Safety Stock
1. The problem asks whether the safety stock is zero when the desired service level is 50%.
2. Safety stock is extra inventory held to prevent stockouts due to demand variability or supply delays.
3. The formula for safety stock often involves the z-score corresponding to the desired service level: $$\text{safety stock} = z \times \sigma_{demand} \times \sqrt{L}$$ where $z$ is the z-score, $\sigma_{demand}$ is the standard deviation of demand, and $L$ is the lead time.
4. The z-score for a 50% service level is 0 because the 50th percentile corresponds to the mean demand.
5. Therefore, $$\text{safety stock} = 0 \times \sigma_{demand} \times \sqrt{L} = 0$$
6. This means at a 50% service level, safety stock is indeed zero.
Final answer: True