$($Ch$.8\mathrm{.}10$ Prob$)$: Consider a simple two$-$station line as shown in below $($Two$-$station line

with a finite buffer$).(30pt)$

Both machines take $20$ minutes per job and have $SCV=1.$ The first machine can always

pull in material, and the second machine can always push material to finished goods.

Between the two machines is a buffer that can hold only $10$ jobs $($see Section $8\mathrm{.}7\mathrm{.}1).$

a$)$ Model the system using an $\frac{M}{M}\frac{?}{?}\frac{1}{b}$ queue. $($Note that $b=12,$ considering the two

machines.$)$

i$.$ What is the throughput?

ii$.$ What is the partial WIP $($i$.$e$.$ WIP waiting at the first machine or at the second

machine, but not in process at the first machine$)?$ Hint: WIPP $=\frac{b}{2}$

iii. What is the total cycle time for the line $($not including time in raw material$)?$

$($Hint: Use Little's Law with the partial WIP and the throughput and then add the

iv$.$ What is the total WIP in the line? $($Hint: Use Little's Law with the total cycle time

and the throughput.$)$