A product with an annual demand of 1000 units has C 0 = $25.50 and C c = $8. The

Question

A product with an annual demand of 1000 units has C0 = $25.50 and Cc = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with = 25 and = 5.

a) What is the recommended order quantity?

b) What are the reorder point and safety stock if the firm desires at most a 2% probability of stock-out on any given cycle?

c) If the manager sets the reorder point at 30, what is the probability of a stock-out on any given cycle? How many times would you expect a stock-out during the year if this reorder point were used?

Explanation / Answer

a) Recommended order quantity is calculated by EOQ model = 2*D*Co/Cc) = (2*1000*25.5/8) = 80   (in this eq, D is annual demand)

b) For 2% stockout, service level = 1-2% = 0.98

z value for 0.98 service level = NORMSINV(0.98) = 2.054

Safety stock = z* = 2.054*5 = 10.3

Reorder point = µ + z* = 25 + 10.3 = 35.3

d) For reorder point set at 30,

µ + z* = 30

z = (30-25)/5 = 1

Corresponding Service level = NORMSDIST(z)

= NORMSDIST(1) = 0.8413

Probability of stockout on any given cycle = 1 - 0.8413 = 0.1587 or 15.87%

Number of orders per year = D/Q = 1000/80 = 12.5

Expected number of stockouts per year = number of orders per year * Stockout prob = 12.5*0.1587 = approx 2 stockouts per year

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