You operate a service firm that has three important maintenance, repair, and operating $($MRO$)$ supplies

that it carries in stock, each of which has independent demand. A perpetual review system is used for

all three items, and they can be ordered at any time. The firm operates $360$ days per year. The

following information is available regarding each item, including the breakdown for any quantity

discounts that are available:

Item: $123$

Purchase $$3\mathrm{.}50$ if Q$<200$ $$\mathrm{.}80$ if Q$<500$ $$3\mathrm{.}20($no discounts$)$

Price $$3\mathrm{.}48$ if $2002000$

$$3\mathrm{.}45$ if Q$>800$

Stockout Cost: $$5/$unit $$1/$unit $$20/$unit

Order Cost: $$20$ $$15$ $$42$

Holding Cost Rate: $35\%35\%35\%$

Sample Daily $16,19,10,9,22,23,24,20,19,21,15,21,19,19,14,$

Demands: $25,7,17,14,15,27,30,18,23,23,23,24,20,19,18,$

$18,11,12,20,2526,2219,17,16,21,15,$

$20,21,21,19,19$

Sample Lead Times: $1,5,3,10,8,6,5,10,9,11,7,9,11,12,10,$ Constant $3$ days

$4,6,6,5,4,9,1,210,11,9,8,10,10,12,$

$11,10,9,11,10$

a$.(15$ points$)$ Determine the best order quantity for each item, using the applicable Excel spreadsheet in

Canvas $(5$ points each$).$ Attach a copy or screenshot of the spreadsheet for each item after your

answer sheet$($s$)$ for this question.

b$.(30$ points$)$ Determine the optimal safety stock levels for all three items $(10$ points each$).$

c$.(15$ points$)$ Determine the total annual inventory related costs $($order costs, holding costs, and

purchase costs$)$ for all three MRO items $(5$ points each$),$ given the decisions already made in the

previous parts to this question. Show specifically how you computed order costs, holding costs, and

purchase costs for each individual item.

d$.(15$ points$)$ Determine the average number of units each year that company employees will find

stocked out when needed.

$5$

e$.(15$ points$)$ Suppose that your supervisor has indicated that they would like an inventory policy that

yields an average of $100$ units short per year for item $2.$ What would be $(1)$ the implied stockout cost

per unit, $(2)$ the implied number of lead times each year during which the retailer would experience a

stockout, and $(3)$ the maximum inventory level generated by such a policy