Question

A product with an annual demand of 1,000 units costs . The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with mean = 25 and σ=5

(a) What is the recommended order quantity?
(b) What are the reorder point and safety stock if the firm desires at most a 5% probability of stock-out on any given order cycle?

Answer 1

To determine the recommended order quantity, use the EOQ formula. To calculate the reorder point and safety stock, consider the lead-time demand and desired probability of stock-out.

Step-by-step explanation:

To determine the recommended order quantity, we need to consider the demand variability and the desired probability of stock-out. The recommended order quantity can be calculated using the EOQ formula: Q = sqrt((2DS)/H), where Q is the order quantity, D is the annual demand, S is the ordering cost, and H is the holding cost. To calculate the reorder point and safety stock, we need to consider the lead-time demand and desired probability of stock-out using the normal distribution.

(a) Recommended order quantity:

Q = sqrt((2 * 1000 * C) / H)

(b) Reorder point:

Reorder point = Lead time demand = mean * Lead time

Safety stock = Z * sqrt(Lead time * variance)

Z = Z score corresponding to the desired probability of stock-out