Question

1. Ace Steel Mill estimates the Demand for steel in millions of tons per year as follows

Millions of t tons	Probability
10	10
12	25
14	30
16	20
18	15

1. If capacity is set at 18 Million tons what is the capacity cushion
2. What is the probability of Idle capacity
3. What is the average utilization of the plant at 18 million ton capacity
4. If it costs $8 million per ton of lost business and $80 million to build a million ton of capacity how much capacity should be built to minimize the total cost

Answer 1

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(a)

Capacity Cushion = Capacity(Nominal) – Average Demand

Capacity(Nominal) = 18

Average Demand = ((10x.10)+(12x.25)+(14x.30)+(16x.20)+(18x.15) = 14.1

Capacity Cushion = 18 - 14.1

Capacity Cushion = 3.9 million tons

(b)

To get idle capacity= sum for all probabilities where the demand is less than 18 million tons

Idle capacity=0.1 + 0.25 + 0.3 + 0.2

Idle capacity=0.85 or85%

(c)

Utilization = Output/Nominal Capacity

So we get (0.1x10/18)+(0.25x12/18)+(0.3x14/18)+(0.2x16/18)+(0.15x18/18)

Utilization 0.7833333 or 78.33% of average utilization

(d)

Capacity 10mn: (80 x 10) + 8( (12-10x.25)+(14-10x.3)+(16-10x.2)+(18-10x.15) = 832.8

Capacity 12mn: (80 x 12) + 8( (14-12x.3)+(16-12x.2)+(18-12x.15)) = 978.4

Capacity 14mn: (80 x 14) + 8( (16-14x.2)+(18-14x.15)) = 1128

Capacity 16mn: (80 x 16) + 8( (18-16x.15)) = 1282.4

Capacity 18mn: (80 x 18) + 8(0) = 1440

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