An item that is managed with a periodic review system has av

An item that is managed with a periodic review system has average daily demand of 30 units with a standard deviation of 5. The order interval for this item has been set at 30 days. Lead time for this item averages 5 days, with a standard deviation of 0.4 days. Acceptable stockout risk has been established as 2.5%. At the latest count, there are 180 units in inventory. How many units should be ordered?

Solution

Order Quantity in Periodic Review System Q = d*(t_b+L) + z*_L*d- I

d = Daily demand = 30 units

t_b = 30 days

Lead Time L = 5 days

_L = Standard deviation of lead time = 0.4 days

z = 1.96 at 97.5% service level (2.5% stockout risk)

I = Units in inventory = 180

Q = d*(t_b+L) + z*_L*d- I = 30*(30+5) +(1.96*0.4*30) - 180 = 894 (approx)

Hence, 894 units should be ordered.