Q$1(25$ points$).$ You work for a computer manufacturer. They tasked you to manage the

inventory for a critical part they procure on a regular basis. Historical data and forecasts

indicate a normal distribution for the weekly demand with a mean of $44$ and variance of

$122.$ There is a $4-$week lead time for receiving this part and each part costs $$22.$

Accounting uses $35\%$ interest rate for holding costs estimates a stock$-$out cost of $$155$ per

part and that each order has a fixed cost of $$88$ per order.

a$)(15$ points$)$ Type $1$ Service level$-$based approach: Assuming that the company

wants to use EOQ and achieve a $99\%$ service level in meeting demand, what

would be the order quantity and the reorder point?

b$)(10$ points$)$ What are the average costs related to holding, setup $($ordering$),$ and

stock outs for this inventory control policy.

HINT:

Expected Stockout Per Cycle$=$ n$($R$)=\backslash$sigma dL$*$L$($z$)$ : note the sigma is for demand during

lead time $($or lead time demand$),\backslash$sigma dL $=$sqrt $($L$\backslash$sigma $2$d $+$d$2\backslash$sigma $2$L$)$

L$($z$)=$ NORM.S$.$DIST$($z$,0)-$z$*(1-$NORMSDIST$($z$))$ Standardized Loss Function

Q$2(25$ points$).$ For the same problem in Q$1,$ now we want to take an optimization

approach:

a$)(15$ points$)$ What are the optimal values for order quantity and the reorder point?

b$)(5$ points$)$ What are the average costs related to holding, setup $($ordering$),$ and

stock outs for this inventory control policy. How does it compare to the costs

obtained in Q$1.$

c$)(5$ points$)$ What is the cost associated with uncertainty for this inventory control

process? $($Hint: identify costs without uncertainties and compare$)$

HINT:

n$($R$)=\backslash$sigma dL$*$L$($z$)$ : note the sigma is for demand during lead time $($or lead time demand$)$

$\backslash$sigma dL $=$sqrt $($L$\backslash$sigma $2$d $+$d$2\backslash$sigma $2$L$)$

in Excel you can compute

F$($z$)=$ NORMSDIST$($z$)$Cumulative Normal Distribution

L$($z$)=$ NORM.S$.$DIST$($z$,0)-$z$*(1-$NORMSDIST$($z$))$ Standardized Loss Function