Question

A jeans company uses denim in its manufacturing process. The daily demand for denim is normally distributed with a mean of 4000 metres and standard deviation of 600 metres. The lead time required to receive an order of denim from the textile mill is a constant seven days. What is the reorder point (including safety stock) if the company wants to limit the probability of a stock out to 5% ?

Answer 1

To calculate the reorder point (including safety stock) for the jeans company, consider the lead time and desired level of service. Calculate the safety stock using the z-score for the 5th percentile of a standard normal distribution. Add the safety stock to the mean demand to find the reorder point.

Step-by-step explanation:

To determine the reorder point (including safety stock) in this scenario, we need to consider the lead time and the desired level of service. The lead time is constant at seven days, and the desired level of service is 5%. To calculate the safety stock, we need to find the z-score corresponding to the 5th percentile of a standard normal distribution, which is approximately -1.645. Using the formula: Safety Stock = Z * Standard Deviation * Lead Time, we can calculate the safety stock as follows: Safety Stock = -1.645 * 600 * 7 = -7270.5 meters. The reorder point, including safety stock, is the mean demand plus the safety stock: Reorder Point = Mean Demand + Safety Stock = 4000 + (-7270.5) ≈ -3270.5 meters. However, reorder points cannot be negative in practical situations, so the reorder point would be zero meters. Therefore, the company should reorder when the demand reaches zero meters to limit the probability of a stock out to 5%.