i
th regret ¼ maximum payoff À i
th payoff
À
Á
for the j
th event
The decision alternative S 1 would be chosen since it corresponds to the minimum
of the maximum possible regrets.
Table 16.6 The criterion of rationality
Alternatives
States of nature (product demand)
Expected payoff
High
Moderate Low
Nil
Rs.
Rs.
Rs.
Rs.
Rs.
Expansion
500,000 250,000
À250,000 À450,000 [50 + 25À25 À45] Â 10,000/
4 ¼ 12,500
Construction
700,000 300,000
À400,000 À800,000 [70 + 30À40 À80] Â 10,000/
4 ¼ À50,000
Subcontracting 300,000 150,000
À10,000 À100,000 [30 + 15À1À10] Â 10,000/
4 ¼ 85,000
Table 16.7 Payoff matrix
(Rs)
N 1
N 2
N 3
N 4
S 1
40,000
À1000
60,000
180,000
S 2
200,000
50,000
4000
0
S 3
200,000
150,000
À20,000
10,000
Table 16.8 Payoff matrix (Rs.) under different criteria
Pessimistic (maximin)
value
Optimistic
(maximax) value
Equal probability value
1
n P 1 þ P 2 þ . . . þ P n
½
Š
Rs.
Rs.
Rs.
S 1
À1000
180,000
1/4 (40,000À1000 + 60,000 + 180,000) ¼ Rs.
69,750
S 2
0
200,000
1/4 (200.000 + 50,000 + 4000 + 0) ¼ Rs.
63,500
S 3 À20,000
200,000
1/4 (200,000 + 150,000
À20,000 + 10,000) ¼ Rs. 85,000
Table 16.9 Regret matrix
N 1
N 2
N 3
N 4
Maximum regret
Regret
Regret
Regret
Regret
Rs.
Rs.
Rs.
Rs.
Rs.
S 1
160,000
151, 000
0
0
160,000
S 2
0
100,000
56,000
18,000
180,000
S 3
0
0
80,000
170,000
170,000
452
16 Decision Taking with Infrastructure