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 maximum inventory?
Multiple Choice
50
100
200
20
80
The Correct Answer and Explanation is:
Let’s analyze the problem step-by-step to find the maximum inventory when Ann Chovies orders 80 pounds of pepperoni at a time.
Given data:
- Daily usage (demand), D=20D = 20 pounds per day
- Order quantity, Q=80Q = 80 pounds
- Lead time, L=3L = 3 days
- Order cost = $10 per order (not needed for this question)
- Holding cost = $0.04 per pound per day (not needed for this question)
- Cost per pound = $3.00 (not needed for this question)
What is maximum inventory?
Maximum inventory refers to the highest amount of inventory present in stock at any point in time, immediately after receiving a new order.
When you order QQ pounds at once, immediately upon receipt of the order, the inventory jumps by the full order quantity. Since Ann orders 80 pounds at a time, the maximum inventory is simply 80 pounds — right after the delivery arrives.
Why?
Inventory decreases steadily as pizza parlour uses 20 pounds daily. When the inventory hits the reorder point (calculated by lead time demand), Ann places a new order of 80 pounds, which arrives after 3 days.
- Reorder point =D×L=20×3=60= D \times L = 20 \times 3 = 60 pounds
This means when the inventory drops to 60 pounds, Ann orders 80 pounds more. During the 3 days of lead time, she uses up 60 pounds. When the order arrives, the inventory jumps back up by 80 pounds, making the new inventory: 60 pounds (existing inventory)−60 pounds used during lead time+80 pounds ordered=80 pounds60 \text{ pounds (existing inventory)} – 60 \text{ pounds used during lead time} + 80 \text{ pounds ordered} = 80 \text{ pounds}
Actually, more simply: right after order receipt, inventory = order quantity Q=80Q = 80 pounds.
Additional context:
- The inventory cycle fluctuates between 80 pounds (maximum) and 0 pounds (minimum) as the pepperoni is used at 20 pounds per day.
- The average inventory is Q/2=80/2=40Q/2 = 80/2 = 40 pounds.
- The reorder point ensures Ann never runs out before the order arrives.
- The order cost and holding cost are relevant for Economic Order Quantity (EOQ) calculations but not directly for max inventory.
Answer:
Maximum inventory = 80 pounds
Summary
In inventory management, the maximum inventory after an order is received is the full quantity ordered. Here, since Ann orders 80 pounds at once, the maximum inventory level is 80 pounds. The reorder point (60 pounds) ensures the new stock arrives just in time, preventing a stockout, but does not affect the maximum inventory, which always equals the order size in a simple EOQ system without safety stock.