Question

The manager at Goodstone Tires, a distributor of tires in Illinois, uses a continuous review policy to manage inventory. The manager currently orders 10,000 tires when the inventory of tires drops to 6,000. Weekly demand for tires is normally distributed, with a mean of 2,000 and a standard deviation of 500. The replenishment lead time for tires is two weeks. Each tire costs Goodstone $40, and the company sells each tire for $80. Goodstone incurs a holding cost of 25 percent. How much safety inventory does Goodstone currently carry? At what cost of understocking is the manager’s current inventory policy justified? How much safety inventory should Goodstone carry if the cost of understocking is $80 per tire in lost current and future margin?

Answer 1

Goodstone Tires currently carries a safety inventory of 2,000 tires by deducting the expected demand during lead time from the reorder point. The cost of understocking needed to justify the current policy is not given, but if it's $80 per tire, the current safety inventory level may be justified based on the lost margin from not being able to sell those tires.

Step-by-step explanation:

The student's question deals with inventory management in the context of a tire distribution business, specifically related to safety inventory, understocking costs, and inventory policies. To calculate the safety inventory that Goodstone Tires currently carries, we need to consider the reorder point and the base stock level. Given that the manager orders 10,000 tires when the inventory drops to 6,000, we infer that the reorder point is 6,000 tires. Subtracting the expected demand during lead time (which is 2,000 tires per week x 2 weeks = 4,000 tires) from the reorder point gives us the safety inventory (6,000 - 4,000 = 2,000 tires).

To justify the manager's current inventory policy, we would need to compare the safety inventory to the cost of understocking. The cost of understocking is not provided, which means we cannot directly assess whether the current policy is justified. However, if the cost of understocking is $80 per tire, equal to the lost margin on the sale of each tire, Goodstone should carry safety inventory sufficient to cover the risk of stockouts. This aligns with the lost sales due to understocking, which would justify maintaining the current level of safety inventory at 2,000 tires, or adjust it up or down based on the specific cost of understocking.