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systematic approach to making decisions especially under uncertainty. Although statistics such as
Example 1: Assume the following probability distribution of daily demand for strawberries:
Also assume that unit cost = $3, selling price = $5 (i.e., profit on sold unit = $2), and salvage value on unsold units = $2 (i.e., loss on unsold unit = $1). We can stock either 0, 1, 2, or 3 units. The question is: How many units should be stocked each day? Assume that units from one day cannot be sold the next day. Then the payoff table can be constructed as follows:
*Profit for (stock 2, demand 1) equals (no. of units sold) (profit per unit) - (no. of units unsold)(loss per unit) = (1)($5 - 3) - (1)($3 - 2) = $1
**Expected value for (stock 2) is: -2(.2) + 1(.3) + 4(.3) + 4(.2) = $1.90. The optimal stock action is the one with the highest
Suppose the decision maker can obtain a perfect prediction of which event (state of nature) will occur. The
Expected value with perfect information minusthe expected value with existing information.
Example 2: From the payoff table in Example 1, the following analysis yields the expected value with perfect information:
With existing information, the best that the decision maker could obtain was select (stock 2) and obtain $1.90. With perfect information (forecast), the decision maker could make as much as $3. Therefore, the expected value of perfect information is $3.00 - $1.90 = $1.10. This is the maximum price the decision maker is willing to pay for additional information.