Question

A small oil change shop uses an average of 80 litres of 5W40 synthetic ơl per day. Usage tends y be normally distributed with a standard deviation of 8 litres per day. Lead time is four days, and the desired service level is 92 percent. What amount of safety stock is appropriate under each of these conditions:

(i) Oil is reordered every 45 days.

Answer 1

To calculate the amount of safety stock needed for the small oil change shop, we need to calculate the reorder point using the lead time demand and a certain level of safety stock. The appropriate amount of safety stock is approximately 11.28 liters.

Step-by-step explanation:

To calculate the amount of safety stock needed, we first need to calculate the reorder point. The reorder point is the lead time demand plus a certain level of safety stock. In this case, the lead time is 4 days and the desired service level is 92 percent.

To calculate the lead time demand, we multiply the average usage (80 liters per day) by the lead time (4 days) to get 320 liters. To calculate the safety stock, we need to find the appropriate z-score for a 92 percent service level. Using a standard normal distribution table, we find that the z-score for a 92 percent service level is approximately 1.41.

The safety stock is calculated by multiplying the standard deviation (8 liters per day) by the z-score (1.41) and adding it to the lead time demand. The safety stock is approximately 11.28 liters. Therefore, the appropriate amount of safety stock is 11.28 liters.