Final answer:
To calculate the order quantity, the target inventory level is found by adding the total demand over the lead time and review period to the safety stock. The safety stock is calculated using a z-score associated with a 2.5% stockout risk. The order quantity is the target inventory level minus the on-hand inventory, which results in an order quantity of 821.16 units.
Step-by-step explanation:
To determine the order quantity for the inventory item, we need to calculate the target inventory level first and then subtract the on-hand inventory from this target. The target inventory level is the sum of the average demand during the lead time and review period plus the safety stock needed to ensure we only have a 2.5% risk of a stockout.
First, we calculate the average demand over the lead time plus review period:
- Average weekly demand = 110 units.
- Lead time in weeks = 3 weeks.
- Order interval (review period) = 7 weeks.
- Total demand over period = (lead time + review period) × average weekly demand = (3 + 7) × 110 = 1100 units.
Next, we calculate the safety stock using the z-score associated with the 2.5% stockout risk, which corresponds to a z-score of approximately 1.96 for the upper-tail (from standard normal distribution tables).
- Standard deviation of weekly demand = 13 units.
- Safety stock = z-score × standard deviation of demand over period = 1.96 × 13 × √(3 + 7) = 121.16 units (rounded to 2 decimal places).
Therefore, the target inventory level is:
Total demand + Safety stock = 1100 + 121.16 = 1221.16 units.
Subtracting the on-hand inventory:
Order quantity = Target inventory level - On-hand inventory = 1221.16 - 400 = 821.16 units.
Hence, the order quantity should be 821.16 units (rounded to 2 decimal places).