1. Decision Theory

2. Expected Value of a Decision Alternative
The expected value of a decision alternative is the sum of weighted payoffs for the decision alternative.
The expected value (E) of decision alternative di is defined as:
where: N = the number of states of nature
P(sj) = the probability of state of nature sj
Vij = the payoff corresponding to decision alternative di and state of nature sj

3. Example ( 1 ) : Marketing Strategy
If data are available for the quantity sold and the corresponding probability in one of the companies shown in the following table:
Find the expected value of the units sold ? 14 12 10
Quantity
0.2
0.5
0.3
Probability

4. E ( q ) = ∑ p* q = 10 * * * 0.2 = =

5. Example ( 2)
If data are available for the quantity sold and the corresponding probability in one of the companies shown in the following table:
The purchase price 20 pounds and the selling price 30 pounds
Find the quantity to be maintained ? 12 11 10
Quantity
0.3
0.5
0.2
Probability

6. Profit = selling price - purchase price 20 = 30 - 20 = 10
0.3
0.5
0.2 12 11 10
100
110 80
120 90 60

7. The quantity to be maintained is 11
E ( q ) = ∑ p * q
E ( 10 ) = 100 * * * 0.3 = 100
E ( 11) = 80 * * * 0.3
= = 104
E ( 12) = 60 * * * 0.3
= = 93
The quantity to be maintained is 11

8. Example ( 3)
If data are available for the quantity sold and the corresponding probability in one of the companies shown in the following table:
The purchase price 20 pounds and the selling price 30 pounds
Find the quantity to be maintained ? 14 12 10
Quantity
0.3
0.5
0.2
Probability

9. Profit = selling price - purchase price 20 = 30 - 20 = 10
0.3
0.5
0.2 24 12 10
100
120 60
140 80 20

10. The quantity to be maintained is 12
E ( q ) = ∑ p * q
E ( 10 ) = 100 * * * 0.3 = 100
E ( 12) = 60* * * 0.3
= = 108
E ( 14) = 20 * * * 0.3
= = 86
The quantity to be maintained is 12