Final answer:
To calculate the reorder point for an item in a continuous review inventory system, consider the average demand during the lead time and add the calculated safety stock. For the elastic band with a 99% service level, the reorder point would be greater than 750 but less than or equal to 850 boxes.
Step-by-step explanation:
The student is asking about determining the reorder point for an item in a continuous review inventory system with a high service level. The reorder point is calculated by taking into account the average demand, the lead time, the variability in demand, and the desired service level.
Calculation of the Reorder Point To calculate the reorder point, the formula is:
- Average demand during lead time
- Plus safety stock to account for variability and desired service level.
The safety stock can be calculated using the standard deviation and the z-value that corresponds to the desired service level:
- Multiply the demand standard deviation by the square root of the lead time.
- Look up the z-value for a 99% service level (approximately 2.33).
- Multiply this z-value by the result from step 1 to get the safety stock.
- Add the safety stock to the product of the average demand and lead time.
For the values given:
- Average demand = 200 boxes/week
- Lead time = 3 weeks
- Standard deviation = 50 boxes/week
- Service level = 99%, z-value ≈ 2.33
The calculation is as follows:
- Average demand during lead time = 200 × 3 = 600 boxes
- Safety stock = 50 × √3 × 2.33 ≈ √3 × 116.5 ≈ 201.8 boxes
- Reorder point = 600 boxes (demand during lead time) + 201.8 boxes (safety stock) ≈ 801.8 boxes
Thus, the reorder point for the elastic band is greater than 750 boxes but less than or equal to 850 boxes, which corresponds to option a.