Question

A process has two stages. In the first stage, a machine makes two components, call them type A and B. It takes 250 seconds to switch production between the component types. During that time no production occurs. When in production, each component (A or B) requires 0.6 seconds to be completed. In the second stage, the components, A and B, are assembled to make a final product, call it C. The assembly stage can combine the two components into 1 unit every 2 seconds, or 30 units per minute (1 unit 1 pair of A and B). For questions below, round answers to a) If the batch size is 3750 units, the capacity of the machine in the first stage is (units/minute) ( unit 1 pair of A and B) b) By eliminating the setup time of the first stage, the largest possible capacity of the first stage is(units/minute) unit 1 pair of A and B) c) The largest possible capacity of the process is batch size that can achieve the largest possible process capacity is units/minute) ( unit- 1 pair of A and B) (units/minute). The smallest

Answer 1

(a)

Total time to process 3,750 units of A and B = (setup time) + processing time = (250 x 2) + 3,750*0.6 + 3,750*0.6 = 5,000 seconds

So, the capacity is 3,750 units in 5,000 seconds = 3750 x 60 / 5000 unit per minute = 45 units per minute

(b)

If there is no setup,

Total time to process 3,750 units of A and B = processing time = 3,750*0.6 + 3,750*0.6 = 4,500 seconds

So, the capacity is 3,750 units in 4,500 seconds = 3750 x 60 / 4500 unit per minute = 50 units per minute

(c)

Note that the capacity of the second stage is only 30 units per minute and hence this is the bottleneck stage and the largest possible capacity is 30 units per minute.

The corresponding batch size = 30*(250*2) / (60 - 30*2*0.6) = 625 units