Ch$.9\mathrm{.}11$ Prob$)$: A particular workstation has a capacity of $1,000$ units per day and variability is moderate, such that V$=($c

a

$2$

$$

$+$c

e

$2$

$$

$)/2=1.$ Demand is currently $900$ units per day. Suppose management has decided that cycle times should be no longer than $1\mathrm{.}5$ times raw process time. $(20$ pt$)($Hint: Calculation, one machine at this workstation, u$=900/1,000=0\mathrm{.}9)$ a$)$ What is the current cycle time in multiples of the raw process time? $($Hint: Eq$.8\mathrm{.}25$ for CT

q

$$

$,$CT$=$CT

q

$$

$+$t

e

$$

$,5$pt$)$ b$)$ If variability is not changed, what would the capacity have to be in order to meet the cycle time and demand requirements? What percentage increase does this represent? $($Hint: CT to be $1\mathrm{.}5$t

e

$$

$,($

$1$u

u

$$

$+1)=1\mathrm{.}5,$ compute u$,$r

e

$$

$,\%$ increase in TH$,5$pt $)$ c$)$ If capacity is not changed, what value would be needed for V in order to meet the cycle time and demand requirements? What percentage does this represent $($compare CVs$,$ not SCVs$)?($Hint: CT$=1\mathrm{.}5$t

e

$$

$,$CT$=($V

$1$u

u

$$

$+1)$t

e

$$

$,$ find V$,$

V

$$

$,\%$ decrease, $5$pt$)$ d$)$ Discuss a realistic strategy for achieving management's goal. $($Hint: Discuss the increase in capacity vs$.$ the decrease in variability, $5$ pt$)$