What is the expected on-hand inventory?

Question

ACold Inc is a frozen food distributor with 10 warehouses across the country. Ivan Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery to ACold’s customers. Since the warehouse carries hundreds of different products, Ivan decided to study one. He picked Caruso’s Frozen Pizza (CFP). Average daily demand for CFPs is normally distributed with a mean of 411 and a standard deviation of 156. Since ACold orders at least one truck from their supplier each day, ACold can essentially order any quantity of CFP it wants each day. In fact, ACold’s computer system is designed to implement an order-up-to policy for each product. Ivan notes that any order for CFPs arrives 5 days after the order.

a. Suppose an order-up-to level of 2478 is used. What is the expected on-hand inventory? Use Table 14.1 and round to nearest integer.

Answer 1

We don't know what table 14.1 looks like and we do not have enough information to calculate the EOQ, the economic ordering quantity.

If we make some assumptions, we do have enough information to calculate the ROP, reorder point inventory, which is the solution that is required.

Given: ACold wants to "minimize inventory while still maintaining quick delivery" quick delivery.

So, daily demand = daily sales = daily inventory.

And, to minimize inventory, inventory varies by 1 standard deviation, a high daily of 567 (411+156=567), a low daily of 255 (411-156=255), with an average daily of 411. The 1 standard deviation means that about 68 percent of inventory data falls between 567 and 255.

ROP = [(DAILY INVENTORY) x (LEAD TIME)] + (SAFETY STOCK).

DAILY INVENTORY = X

LEAD TIME = 5 DAYS.

SAFETY STOCK = 255 UNITS/PIZZAS.

ROP = 2478 UNITS/PIZZAS.

Substituting.

2478 = [5X] + 255, simplifying, 5X = 2223, and X = 444.6, rounded to X = 445.

Is 455 between 567 and 255? Yes, inventory policy is followed.