Scenario $1($Use for problems $1$ through $3.)$

Consider a production system consisting of three workstations $($w$/$s$)$ in series as illustrated below. The

routing for this part is w$/$s $1->$ w$/$s $2->$ w$/$s $3.$

$1.$ Historical data indicates the average defect rate at w$/$s$$s $1,2,$ and $3$ are $3\%,4\%,$ and $6\%,$

respectively. Assuming all defects must be scrapped, how many parts need to be started to achieve an

output of $1000$ parts?

$2.$ To reflect the increasing value added as parts move through production, the costs of a scrapped part

at w$/$s $1,2,$ and $3$ are $$2,$ $$4,$ and $$5$ respectively. What is the total cost of scrap associated with

producing $1000$ first$-$quality parts?

Scenario $1$a

Same system as in Scenario $1$ but now assume you start $2000$ parts and the costs associated with

scrapping is the same as in question $2.$

$3.$ How many parts are scrapped and what is the total cost of scrap?

$4.$ How much would the defect rate at w$/$s $2$ need to be deceased for the total cost of scrap to be

reduced by approximately $10\%?$ If it is not possible, simply says so$.$

$5.$ How much would the defect rate at w$/$s $1$ need to be deceased for the total cost of scrap to be

reduced by approximately $10\%?$ If it is not possible, simply says so$.$

Scenario $2($Use for problems $6$ and $7.)$

There is an identical process to the one in Scenario $1$ except the first two workstations have rework

capability that converts some defects into good parts. As before, the defect rate at the w$/$s $1,2,$ and $3$

are $3\%,4\%,$ and $6\%,$ respectively. Here, however, the fraction of defective parts converted to good

parts is $80\%$ at R$1$ and $65\%$ at R$2.$ Fallout from the rework facilities must be scrapped.

$6.$ How many parts be must now be started to achieve an output of $1000$ parts?

$7.$ How many parts would need to be started to achieve $1000$ parts per day output if a rework station

were added to w$/$s $3$ that converts $80\%$ of the defects into good parts?$123$

d$1$ d$2$ d$3123$

d$1$ d$2$ d$3$

R$1$ R$2$

dR$1$ dR$2$