Final answer:
The Gap store carries a safety stock of 50 jeans to achieve its current cycle service level. To increase the CSL to 95%, the store manager must recalculate the safety stock and ROP based on the corresponding z-score for a 95% confidence level in the standard normal distribution.
Step-by-step explanation:
The weekly demand for jeans at a Gap store is normally distributed with a mean of 100 and a standard deviation of 50. The Gap store reorders jeans when the inventory drops below 350. The safety stock the store carries is calculated by subtracting the product of the lead time demand and the mean demand from the reorder point (ROP). The lead time demand here is 3 weeks, so 3 weeks * 100 jeans/week = 300 jeans. The ROP is 350, hence the safety stock is 350 - 300 = 50 jeans.
The cycle service level (CSL) is the probability that demand during the lead time will not exceed the on-hand inventory. The store currently aims for a CSL that corresponds to the reorder point of 350 jeans, but to target a higher CSL of 95%, we need to calculate the appropriate safety stock level for a higher z-score (since CSL corresponds to the area under the normal distribution curve to the left of the reorder point). We can find the z-score for 95% in the standard normal distribution table and calculate the required safety stock accordingly.
If the store manager wants to achieve a 95% CSL, they need to determine the z-score corresponding to 95% in the standard normal distribution and then use it to calculate the required safety stock. This involves finding the number by which 50 (the standard deviation) should be multiplied, such that when added to the mean lead time demand (300), the total meets or exceeds 95% of the demand distribution. The resulting figure will be the new safety stock, and the sum of the mean lead time demand and this new safety stock will be the updated ROP.