Question

(b) A company is unable to satisfy customer demand for one of their products. The ratios for mixing the outputs from processes C, D and E are 2, 1 and 1 respectively. The ratio for the departments F and G is 3 and 1, and the ratio for departments Hand I is 4 and 1. Using Table Q2(b), Determine; (i) The system capacity and bottleneck; (ii) How much system capacity can be gained by adding capacity to the bottleneck Table Q2(b) Department Capacity (liters/hour) Predecessors A B A B с D E F 450 450 350 250 250 750 C, D and E G H F, and G 300 950 350 1100 1400 J H and I K J

Please answer step by step.

Thank you.

Answer 1

i) Bottleneck resource is the one that limits the overall process capacity or output.

We shall analyze how many liters of output from each resource is required for an input of 1 unit to the subsequent department.

Units of output per hour = Capacity/units required

For example,

For Department C,

Capacity = 350 liters/hour

units required = 2

Units of output per hour = 350/2 = 175 liters/hour of output

Department	Capacity (liters/hour)	Predecessors	units required	Units of output per hour
A	450	-	1	450
B	450	A	1	450
C	350	B	2	175
D	250	-	1	250
E	250	-	1	250
F	750	C, D, E	3	250
G	300	-	1	300
H	950	F, G	4	237.5
I	350	-	1	350
J	1100	H, I	1	1100
K	1400	J	1	1400

Because the output per hour for department C is the least i.e. 175 liters, Department C is the bottleneck.

For process capacity:

We know C is the bottleneck and can contribute to making 175 liters of input for Department F.

Now, the 3 units of F are required to make 1 unit of H.

Hence, input for H = 175 / 3 = 58.33 Liters/hour

Now, the 4 units of H are required to make 1 unit of J.

Hence, input for J = 58.33 / 4 = 14.58 Liters/hour

Hence, process capacity = 14.58 Liters/Hour

ii) Now, we can add capacity to the existing bottleneck resource until the bottleneck gets shifted to the next limiting capacity of the resource.

Here, C is the existing bottleneck, and D and E are the next limiting resources.

So, we can add capacity to C till it matches the output from D and E.

C currently generates 175 liters of output per hour for which it requires a capacity of 350 liters.

We can increase C's output to 250 liters per hour, for which it will require 250 * 2 = 500 liters per hour of capacity.

Hence, additional capacity requirement = 500 - 350 = 150 liters/hour

Now,

the revised input to F will be 250 liters/hour

Now, the 3 units of F are required to make 1 unit of H.

Hence, input for H = 250 / 3 = 83.33 Liters/hour

Now, the 4 units of H are required to make 1 unit of J.

Hence, input for J = 83.33 / 4 = 20.83 Liters/hour

Hence, revised process capacity = 16.67 Liters/Hour

The gain in process capacity = 20.83 - 14.58

The gain in process capacity = 6.25 liters/hour

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