A production line consists of four successive workstations $($A$,$ B$,$ C$,$ and D$)$: It takes $4$ minutes to process a job in station A$,4$ minutes in station $B,4$ minutes in station $C,$ and $16$ minutes in station $D.$ The stations require different resources and work is pushed based on the firstcome$-$first$-$served principle throughout the production line. All workstations are initially empty. There are $100$ jobs to complete. The company considers four different strategies to reduce the WIP inventory:

$($a$)$ The current production line without any modification.

$($b$)$ Adding a new station that will run parallel to station D$.$ Upon arrival of a job any idle station, or the station that becomes idle first, serves the job. It takes $16$ minutes to process a job in the new station.

$($c$)$ Adding three new stations $($instead of one$)$ that will run parallel to station D$.$ Upon arrival of a job any idle station, or the station that becomes idle first, serves the job. It takes $16$ minutes to process a job in each new station.

$($d$)$ Replacing the current server in station $D$ with a faster one that processes a job in $4$ minutes.