Final answer:
The reorder point including safety stock is calculated by adding the safety stock to the average demand during lead time. With a standard deviation of 5, a stockout risk of 3%, and an average demand of 117 units, the reorder point rounds to 126 units.
Step-by-step explanation:
Calculating Reorder Point with Safety Stock
To calculate the reorder point including safety stock for normally distributed demand during lead time, first, we need to establish the average demand and the variability, which is often measured by the standard deviation. In this case, the average demand during lead time is 117 units, and the standard deviation is 5 units. The reorder point is calculated as the sum of the average demand during lead time plus the safety stock, which accounts for demand variability and the desired service level corresponding to the stockout risk that a company is willing to accept.
For a stockout risk of 3%, we refer to a z-score from the standard normal distribution that corresponds to 97% of the demand being satisfied (100% - 3% stockout risk). This z-score can be found in a standard z-table or by using statistical software and is approximately 1.88. To calculate the safety stock, multiply this z-score by the standard deviation of the demand during lead time. Therefore, the safety stock is 1.88 * 5 = 9.4 units, which we round to 9 units for practical purposes.
Finally, to find the reorder point, we add the safety stock to the average demand during lead time: 117 + 9 = 126 units. This is the level of inventory at which a new order should be placed to maintain the desired service level and minimize the risk of stockouts.