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 60 units with a standard deviation of 2. The order interval for this item has been set at 10 days. Lead time for this item averages 5 days, with a standard deviation of 0.5 days. Acceptable stockout risk has been established as 2.5%. At the latest count, there are 480 units in inventory. How many units should be ordered?

Solution

Considering safety limit is set at 2.5% means expected service level is 97.5%

So Z at 97.5% = 2.74778

Safety limilt during 10 days review period = sqrt (10) * Z * Standard deviation = sqrt(10) * 2.74778 * 2 = 17.38

Review period demand = review period * average demand + safety stock = 10 * 60 + 17.38 = 617.38

Safety stock during lead time = sqrt (lead time) * Z* std dev. = sqrt(5) * 2.74778 * 0.5 = 3.07

Demand during lead period = Lead time * daily demand + safety stock during lead time

Demand during lead period = 5 * 60 + 3.07 = 303.07

ROP = Review period demand + Demand during lead period

ROP = 617.38 + 303.07 = 920.45 ~920

Since current inventory is at 480 units which is below reorder point, we have to order 920 + 480 = 1400 units.