Question

annual demand for a particular halogen bulb is 4500 at a business that operates 300 days per year. the cost per order $160 and the holding cost per unit per year is $4.9. the stockout cost is $30/unit. the lead time is 15 days, and demand during lead time follows the empirical distribution given in the following table. number of units probability 90 0.05 135 0.1 180 0.2 225 0.3 270 0.2 315 0.1 360 0.05 what is the average demand during lead time? report as a whole number. what is the average stockout per inventory cycle with a safety stock of 90? round, if necessary, to two decimal digits. what is the stockout cost associated with a safety stock of 90 per inventory cycle? round to a whole number. what is the number of inventory cycles, i.e. number of orders, in a year? round to a whole number. what is the annual stockout cost associated with a safety stock of 90 ? round to a whole number.

Answer 1

The average demand during lead time is 243 units. The average stockout per inventory cycle with a safety stock of 90 is zero units. The stockout cost associated with a safety stock of 90 per inventory cycle is zero.

Step-by-step explanation:

The average demand during lead time can be calculated by multiplying each number of units by its corresponding probability and summing the results. Using the data given, the calculation would be:

(90 * 0.05) + (135 * 0.1) + (180 * 0.2) + (225 * 0.3) + (270 * 0.2) + (315 * 0.1) + (360 * 0.05) = 243 units

The average stockout per inventory cycle with a safety stock of 90 can be calculated by subtracting the average demand during lead time from the safety stock. Therefore, the calculation would be:

90 - 243 = -153 units

Since the result is negative, it means there will always be enough stock to meet demand during lead time, resulting in no stockouts.

The stockout cost associated with a safety stock of 90 per inventory cycle will be zero since there are no stockouts.

To calculate the number of inventory cycles, we can divide the annual demand by the order quantity. The order quantity can be calculated by dividing the annual demand by the number of orders per year. Using the given data, the calculation would be:

4500 / (4500 / 160) = 300 orders

The annual stockout cost associated with a safety stock of 90 can also be zero since there are no stockouts.