Question $2(2+2+2+2=8$ points$)$

We have a process as shown in the right figure. $($M$1-$M$4$ are the names for four machines. The numbers are activity times in minutes$).$ Consider the following schedule:

Schedule a job on M$1$ every $10$ minutes, starting at time $0$; schedule a job on M$2$ every $5$ minutes starting at time $0.$ Jobs finished on M$1$ go to M$3$; jobs finished on M$2$ go to M$4.$

The Gantt chart for the first $6$ jobs is below:

$12345678910111213141516171819202122232425262728$

M$1111111444444$

M$222335566$

M$311111111114444444444$

M$42222333355556666$

You can extend the above chart as needed.

Machine WIP $($units$)$

M$1$

M$2$

M$3$

M$4$

Total

a$)$ Find the WIP on each machine and complete the below table.

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b$)$ What is the average throughput time, i$.$e$.,$ flow time $[$in mins$]?$

$($Hint: Every $10$ minutes, $3$ jobs come to the process $(1$ job to M$1,2$ jobs to M$2).$ To get the average throughput time $($TPT$),$ you need to calculate the TPT for each of the three jobs and then take the average. Do not round your answer. $)$

c$)$ Is the process demand$-$ or supply$-$constrained? What is the flow rate under the given schedule $($in units$/$hour$)?$

d$)$ What is the actual cycle time under this schedule $($in minutes$)?$