Question

The operations manager at J. Hansen Enterprises, Inc. has a historical sample of demand during the lead-time that is normally distributed. She found that the average daily demand is 70 units and the standard deviation of daily demand is 20 units. Lead time is a constant of 3 days. Answer the following questions based on the above data: What is the safety stock at a cycle service level of 95%? What is the reorder point (ROP) to meet a 95% cycle service level? If the reorder point is 250, what is the cycle service level (CSL)? What is the safety stock at a cycle service level of 90% if the manager utilizes a periodic review model with T = 4 days? What is the safety stock if the lead-time has a mean of 3 days and a standard deviation of 1 day? Use a CSL of 0.95 Assume that there is no demand uncertainty, but only supply uncertainty as noted in # 5 above exists. Daily demand is 70 units. What is the safety stock at CSL of 0.95?

Answer 1

To calculate the safety stock at a cycle service level of 95%, we multiply the z-score for the desired CSL by the standard deviation of the demand during the lead time. The reorder point is calculated by multiplying the average daily demand by the lead time and adding the safety stock. In a periodic review model, the safety stock is also affected by the square root of the review period. If the ROP is known, we can calculate the safety stock by subtracting the product of the average daily demand and the lead time from the ROP. Safety Stock = 1.645 * 1 day = 1.645 days

Step-by-step explanation:

To calculate the safety stock at a cycle service level (CSL) of 95%, we need to calculate the z-score for the desired CSL and then multiply it by the standard deviation of the demand during the lead time. The z-score for a 95% CSL is 1.645. The safety stock is calculated as:

Safety Stock = z-score * standard deviation

Safety Stock = 1.645 * 20 units = 32.9 units

To calculate the reorder point (ROP), we need to multiply the average daily demand by the lead time and add the safety stock. The ROP is calculated as:

ROP = (Average Daily Demand * Lead Time) + Safety Stock

ROP = (70 units * 3 days) + 32.9 units = 243.9 units

If the ROP is 250 units, we can rearrange the equation to solve for the safety stock:

Safety Stock = ROP - (Average Daily Demand * Lead Time)

Safety Stock = 250 units - (70 units * 3 days) = 40 units

For a periodic review model with a review period (T) of 4 days, the safety stock is calculated as:

Safety Stock = z-score * standard deviation * square root of T

The z-score for a 90% CSL is 1.282. The safety stock is calculated as:

Safety Stock = 1.282 * 20 units * square root of 4 days = 25.64 units

If the lead time has a mean of 3 days and a standard deviation of 1 day, the safety stock is calculated as:

Safety Stock = z-score * lead time standard deviation

The z-score for a 95% CSL is 1.645. The safety stock is calculated as:

Safety Stock = 1.645 * 1 day = 1.645 days

If there is no demand uncertainty, the safety stock is not needed, as there will always be enough supply to meet the demand.