Page 131 - DMTH404_STATISTICS

Unit 8: Expected Value with Perfect Information (EVPI)

Let D be the event that the survey predicts high demand. Therefore, Notes

P(D/H) = 0.60 and P(D /H) = 0.80
We have to find P(H /D) and P(H /D). For this, we make the following table:

H H Total
0.4 0.6
´
D 0.12 0.36
= 0.24
0.6 0.8
´
D 0.16 0.64
= 0.48
Total
0.40 0.60 1.00
From the above table, we can write
0.24 2 0.12 1
P ( / ) = = and ( / ) = =
H
D
P
D
H
0.36 3 0.36 3
2 1
The EMV of the act 'don't expand' = 5000 ´ + 5000 ´ = Rs 5,000
3 3
2 1
and the EMV of the act 'expand' = 7500 ´ + 2100 ´ = Rs 5,700
3 3
Since the EMV of the act 'expand' > the EMV of the act 'don't expand', the manufacturer should
expand his production capacity.
It can be shown that, in the absence of survey the EMV of the act 'don't expand' is Rs 5,000 and the
EMV of the act expand is Rs 4,260. Hence, the optimal act is 'don't expand'.

Decision Tree Approach

The decision tree diagrams are often used to understand and solve a decision problem. Using
such diagrams, it is possible to describe the sequence of actions and chance events. A decision
node is represented by a square and various action branches stem from it. Similarly, a chance
node is represented by a circle and various event branches stem from it. Various steps in the
construction of a decision tree can be summarised as follows:

(i) Show the appropriate action-event sequence beginning from left to right of the page.
(ii) Write the probabilities of various events along their respective branches stemming from
each chance node.

(iii) Write the payoffs at the end of each of the right-most branch.
(iv) Moving backward, from right to left, compute EMV of each chance node, wherever
encountered. Enter this EMV in the chance node. When a decision node is encountered,
choose the action branch having the highest EMV. Enter this EMV in the decision node and
cut-off the other action branches.

Following this approach, we can describe the decision problem of the above example as given
below:

LOVELY PROFESSIONAL UNIVERSITY 123