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SCM $4370$ Forecasting and Inventory Management

HWA $$ EOQ, TAC, Safety Stock, etc.

Name: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

As an intern at Abilene Cracker Distribution Company $($ACDC$),$ you have been asked to

analyze the inventory policies for the company$$s single$-$serve two$-$cracker packages distributed

across Texas, New Mexico and Oklahoma.

Your manager provided you the following worksheet to complete:

$($Your manager provided helpful equations at the bottom of the worksheet $)$

For all questions show your work.

Part A: EOQ, TAC,...

$$ Average demand: $75,000$ cases of crackers per year

$($demand and lead time uncertainty will be addressed in part B$)$:

$$ Cracker cost: $$5\mathrm{.}50$ per case

$$ Each order delivery cost: $$250$

$$ Carrying cost: $26\%($Money spent on crackers has an alternative investment with annual

interest of $26\%)$

$1)$ Calculate the EOQ:

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

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$2$a$)$ Round up your EOQ solution to the whole case and calculate TAC $($$$).$

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$2$b$)$ Round down your EOQ solution to the whole case and calculate TAC $($$$).$

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$2$c$)$ For Q $($EOQ$),$ should you:

$$ Round up to the whole case?

$$ Round down to the whole case?

$$ For this product for ACDC $$ it does not matter.?

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$3)$ How many times per year do you expect to order the single$-$serve cracker package cases?

$($no need to round$)$

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$4)$ What do you expect the average number of days between single$-$serve cracker package cases

will be$?($no need to round$)$

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

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Part B: Safety Stock, etc...

Nothing at ACDC ever quite operates on time and customers can be finicky about when and how

much they order; however, over the years a rhythm has been tracked that when aggregated

among all customers follows a $$predictably$$ random normal distribution.

$$ Average demand: $75,000$ cases of crackers per year $($from part A$)$

$$ Standard deviation of demand: $15,000$ cases of crackers per year

$$ Average lead time: $6$ days

$$ Standard deviation of lead time: $3$ days

$$ Service level: $97\mathrm{.}5\%($ACDC believes in high levels of service and quality$)$

$5)$ How much safety stock should ACDC carry to meet a $97\mathrm{.}5\%$ service level?

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

For the final questions consider the following appropriate assumption for a fixed order

quantity EOQ inventory management system to be true:

$$ Order quantity, Q$,$ from the EOQ equation is equal to cycle stock, CS$,$ for ACDC.

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$6)$ What is the average inventory for the single$-$serve cracker package cases?

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$7)$ What is the reorder point?

Answer: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Official Abilene Cracker Distribution Company One$-$tail Z Statistic Chart

Z$1$tail Stat Service Level Percent Z$1$tail Stat Service Level Percent

$00\mathrm{.}550\%1\mathrm{.}440\mathrm{.}92593\%$

$0\mathrm{.}260\mathrm{.}660\%1\mathrm{.}640\mathrm{.}9595\%$

$0\mathrm{.}530\mathrm{.}770\%1\mathrm{.}960\mathrm{.}97598\%$

$0\mathrm{.}680\mathrm{.}7575\%2\mathrm{.}330\mathrm{.}9999\%$

$0\mathrm{.}850\mathrm{.}880\%2\mathrm{.}570\mathrm{.}995100\%$

$1\mathrm{.}040\mathrm{.}8585\%3\mathrm{.}80\mathrm{.}999100\%$

$1\mathrm{.}290\mathrm{.}990\%$

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Official Abilene Cracker Distribution Company Inventory Equations Catalog

Total Annual Cost $($TAC$)$:

$($dollars$)$

TAC $=$ QVW

$2+$

AR

Q TAC $=$ QS

$2+$

AR

Q

Economic order quantity $($EOQ$)$:

$($units$)$ Q $=2$RA

VW Q $=2$RA

S

R $=$ Annual rate of demand $($# units$)$ W $=$ Carrying cost per dollar value of

Q $=$ Replenishment order qty $($# units$)$ inventory $(\%$ of product value$)$

A $=$ Cost of placing an order $($$$/$order$)$ S $=$ V$*$W $=$ Storage cost $($$$/$unit$/$yr$)$

V $=$ Value of $1$ unit of inv. $($$$/$unit$)$ D $=$ Daily demand

Note: S $=$ V $\backslash$times W

$$ Use V $\backslash$times W if you are provided an item cost and an annual percentage for carrying cost

percentage.

$$ Use S if you are provided and annual $$storage$$ cost per item.

Number of orders per year $=$ R

Q Appx days btw deliv. $=365$ days

num orders year

safety stock $=\backslash$times $$

$\backslash$mu LT

TD

$\backslash$times $\backslash$sigma D

$2+\backslash$sigma LT $\backslash$times

$\backslash$mu D

TD

$$

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Z$1$tail $=$ One$-$tail Z$-$statistic $\backslash$mu D $=$ Average demand $($typically in days,

weeks, months, etc.$)$

$\backslash$mu LT $=$ Average time $($typically in days$)\backslash$sigma D$=$ Standard dev. of demand $($typically in

days, weeks, etc.$)$

$\backslash$sigma LT $=$ Standard deviation of lead time

$($typically in days$)$

TD $=$ Unifies different time units $($the secret

sauce to unifying time unit measuring

differences in demand.$)$

$$ If demand is given in days, TD $=1.$

$$ If demand is given in weeks, TD $=7$

$$ If demand is given in months, TD $=30.$

$$ If demand is given in years, TD $=365$

ROP $=\backslash$mu Ddaily $\backslash$times $\backslash$mu LT $+$ SS Avg Inv $=$ CS

$2+$ SS or

Q

$2+$ SS

ROP $=$ Reorder point $\backslash$mu LT $=$ average lead time

$\backslash$mu Ddaily $=$ average daily demand $$ typically $\backslash$mu D

TD

$($hint $$ divide average annual demand by $365)$

CS $=$ Cycle Stock Q $=$ Order Quantity

SS $=$ Safety Stock