Homework $1-$ Process Fundamentals

Question $1$: $(15$ points$)$

A process flow diagram is as follows. In step $1,$ the two machines $($M$1$ & M$2)$

A$.(6$ points$)$ Suppose the starting times of $M1$ and $M2$ are staggered by $4$

minutes, i$.$e$.,$ M$1$ starts at time $0$ and M$24$ minutes later. Then new parts

are fed into M$1$ and M$2$ whenever they become available. Draw a Gantt

chart, and identify the cycle time and average manufacturing lead$-$time of

the whole process.

B$.(2$ points$)$ What's the bottleneck?

C$.(5$ points$)$ Calculate each machine's contribution to WIP and total WIP.

D$.(2$ point$)$ Verify Little's law.

Question $2$: $(5$ points$)$

The department of tax regulations of the IRS is in charge of writing tax

regulations in accordance with tax laws passed by the congress. The

department completes $720$ projects per year, on average. It was reported by

the WSJ $($Wall Street Journal$)$ that the average number of projects $"$on their

plate" is $348.$ The department head claims that on average, the time to

complete a project is less than six months. Do you have any reason to disagree?

Explain why.

Question $3$: $(10$ points$)$

A facility conducts three$-$day programs and operates $7$ days per week. A new

batch of $400$ starts a program on each day of the week except Saturday and

Sunday $($A person joining on Monday will leave on Thursday; one joining on

Tuesday will leave on Friday and so on$).$ Assume that January $1$ is a Monday

and the facility is just opening after a long Christmas break.A facility products three day programs and operates $7$ days per week. A new batch of $400$ starts a program on each day of the week except saturday and sunday Question $2$: $(5$ points$)$

The department of tax regulations of the IRS is in charge of writing tax

regulations in accordance with tax laws passed by the congress. The

department completes $720$ projects per year, on average. It was reported by

the WSJ $($Wall Street Journal$)$ that the average number of projects $"$on their

plate" is $348.$ The department head claims that on average, the time to

complete a project is less than six months. Do you have any reason to disagree?

Explain why.