The best expected daily profit without information was found to be Rs. 2225. The
difference of Rs. 275 is the highest daily amount the newsgirl should be prepared to
pay, for a perfect predictor because this is the maximum increase she can obtain on
her expected daily profit. This difference is called the expected value of perfect
information (EVPI). It is not justified to pay more than Rs. 275 to the predictor
because that will lower the expected daily profit. It may be noted that in Example
16.4, Rs. 275 was the minimum expected loss (EOL). It can thus be concluded that
EVPI equals to the minimum EOL.
EVPI is an important concept in decision analysis. For a given problem, EVPI
represents the maximum amount a person should be prepared to pay in order to
obtain additional information on which may be based the decision alternative. On the
other hand, it does not make sense either, to pay the full EVPI, because that would
bring the net profit back to what can be expected without the additional information!
Example 16.5
A dairy firm wishes to estimate the quantity of butter it should produce to satisfy the
demand. Past records have yielded the following demand patterns:
The stock levels are limited to the range 15 to 50 kg because of inadequate storage
facilities. Butter is bought at Rs. 400 per kg, while the selling price is Rs. 500 per kg.
(i) Build a conditional profit table.
(ii) Calculate the action alternative corresponding to the maximum of expected
profit.
(iii) Determine EVPI.
Solution
(i) Obviously, the dairy firm should not produce butter outside the range of 15 to
50 kg. From the problem data, the conditional profit values can be determined for
every combination of stock action and event (demand). Denoting CP as the
conditional profit (in rupees), S as the stock quantity (kg) and D the demand
(kg), then
CP ¼
100 S
when D ! S
500D À 400 S when D S
The payoff is displayed in Table 16.17a. Given that 15 kg of butter is needed
for 6 days out of a total of 200 days implies an corresponding probability of
6/200 ¼ 0.03 for this quantity of butter. Other probabilities can similarly be
determined and are given in column (i) of Table 16.17b.
(ii) Table 16.18 displays the calculations for expected payoffs and EMV for each
action. As EMV becomes a maximum at Rs. 2175 for both 25 kg and 30 kg of
butter, the dairy firm may produce either 25 kg or 30 kg of butter for this
maximum daily profit.
(iii) Table 16.19 shows how the EVPI is computed.
16.6 Decision Making Under Conditions of Risk
459
difference of Rs. 275 is the highest daily amount the newsgirl should be prepared to
pay, for a perfect predictor because this is the maximum increase she can obtain on
her expected daily profit. This difference is called the expected value of perfect
information (EVPI). It is not justified to pay more than Rs. 275 to the predictor
because that will lower the expected daily profit. It may be noted that in Example
16.4, Rs. 275 was the minimum expected loss (EOL). It can thus be concluded that
EVPI equals to the minimum EOL.
EVPI is an important concept in decision analysis. For a given problem, EVPI
represents the maximum amount a person should be prepared to pay in order to
obtain additional information on which may be based the decision alternative. On the
other hand, it does not make sense either, to pay the full EVPI, because that would
bring the net profit back to what can be expected without the additional information!
Example 16.5
A dairy firm wishes to estimate the quantity of butter it should produce to satisfy the
demand. Past records have yielded the following demand patterns:
The stock levels are limited to the range 15 to 50 kg because of inadequate storage
facilities. Butter is bought at Rs. 400 per kg, while the selling price is Rs. 500 per kg.
(i) Build a conditional profit table.
(ii) Calculate the action alternative corresponding to the maximum of expected
profit.
(iii) Determine EVPI.
Solution
(i) Obviously, the dairy firm should not produce butter outside the range of 15 to
50 kg. From the problem data, the conditional profit values can be determined for
every combination of stock action and event (demand). Denoting CP as the
conditional profit (in rupees), S as the stock quantity (kg) and D the demand
(kg), then
CP ¼
100 S
when D ! S
500D À 400 S when D S
The payoff is displayed in Table 16.17a. Given that 15 kg of butter is needed
for 6 days out of a total of 200 days implies an corresponding probability of
6/200 ¼ 0.03 for this quantity of butter. Other probabilities can similarly be
determined and are given in column (i) of Table 16.17b.
(ii) Table 16.18 displays the calculations for expected payoffs and EMV for each
action. As EMV becomes a maximum at Rs. 2175 for both 25 kg and 30 kg of
butter, the dairy firm may produce either 25 kg or 30 kg of butter for this
maximum daily profit.
(iii) Table 16.19 shows how the EVPI is computed.
16.6 Decision Making Under Conditions of Risk
459