# Step-by-Step Solution to Assignment #38 ```Step-by-Step Exercises on Decision Making under Risk
- EMV and EVPI BSNS2120, J. Wang
Name __Jinchang Wang___
A payoff table is given as below.
States of Nature
A
B
C
Alternatives P(A)=0.7 P(B)=0.1 P(C)=0.2
1
120
-100
60
2
90
100
70
3
80
100
80
4
-50
80
90
Show your calculations in Part 1 and Part 2.
Part 1. What is the best decision? – Do the two steps below.
Step 1. Calculate EMV (expected payoff) of each alternative:
EMV(Alt. 1) = 120*0.7 + (-100)*0.1 + 60*0.2 = 84 +(-10) + 12 = 86
EMV(Alt. 2) = 90*0.7 + 100*0.1 +70*0.2 = 63 + 10 +14 = 87*
EMV(Alt. 3) = 80*0.7 + 100*0.1 + 80*0.2 = 56 +10 +16 = 82
EMV(Alt. 4) = (-50)*0.7 + 80*0.1 + 90*0.2 = -35 +8 +18 = -9
Step 2. Pick up the alternative with highest EMV, which is _alternative 2_ .
The best decision is selecting Alternative _2_ whose expected payoff is _87_.
Part 2. What is EVPI (expected value of perfect information) ? – Do the three steps below.
Note: EVPI = (EV with PI)  (EV without PI)
Step 1.
EV without PI = Expected payoff of your decision without using additional PI
Alternative _2_ ,
EMV of the decision: _87______ .
Therefore,
EV without PI = Max EMV = 87.
Step 2.
Calculate (EV with PI).
If PI says ‘A will occur’, then you would select Alternative __1__ with payoff _120_ .
If PI says ‘B will occur’, then you would select Alternative _2 or 3_ with payoff _100_ .
If PI says ‘C will occur’, then you would select Alternative __4__ with payoff _90_ .
The probability for PI to say ‘A will occur’ is _0.7__ .
The probability for PI to say ‘B will occur’ is _0.1___ .
The probability for PI to say ‘C will occur’ is _0.2___ .
The expected payoff with PI
= sum of all possible payoffs weighted by their probabilities
= 120*0.7 + 100*0.1 +90*0.2
= 84 + 10 + 18
= 112
Step 3.
EVPI = (EV with PI)  (EV without PI)
= _112 – 87 _
= _25__
Part 3.
Part 1 and Part 2 can be put in the extended Payoff table.
(1) Put your results in Part 1 and Part 2 into the extended payoff table below.
Alternatives
1
2
○
3
4
column Max
States of Nature
A
B
C
P(A)=0.7 P(B)=0.1 P(C)=0.2
120
-100
60
90
100
70
80
-50
120
100
80
100
80
90
90
EMV’s
(expected values)
120*0.7+(-100)*0.1+60*0.2 = 86
90*0.7+100*0.1+70*0.2 = ○
87
80*0.7+100*0.1+80*0.2 = 82
(-50)*0.7+80*0.1+90*0.2 = -9
120*0.7+100*0.1+90*0.2 = 112
(2) Circle and label your decision and its EMV you calculated in Part 1 in the table.
(3) Circle and label (EV without PI) and (EV with PI) in the table.
EVPI = EVvPI – EVw/oPI = 112 – 87 = 25.
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