Question

We use a Periodic Review system to manage an inventory item for which demand averages 40 units a week with a standard deviation of 14 units. Lead time for this item is 3 units and our order interval is 8 weeks. Our policy is to manage our inventory such that we run not more than a 2.5% risk of a stockout. Suppose we are about to place an order for this item and have determined that our onhand inventory is 400 units. What should our order quantity be? (Round to 2 decimal places and report only the number.)

Answer 1

Using a Periodic Review system with the given data, the calculated order quantity for the inventory item is 131.24 units after rounding to two decimal places.

Step-by-step explanation:

To determine the order quantity for an inventory item using a Periodic Review system, we need to consider the demand, its variability, lead time, review interval, and the desired service level. In this instance, the demand averages 40 units per week with a standard deviation of 14 units, the lead time is 3 weeks, and the review period is 8 weeks. The service level corresponds to a 2.5% risk of a stockout, which implies a Z-score from the standard normal distribution for service level calculation.

Firstly we calculate the average demand during the lead time and review period combined (11 weeks):
Average demand = (Weekly demand × Total weeks) = 40 units/week × 11 weeks = 440 units

The safety stock is calculated using the standard deviation of demand, the combined lead and review period's square root, and the Z-score for the chosen service level. As the Z-score for a 2.5% risk of a stockout roughly translates to 1.96 (from standard normal distribution tables), the safety stock can be computed as follows:
Safety Stock = Z-score × Standard deviation of weekly demand × √(Lead time + Review period) = 1.96 × 14 units × √11 ≈ 91.24 units

Finally, we determine the target inventory level by adding the average demand during the lead time and review period to the safety stock, then subtracting the current on-hand inventory to find the order quantity:
Target Inventory Level = Average demand + Safety Stock = 440 units + 91.24 units = 531.24 units
Order Quantity = Target Inventory Level - On-hand Inventory = 531.24 units - 400 units = 131.24 units

After rounding to two decimal places, the order quantity is 131.24 units.