Consider the following batch flow process consisting of three process steps performed by three machines:

Activ

Setur

Work is processed in batches at each step. Before a batch is processed at step $1,$ the machine has to be set up$.$ During a setup, the machine is unable to process any product.

$($a$)$ Assume that the batch size is $30$ parts. What is the capacity of the process?

$($b$)$ For a batch size of $4$ parts, which step is the bottleneck for the process?

$($c$)$ Using the current production batch size of $30$ parts, how long would it take to produce $12$ parts starting with an empty system? Assume that the units in the batch have to stay together $($no smaller transfer batches allowed$)$ when transferred to step $2$ and to step $3.$ A unit can leave the system the moment it is completed at step $3.$ Assume step $1$ needs to be set up before the beginning of production.

$($d$)$ Using the current production batch size of $30$ parts, how long would it take to produce $20$ parts starting with an empty system? Assume that the units in the batch do not have to stay together; specifically, units are transferred to the next step the moment they are completed at any step. Assume step $1$ needs to be set up before the beginning of production.