SCV $=1.$ The rst machine can always pull in material, and the second machine can always

push material to nished goods. Between the two machines is a buffer that can hold only $10$

jobs $($see Sections $8\mathrm{.}7\mathrm{.}1$ and $8\mathrm{.}7\mathrm{.}2).$

a$.$ Model the system using an M$/$ M$/1/$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 rst machine or at the second

machine, but not in process at the rst machine$)?$

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 process

time at the rst machine.$)$

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

and the throughput.$)$

b$.$ Reduce the buffer to one $($so that b $=3)$ and recompute the above measures. What

happens to throughput, cycle time, and WIP? Comment on this as a strategy.

c$.$ Set the buffer to one and make the process time at the second machine equal to $10$

minutes. Recompute the above measures. What happens to throughput, cycle time, and

WIP? Comment on this as a strategy.

d$.$ Keep the buffer at one, make the process times for both stations equal to $20$ minutes $($as

in the original case$),$ but set the process CVs to $0\mathrm{.}25($SCV $=0\mathrm{.}0625).$

i$.$ What is the throughput?

ii$.$ Compute an upper bound on the WIP in the system.

iii. Compute an approximate upper bound on the total cycle time.

iv$.$ Comment on reducing variability as a strategy.