A two stage production system uses kanbans at each stage to authorize production. The stages

are in series and each part must go stage one and then stage two. $($Material flow is shown in the

figure below$).$ Stage one can produce at the rate of $200$ units per hour when it is operational.

However, after three hours of operation the stage has to stop for one hour of maintenance. The

second stage has $100\%$ availability and can produce at the rate of $150$ units per hour. The system

is scheduled for $8$ hours per day. Each container holds $4$ units. The system feeds a final

assembly line that demands one unit every $0\mathrm{.}4$ minutes $(1200$ units per day$).$

a$.$ Can the system meet demand using a kanban system? $($Assume you can use as many kanbans

as you want at each stage.$)$

b$.$ How many kanbans are required for each stage?

c$.$ Using the number of kanbans determined in part b$,$ plot the inventory level in the output buffer

of stage $1$ for an $8$ hour day assuming inventory level is $0$ at the start of the day and maintenance

at stage one occurs at the end of the $3$rd and $7$th hours.

d$.$ Suppose the two maintenance intervals occurred at random times of the day due to machine

breakdowns instead of regularly scheduled maintenance. Would the system still be able to meet

demand using the same number of kanbans? If not, explain why.