Question

The daily demand of a product is very stable at 260 units per day. However, its delivery lead time varies and can be specified by a normal distribution with a mean lead time of fourteen days and standard deviation of two days. What are the safety stock and reorder point for a 97.5 percent service level? Do not round intermediate calculations. Round your answer: to the nearest whole number. Safety stock: units Statistical reorder point: units

Answer 1

The reorder point for a 97.5 percent service level is 429 units, with a safety stock of 169 units.

Step-by-step explanation:

To calculate the safety stock, we first need to calculate the reorder point. The reorder point is the lead time demand plus the safety stock. The lead time demand is the average daily demand multiplied by the lead time. In this case, the average daily demand is 260 units and the lead time is normally distributed with a mean of 14 days and a standard deviation of 2 days. To find the reorder point for a 97.5 percent service level, we need to find the lead time demand at the 97.5 percentile of the lead time distribution. Using a Z-table, we can find that the Z-score corresponding to a 97.5 percentile is approximately 1.96. Therefore, the reorder point, which is the lead time demand at the 97.5 percentile, will be 260 units multiplied by (14 + (1.96 * 2)), which is equal to 428.64. Rounding this up to the nearest whole number, the reorder point is 429 units.

The safety stock is the difference between the reorder point and the average daily demand. So, the safety stock will be 429 units minus 260 units, which is equal to 169 units.