$($Ch$\mathrm{.}7\mathrm{.}10$ Prob$)$: Floor$-$On$.$ Ltd$.,$ operates a line that produces self$-$adhesive tiles. This

line consists of single$-$machine stations and is almost balanced $($i$.$e$.$ station rates are

nearly equal$).$ A manufacturing engineer has estimated the bottleneck rate of the line to

be $2,000$ cases per $16-$hour day and the raw process time to be $30$ minutes. The line has

averaged $1,700$ cases per day, and cycle time has averaged $3\mathrm{.}5$ hours. $(30pt,$ Hint:

quantitative answers$)$

$($a$)$ What would you estimate average WIP level to be$?($Hint: WIP$=$TH x CT$)$

$($b$)$ How does this performance compare to the practical worst case?

Hint:

$T{H}_{PWC}=\frac{w}{W_0+w-1}{r}_b$

$($need to calculate $r_b,T_0,W_0)$

$($c$)$ What would happen to the throughput of the line if we increased capacity at a non$-$

bottleneck station and held WIP constant at its current level?

$($d$)$ What would happen to the throughput of the line if we replaced a single$-$machine

station with four machines whose capacity equaled that of the single machine and

held the WIP constant at its current level?

$($e$)$ What would happen to the throughput of the line if we began moving cases of tiles

between stations in large batches instead of one at a time?