subjective judgement. Under conditions of risk, the different decision criteria available to the decision maker are given in Table 16.1 and elaborated below.
16.6.1 Expected Value Criterion
The expected value, in statistics, is determined by the sum of expected outcomes
multiplied by their respective probabilities. The expected monetary value (EMV) is
the sum of the expected payoffs for the different alternatives, weighted by respective
allocated probabilities of the different events that can occur. (The different probabilities of the alternatives must add up to 1). The procedure to apply the expected
monetary value (EMV) criterion, comprises the following steps:
1. Create a payoff table, using the alternative decision possibilities and probabilities
allocated to the various events (states of nature) (first two columns of
Table 16.10a). Determine the conditional profit for every combination of decision
and different event (see other columns).
2. Determine, for each decision alternative, the EMV ¼ conditional profits 3 probability. Add up to obtain the total EMV, for each alternative decision.
3. Choose the alternative that produces the highest EMV.
Example 16.3
A newspaper girl sells a magazine with the following probabilities (obtained from
past sales records):
She buys each copy at Rs. 30 and sells them at Rs. 50. She cannot get any
reimbursement for unsold copies. How many copies can she order to maximise her
profit?
Solution
The number of copies for purchases and for sales which are relevant to the
newsgirl are 100, 110, 120, 130 or 140. These are her sales magnitudes. There is
no justification for her to purchase fewer than 100 nor more than 140 copies.
Table 16.10b, the conditional profit table gives the profit arising from any possible
demand and supply combination. The profit per copy is Rs. 20 (¼ 50À30). If she
stocks 100 copies every day, she will always obtain profit of Rs. 2000 irrespective of
the demand. For instance, even if on some day, customers are willing to buy
130 copies, she can only sell 100 copies and hence her conditional profit is Rs. 2000.
Table 16.10a Newspaper
statistics
No. of copies sold
Probability
100
0.10
110
0.15
120
0.20
130
0.25
140
0.30
TOTAL
1.00
454
16 Decision Taking with Infrastructure
16.6.1 Expected Value Criterion
The expected value, in statistics, is determined by the sum of expected outcomes
multiplied by their respective probabilities. The expected monetary value (EMV) is
the sum of the expected payoffs for the different alternatives, weighted by respective
allocated probabilities of the different events that can occur. (The different probabilities of the alternatives must add up to 1). The procedure to apply the expected
monetary value (EMV) criterion, comprises the following steps:
1. Create a payoff table, using the alternative decision possibilities and probabilities
allocated to the various events (states of nature) (first two columns of
Table 16.10a). Determine the conditional profit for every combination of decision
and different event (see other columns).
2. Determine, for each decision alternative, the EMV ¼ conditional profits 3 probability. Add up to obtain the total EMV, for each alternative decision.
3. Choose the alternative that produces the highest EMV.
Example 16.3
A newspaper girl sells a magazine with the following probabilities (obtained from
past sales records):
She buys each copy at Rs. 30 and sells them at Rs. 50. She cannot get any
reimbursement for unsold copies. How many copies can she order to maximise her
profit?
Solution
The number of copies for purchases and for sales which are relevant to the
newsgirl are 100, 110, 120, 130 or 140. These are her sales magnitudes. There is
no justification for her to purchase fewer than 100 nor more than 140 copies.
Table 16.10b, the conditional profit table gives the profit arising from any possible
demand and supply combination. The profit per copy is Rs. 20 (¼ 50À30). If she
stocks 100 copies every day, she will always obtain profit of Rs. 2000 irrespective of
the demand. For instance, even if on some day, customers are willing to buy
130 copies, she can only sell 100 copies and hence her conditional profit is Rs. 2000.
Table 16.10a Newspaper
statistics
No. of copies sold
Probability
100
0.10
110
0.15
120
0.20
130
0.25
140
0.30
TOTAL
1.00
454
16 Decision Taking with Infrastructure