Use the following decision tree, but update the probabilities as follows: Probab
ID: 387336 • Letter: U
Question
Use the following decision tree, but update the probabilities as follows:
Probability of Small Demand = 29%
Probability of Medium Demand = 36%
Probability of Large Demand = remaining probability
What is the expected monetary value of the best decision (in millions)?
Probability of Small Demand = 40%
Probability of Medium Demand = 26%
Probability of Large Demand = remaining probability
What is the expected value with perfect information (in millions)?
$1.0 hing $1.3 Do n xpand $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 $2.4 hing ge de Do n Expand 8 hing Do n Other use #1 r use #2 Expand Medium demand (.5) thing Do Subcontract Build nothing Do Other use #1 Sma r use #2 di hing Do Other use #1 r use #2 Net present value in millionsExplanation / Answer
Using the following decision tree, but update the probabilities as follows:
Probability of Small Demand = 29%
Probability of Medium Demand = 36%
Probability of Large Demand = 1 - 29% - 36% = 35%
Expected Monetary Value of Subcontract = 0.29*1+0.36*1.3+0.35*MAX(1.5,1.6,1.8) = 1.388
Expected Monetary Value of Expand = 0.29*MAX(0.7,1.5,1)+0.36*1.6+0.35*MAX(1.6,1.5,1.7) = 1.606
Expected Monetary Value of Build = 0.29*MAX(-0.9,1.4,1)+0.36*MAX(1,1.1,0.9)+0.35*2.4 = 1.642
EMV of Buils is the maximum.
Expected monetary value of the best decision (in millions) = 1.642
____________________________________________
Probability of Small Demand = 40%
Probability of Medium Demand = 26%
Probability of Large Demand = 1 - 40% - 26% = 34%
Expected Monetary Value of Subcontract = 0.40*1+0.26*1.3+0.34*MAX(1.5,1.6,1.8) = 1.35
Expected Monetary Value of Expand = 0.40*MAX(0.7,1.5,1)+0.26*1.6+0.34*MAX(1.6,1.5,1.7) = 1.594
Expected Monetary Value of Build = 0.40*MAX(-0.9,1.4,1)+0.26*MAX(1,1.1,0.9)+0.34*2.4 = 1.662
Max EMV or EV(w/o)PI = MAX(1.35,1.594,1.662) = 1.662
Expected Value WITH Perfect Information (EVwPI) = 0.40*1.5+0.26*1.6+0.34*2.4 = 1.832
Expected Value OF Perfect Information EVPI = EVwPI - EV(w/o)PI = 1.832 - 1.662 = 0.17
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