Ann Chovies,owner of the Perfect Pasta Pizza Parlour,uses 20 pounds of pepperoni each day in preparing pizzas.Order costs for pepperoni are $10.00 per order,and holding costs are 4 cents per pound per day.Lead time for each order is 3 days,and the pepperoni itself costs $3.00 per pound. If she were to order 80 pounds of pepperoni at a time,what would be the average inventory level?

Question

Quizplus · Accepted Answer

First, we need to calculate the annual ordering cost and the annual holding cost for the pepperoni.

Annual ordering cost = (demand/order quantity) * order cost
Since Ann uses 20 pounds of pepperoni each day, her daily demand is 20 pounds. Therefore, her annual demand is:
Annual demand = 20 pounds/day * 365 days/year = 7,300 pounds/year

Ordering cost per order is $10. If Ann orders 80 pounds at a time, she will order:
Order quantity = 80 pounds/order
Number of orders = Annual demand/order quantity = 7,300 pounds/year / 80 pounds/order = 91.25 orders/year
Since Ann cannot order a fraction of an order, she will round up to 92 orders/year.

The annual ordering cost is therefore:
Annual ordering cost = 92 orders/year * $10/order = $920/year

Annual holding cost = (average inventory level) * (holding cost per pound per day) * (days per year)
Since the lead time is 3 days, Ann needs to order the pepperoni 3 days before she runs out, which means that she wants to keep 3 days' worth of inventory on hand.

Average inventory level = (order quantity/2) + safety stock
Safety stock = demand during lead time = 20 pounds/day * 3 days = 60 pounds
Average inventory level = (80 pounds/2) + 60 pounds = 100 pounds

Holding cost per pound per day is 4 cents, or $0.04. The number of days per year is 365.

Annual holding cost = (100 pounds) * ($0.04/pound/day) * (365 days/year) = $1,460/year

The total annual cost (TAC) is the sum of the annual ordering cost and the annual holding cost:
TAC = $920/year + $1,460/year = $2,380/year

If Ann were to order a different quantity of pepperoni, she would have a different annual holding cost and annual ordering cost, and her total annual cost would be different.

To find the optimal order quantity, Ann should calculate the total annual cost for different order quantities and choose the order quantity that minimizes the total annual cost. However, since the question only asks for the average inventory level, we can simply use the formula for average inventory level:

Average inventory level = (order quantity/2) + safety stock
If Ann orders 80 pounds of pepperoni at a time, the average inventory level is:
Average inventory level = (80 pounds/2) + 60 pounds = 100 pounds

Therefore, the best choice is B, an average inventory level of 40 pounds.

Ann Chovies,owner of the Perfect Pasta Pizza Parlour,uses 20 Pounds