Problem $2$: Inventory Management $(35$ points total$)$

Part $1$: Assessing the inventory level at the Perfect Pasta Pizza Parlor

Ann Chovies, owner of the Perfect Pasta Pizza Parlor is interested in doing a better job of

calibrating her inventory policy for pepperoni, one of the most important ingredients she uses to

prepare her delicious pizzas.

Overall, she uses $5000$ pounds of pepperoni in a year in preparing pizzas. Order costs for

pepperoni are $$10$ per order, and carrying costs are $$10$ per pound per year. Lead time for each

order is three days, and the pepperoni itself costs $$3$ per pound.

$($a$)(2$ points$)$ Given these values, what is the optimal order quantity for pepperoni?

$($b$)(3$ points$)$ What is the total cost of this optimal policy including the price of the pepperoni?

$($c$)(2$ points$)$ If the owner assumes a fixed, constant demand of $20$ pounds per day and the

supplier has a fixed, constant lead time of $3$ days. What is the Re$-$order Point?

$($d$)(2$ points$)$ How much safety stock is required with these assumptions?

$($e$)(2$ points$)$ What is the cost of that Safety Stock?

$($f$)(3$ points$)$ The owner is concerned that the management team is not perfectly modeling

their daily demand and might be missing out on sales as a result. Thus, she decided to

tackle further the demand distribution of pepperoni and found out that it averages $19$

pounds$/$day with a standard deviation of $2.$ Using this information, and the fact that the

supplier's lead time is fixed and constant at $3$ days, what is the new reorder point if they

would like a $97\mathrm{.}5\%$ service level?

$($g$)(2$ points$)$ How much safety stock is required when including the variability of demand?

$($h$)(2$ points$)$ What is the additional cost incurred by the company due to this safety stock?

$($i$)(3$ points$)$ What is the total cost of the inventory policy with variable demand including the

price of the products and the additional safety stock cost?

$($j$)(2$ points$)$ What should Ann Chovies do $-$ should they carry safety stock or not? Justify

your answer with at least two arguments.

Part $2$: Looking further into the pizza leftovers

After assessing the model used in part $1,$ Ann Chovies, found out that he is missing the assessment

of pepperoni leftovers. In fact, they can purchase the pepperoni from a distributor for $$3$ per pound

and sell it within a week $($before the expiry date$)$ for $$4$ per pound. Ann Chovies and her staff eat

any pepperoni leftovers.

$($a$)(2$ points$)$ Which type of inventory model should we use?

$($b$)(2$ points$)$ In these conditions, what is the optimal service level that Ann Chovies should

target?

$($c$)(2$ points$)$ Assuming that, as mentioned above, demand for pepperoni follows a normal

distribution with a mean of $19$ pounds$/$day and a standard deviation of $2,$ what is the

optimal pepperoni weight $($in pounds$)$ that Ann Chovies should stock?

$7$

$($d$)(2$ points$)$ In $2023,$ Ann Chovies discovered that Dr$.$ Nader and her VIP team were working

on waste management and they were willing to buy the pepperoni leftovers for $$1$ the

pound. Aiming at encouraging the circular economy, Ann Chovies signed a recycling

contract with Dr$.$ Nader. What would become the new optimal pepperoni quantity $($in

pounds$)$ that Ann Chovies should stock?

$($e$)(2$ points$)$ Name one positive and one negative aspect in terms of the buy$-$back policy?

$($f$)(2$ points$)$ Now that the demand for pepperoni pizzas is considerably increasing, Ann

Chovies took the decision to not accept a stockout risk more than $1\%.$ Accordingly, as a

consultant, Dr$.$ Nader had to adjust her buy$-$back policy to avoid losing the agreement with

Ann Chovies. Would you help her out to identify the new discount price $($i$.$e$.$ salvage$)$

should she offer to Ann Chovies?