So, EMV = (1.4 x 0.11) + (1.1 x 0.35) + (2.4 x 0.54) = 0.154 + 0.385 + 1.296 = 1.835
B. Decision: Expand
Small demand, max pay-off decision: Other use # 1 with pay-off = 1.5 and probability 0.11
Medium demand, only option with pay-off = 1.6 and probability 0.35
Large demand, max pay-off decision: Build with pay-off = 1.7 and probability 0.54
So, EMV = (1.5 x 0.11) + (1.6 x 0.35) + (1.7 x 0.54) = 0.165 + 0.56 + 0.918 = 1.643
C. Decision: Sub-contract
Small demand, only option with pay-off = 1.0 and probability 0.11
Medium demand, max pay-off decision: Build/Do Nothing with pay-off = 1.3 and probability 0.35
Large demand, max pay-off decision: Build with pay-off = 1.8 and probability 0.54
So, EMV = (1.0 x 0.11) + (1.3 x 0.35) + (1.8 x 0.54) = 0.11 + 0.455 + 0.972 = 1.537
Since of the three EMV’s, 1.835 is the maximum, optimal decision is: Build ANSWER
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.