Question

A car dealership uses 1,200 cases of oil a year. The ordering cost is 40, and the annual carrying cost is3 per case. The manager wants a service level of 99 percent. What is the optimal order quantity? What level of safety stock is appropriate if the lead time demand is normally distributed with a mean of 80 cases and a standard deviation of 6 cases?

Answer 1

To determine the optimal order quantity for a car dealership, use the Economic Order Quantity (EOQ) formula. The optimal order quantity is approximately 310.28 cases. To determine the appropriate level of safety stock, consider the lead time demand, which is normally distributed.

Step-by-step explanation:

To determine the optimal order quantity, we can use the Economic Order Quantity (EOQ) formula: EOQ = sqrt((2 * D * S) / H), where D is the annual demand (1,200 cases), S is the ordering cost ($40), and H is the annual carrying cost per case ($3).

Using the given information, the EOQ calculation becomes: EOQ = sqrt((2 * 1200 * 40) / 3) = sqrt(96000) ≈ 310.28 cases.

For the level of safety stock, we need to consider the lead time demand, which is normally distributed with a mean of 80 cases and a standard deviation of 6 cases. We can calculate the appropriate safety stock level using the z-score formula: Safety stock = z * sigma, where sigma is the standard deviation (6 cases) and z represents the desired service level.

To achieve the desired service level of 99 percent (corresponding to 2.33 standard deviations from the mean), the safety stock can be calculated as follows: Safety stock = 2.33 * 6 ≈ 13.98 cases (rounded to 2 decimal places).