Final answer:
To determine how many units should be ordered, we can use the reorder point formula. In this case, the reorder point is 2,428.67 units. To determine the order quantity, we subtract the current stock of 70 units from the reorder point, which gives us an order quantity of 2,359 units.
Step-by-step explanation:
To determine how many units should be ordered, we can use the reorder point formula:
Reorder point = (Average demand per day * Review period) + Safety stock
In this case, the average demand per day is 160 units, the review period is 15 days, and the lead time is 2 days. The safety stock is the desired service level multiplied by the standard deviation of demand during the lead time. Since a 90 percent service probability is desired, the safety stock can be calculated as 1.28 (from the z-table for the desired service level) multiplied by the standard deviation of 20 units and multiplied by the square root of the lead time of 2 days.
Safety stock = 1.28 * 20 * sqrt(2) = 28.67 units
Therefore, the reorder point is:
Reorder point = (160 * 15) + 28.67 = 2,428.67 units
To determine the order quantity, we can subtract the current stock of 70 units from the reorder point:
Order quantity = Reorder point - Current stock = 2,428.67 - 70 = 2,358.67 units
Since we cannot order a fraction of a unit, we should round up the order quantity to the nearest whole number:
Order quantity = 2,359 units