Expected value of perfect information, Mathematics

Expected Value of Perfect Information

In the above problems we have used the expected value criterion to evaluate the decisions under the conditions of risk. But, as long as uncertainty exists, there is the possibility that the expected value criterion may lead to the wrong course of action. The retailer can remove all uncertainty from this problem by obtaining an accurate and complete information about the future, referred to as perfect information. When the demand is known ahead, the prudent stock decision is to stock the quantity demanded. This prevents overstocking and understocking. In the example above, for instance, 3,000 shirts will be stocked whenever 3,000 units are demanded, 8,000 shirts will be stocked whenever 8,000 units are demanded, etc.

We can calculate the expected profit under certainty and expected value of information of the above example, assuming that the uncertainty has been removed by using conditional profit table as shown below.

Conditional Profit Table under Certainty

Stock Decision

Possible demand (shirts)

(3,000)

(5,000)

(8,000)

(10,000)

3,000

1,50,000

-

-

-

5,000

-

2,50,000

-

-

8,000

-

-

4,00,000

-

10,000

-

-

-

5,00,000

If the chain store estimates its future demand to be 3,000 shirts, it stocks only 3,000 shirts and makes a profit of Rs.1,50,000. Similarly, the profit values for other levels of stock are calculated. Thus, with perfect information the chain store can realize profits as under:

Expected Profit Under Certainty

Stock Decision

Conditional Profit

Probability

Expected profit under certainty

3,000

1,50,000

0.20

30,000

5,000

2,50,000

0.25

62,500

8,000

4,00,000

0.45

1,80,000

10,000

5,00,000

0.10

50,000

 

 

 

3,22,500

The expected profit under certainty is Rs.3,22,500. Thus, the maximum possible expected profit is Rs.3,22,500.

The expected value of perfect information is the difference between the expected profit under certainty and the best expected monthly profit without any predictions of the future as calculated before.

Thus, in the above problem, expected value of perfect information is Rs.53,750 (3,22,500 - 2,68,750).

Posted Date: 9/15/2012 2:19:27 AM | Location : United States







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