Consider a simple two$-$station line as shown in Figure. The first machine takes $20$ minutes per job and

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

material to finished goods. The process time at the second machine is equal to $10$ minutes with SCV$=$

Between the two machines is a buffer that can hold only $1$ job $($see Sections $8\mathrm{.}7\mathrm{.}1$ and $8\mathrm{.}7\mathrm{.}2).$

Model the system using an M$//$M$//1//$b queue.

Note that b$=3$ considering the two machines. Compute the below measures. Comment on this

as a strategy.

What is the throughput and utilization of the line and the first machine?

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$)?$

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 first

machine.$)$

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

throughput.$)$

What is the utilization of the second machine?

Keep the buffer at one $($b$=3),$ make the process times for both stations equal to $20$ minutes, but

set the process CVs to $0\mathrm{.}25($SCV$=0\mathrm{.}0625).$

What is the throughput?

Compute an upper bound on the WIP in the system.

Compute an $($approximate$)$ upper bound on the total cycle time. Is this upper bound an

acceptable cycle time?

What is the utilization of the line?

Comment on reducing variability as a strategy.

PLEASE SOLVE QUESTION $2,$ THANK YOU :)