Question

An Automotive warehouse stocks a variety of spare parts that are sold at neighborhood stores. One part, an oil filter, is purchased by the warehouse from an overseas supplier for $1.50 each. It is estimated that the cost of purchase order processing, receipt, inspection, and put away is $100 per order. The company uses an inventory holding cost of 28% per year. The monthly demand for the part is random, normally distributed with mean 280 units and standard deviation of 77 units. The replenishment lead time from the supplier is 5 months. Assume that if a part is demanded when the warehouse is out of stock, the demand is back-ordered (the customer waits), and the cost assessed for each back-ordered demand is $12.80 per unit, the cost of expediting a unit.

Consider an alternative supplier. The replenishment lead time from this new supplier would be 1 month. By how much (percentage) would safety stock decrease?
A -35%
B -85%
C -55%
D -75%

Answer 1

To calculate the decrease in safety stock, we need to compare the lead times and the demands. The decrease in safety stock would be 80%, which is closest to option B: -85%.

Step-by-step explanation:

To calculate the decrease in safety stock, we need to compare the lead times and the demands.

The daily demand can be calculated by dividing the monthly mean of 280 units by 30 (assuming 30 days in a month), which gives us approximately 9.33 units.

The standard deviation of the demand per month can be converted to a standard deviation per day by dividing it by the square root of 30, which is approximately 4.44 units.

The current safety stock is calculated by multiplying the lead time of 5 months by the daily demand, which is 5 * 9.33 units = 46.65 units.

With the new supplier, the lead time is 1 month, so the new safety stock would be 1 * 9.33 units = 9.33 units.

Therefore, the decrease in safety stock would be (46.65 - 9.33) / 46.65 * 100% = 80%, which is closest to option B: -85%.