A small facility is expected to earn an after-tax net present value of just $18,000 if demand is low. If demand is average, the small facility is expected to earn $75,000; it can be increased to medium size to earn a net present value of $60,000. If demand is high, the small facility is ex- pected to earn $75,000 and can be expanded to medium size to earn $60,000 or to large size to earn $125,000.
A medium-sized facility is expected to lose an estimated $25,000 if demand is low and earn $140,000 if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of $150,000; it can be expanded to a large size for a net payoff of $145,000.
If a large facility is built and demand is high, earnings are expected to be $220,000. If demand is average for the large facility, the present value is expected to be $125,000; if demand is low, the facility is expected to lose $60,000.
a. Draw a decision tree for this problem.
L(18000)
A(75000)
small H(75000)
medium L(-25000)
A(140000) H(150000) large
L(-60000) A(125000) H(220000
b. What should management do to achieve the highest expected payoff?
The highest payoff is with LARGE size= 112000 LOW
AVERAGE
HIGH prob
0.25
0.4
0.35
expected value
SMALL
18000
75000
75000
60750
MEDIUM
-25000
140000
150000
102250
LARGE
-60000
125000
220000
112000
c. Which alternative is best, according to each of the fol- lowing decision criterion?
Maximin
SMALL size. This is because the min of all 3 options is 18000, -25000, -60000. The maximum out of these is 18000 Maximax
LARGE size. This is because the max of all 3 options is 75000, 150000, 220000. The maximum out of these is 220000 Minimax regret
MEDIUM size. This is because the min of the max regret values is 75000
REGRET TABLE LOW
AVERAGE
HIGH max regret prob 0.25
0.4
0.35 SMALL
78000
0
0
78000
MEDIUM
35000
65000
75000
75000
LARGE
0
50000
145000
145000
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