Question

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 a time $0$ ; schedule a job on M$2$ every $5$ minutes starting at time $0.$ Jobs finished on M$1$ go to M$3$; juvs inimieu uli ivic gu iv ivis.

a$)$ Plot this schedule for the first $6$ jobs in the following Gantt chart. The first job and the $\backslash (4^\{\backslash$text $\{$th $\}\}\backslash )$ job start on M$1.$ The second, third, $\backslash (5^\{\backslash$text $\{$th $\}\}\backslash ),$ and the $\backslash (6^\{\backslash$text $\{$th $\}\}\backslash )$ jobs start on M$2.$ The first block of job $1-5$ is plotted for you.

You can extend the above chart as needed.

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

a$)$ 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? $($Explain your answer$)$