Daily demand for a product is 120 units, with a standard deviation of 30 units. The review period is 14 days and the lead time is 7 days. At the time of review 130 units are in stock. If only a 1% risk of stocking out is acceptable, how many units should be ordered?
To determine how many units should be ordered, we need to consider the average demand during the lead time along with the desired service level.
First, let's find the average demand during the lead time. The average daily demand is given as 120 units, and the lead time is 7 days. Therefore, the average demand during the lead time is 120 units/day * 7 days = 840 units.
Next, let's calculate the standard deviation of the demand during the lead time. Since the standard deviation of the daily demand is provided as 30 units, the standard deviation of the demand during the lead time is the square root of the product of the lead time and the squared daily standard deviation.
Standard deviation of the lead time demand = sqrt(7 days * 30 units^2) = 60 units.
Now, we need to calculate the safety stock, which is the amount of inventory kept above the average demand during the lead time to account for any fluctuations in demand. We can use the service level and the standard deviation of the lead time demand to calculate the safety stock.
Since a 1% risk of stocking out is acceptable, the desired service level will be 99%, which translates to a Z-score of 2.33 (using a standard normal distribution table).
Safety stock = Z * Standard deviation of lead time demand
= 2.33 * 60 units
= 139.8 units (rounded up to 140 units for practical purposes)
Finally, we can calculate the reorder point, which is the sum of the average demand during the lead time and the safety stock.
Reorder point = Average demand during lead time + Safety stock
= 840 units + 140 units
= 980 units.
Since there are currently 130 units in stock, the quantity to be ordered can be calculated as the difference between the reorder point and the current inventory level.
Quantity to be ordered = Reorder point - Current inventory
= 980 units - 130 units
= 850 units.
Therefore, 850 units should be ordered to maintain a 1% risk of stocking out.