2. The Elements common to Decision-Theory
Problem
• The Decision- Maker
• An objective the decision-maker is trying to reach
• Several Courses of Action
• Events/ States of Nature/ Outcomes
• Pay-offs : It measures the net benefit It is also known as
conditional-payoffs.
4. Example
A newspaper dealer buys newspapers for Rs 1 each and sells them
for Rs 3 each. Any papers not sold by the end of the day are
completely worthless to him. The dealer’s problem is to determine
the optimal number he should order each day. On days when he
stocks more than he sells , his profits are reduced by the cost of the
unsold papers. On days when buyers request more copies than he
has in stock, he loses sales and makes smaller profits than he could
have.
The dealer has kept a record of his sales for the past 100 days.
5. Distribution of Newspaper Sales
Daily Sales Number of Days Sold Probability of each no. being sold
10 15 0.15
11 20 0.20
12 40 0.40
13 25 0.25
Total 100
6. Conditional Pay-off Table
Possible Stock Action
Possible 10 11 12 13
Demand
10
11
12
13
Pay-off= profit per unit x (no of units sold)– loss per unit x (no. of units
unsold)
7. Expected Conditional Pay-off Table
Possible Stock Action
Possible Probability 10 11 12 13
Demand
10 0.15
11 0.20
12 0.40
13 0.25
Total
Pay-off= profit per unit x (no of units sold)– loss per unit x (no. of units
unsold)
8. The optimal stock action is the one that results in the
greatest expected profit.
