Practice Problems Capacity Planning Solutions PDF

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Solutions to Practice Questions on Capacit y Planning

10. Plastic

Year 1

Year 2

Year 3

Year 4

97

115

136

141

Percentage of capacity used

48.5%

57.5%

68.0%

70.5%

Machine requirements

.485

.575

.680

.705

Labor requirements

1.94

2.30

2.72

2.82

Year 1

Year 2

Year 3

Year 4

21

24

29

34

Percentage of capacity used

58.3%

66.7%

80.6%

94.4%

Machine requirements

1.75

2.00

2.42

2.83

Labor requirements

3.50

4.00

4.84

5.66

Demand for plastic sprinklers

Bronze Demand for bronze sprinklers

Note that: Machine requirements = percentage of capacity used * number of machines available Labor requirements = machine requirements * number of operators needed for each machine.

14.

.40 High Small Facility

$12 Million

$6 Million Low .60 Do nothing

$0

.40

Large Facility

High $9 Million

$10 Million

Low .60

18 Million

$10 Million

For the small facility, NPV = .40 ($12 Million) + .60 ($10 Million) - $6 Million = $4.8 Million Do nothing, NPV = $0 For the large facility NPV = .40($18 Million) + .60($10 Million) - $9 Million = $4.2 Million Therefore, build the small facility. To calculate value of perfect information, first find the optimal capacity decision under each demand scenario: if demand is high, then the best option is building large facility, because it results in a profit of $18-$9 = $9M, higher than building small facility ($12$6=$6M), or doing nothing ($0); if demand is low, then the best option is building small facility, as $10 - $6 = $4M > $10 - $9 >$0. Hence, after acquiring the perfect information, the expected profit is $9 * 0.4 + $4 * 0.6 = $6M. Comparing with the case without the perfect information (when you have to rely on expectations to make the capacity decision and as calculated above, you get $4.8M), the increase in profit is $6 $4.8 = $1.2. Hence, the value of perfect information equals to $1.2.

15.

.70 Shopping Center

.30 1

Rezoned .60

.60

$3 Million

3

$5 Million

$3,000 x 1500 =$4.5 Million

Apartments 2

.40 Not Rezoned

$4 Million

.40

$2,000 x 1500 = $3 Million

$2 Million Houses $4,000 x 600 = $2.4 Million

Rezoned shopping center: Point 1: Expected value = .70($4 Million) + .30($5 Million) = $4.3 Million Rezoned apartments: Point 2: Expected value = .60($4.5 Million) + .40($3 Million) = $3.9 Million Since a shopping center has more value, prune the apartment choice. In other words, if rezoned, build a shopping center with a profit of $4.3 Million - $3 Million = $1.3 Million If not rezoned: Point 3: Expected Profit is $2.4 Million - $2 Million = $.4 Million Expected profit is .60($1.3 Million) + .40($.4 Million) = $.94 Million...