Question $1.(27$ pts$)$ Consider the following system with $7$ processes.

Process Processing Time $($minute$/$job$)$ Number of workers

$15$ minutes $1$

$25$ minutes $1312$ minutes $2$

$415$ minutes $2$

$53$ minutes $1$

$620$ minutes $3$

$75$ minutes $1$

$($a$)[3$pts$]$ Determine:

the critical path:

length of the critical path:

theoretical flow time $($TFT$)$:

$($b$)[4$pts$]$ As an OM business process reengineering expert, you can automate any of processes $2,3,4,5,6($but not processes $1$ or $7)$ to reduce the processing time. Answer parts $($i$)$ and $($ii$)$ independently based on the current system. Your answer should be specific, and in the form: $$reduce the processing time for process X$1$ by Y$1$ minutes, and process X$2$ by Y$2$ minutes,$$ etc.

$($i$)$ Explain how you can reduce the theoretical flow time $($TFT$)$ by exactly $2$ minutes $($from the current time in part $($a$))$

$($ii$)$ Explain how you can reduce the theoretical flow time $($TFT$)$ by exactly $3$ minutes $($from the current time in part $($a$))$

$($c$)[12$pts$]$ Complete the resource utilization table based on the current system and answer the following questions:

Resource unit load unit cap # units total process cap utilization

$($min$/$job$)($job$/$hr$)$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

Identify the process capacity $($throughput$)($jobs$/$hr$)$ and the bottleneck resource$($s$).$

$($d$)[8$pts$]$ To be able to produce a minimum of $4$ per hour, how many workers are needed for each process? Please complete the following table to answer this question.

Resource unit load unit cap # units total process cap utilization

$($min$/$job$)($job$/$hr$)$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

Identify the new bottleneck and the new process capacity