Consider the following three$-$station production line with a single product that must visit

station $1,2,$ and $3$ in sequence:

$$ Station $1$ has five identical machines with average processing times of $15$ minutes per

job.

$$ Station $2$ has $12$ identical machines with average processing times of $30$ minutes per job.

$$ Station $3$ has one machine with average processing times of $3$ minutes per job.

Punch Bind

$2$

$($a$)$ What are the bottleneck rate, the raw processing time, and the critical WIP?

$($b$)$ Compute the average cycle time when the WIP level is set at $20$ jobs, under the

assumptions of:

$($i$)$ Best case

$($ii$)$ Worst case

$($iii$)$ Practical worst case