$9.$ Management has stated that it will tolerate one stockout per year. The forecast of annual demand for a particular SKU is $100,000$ units, and it is ordered in quantities of $10,000$ units. The lead time is $2$ weeks. Sales history for the past $10$ weeks follows. Calculate:

a$.$ Sigma for the demand history time interval

b$.$ Sigma for the lead time interval

c$.$ The service level

d$.$ The safety stock required for this service level

e$.$ The order point

Prof. A$.$ Wojtus BU$1283$ F$2023$

Week

$1$

$2$

$3$

$4$

Actual Demand

Deviation

Deviation Squared

$2100$

$1700$

$2600$

$1400$

S

$1800$

$6$

$7$

$8$

$9$

$10$

$2300$

$2200$

$1600$

$2100$

$2200$

Total

$10.$ If in problem $9,$ management said that it is increasing the service level to one stockout every $2$ years, what would the new safety stock be$?$ If the cost of carrying inventory on this item is $$10$ per unit per year, what is the cost of increasing the inventory from one stockout per year to one every $2$ years?