Question: Mike's Garage, a local automotive service and repair shop, uses oil filters at a fairly steady rate of 2,400 per year. Mike estimates that the cost of his time to make and process an order is about $50. It takes one month for the supplier to deliver the oil filters to the garage, and each one costs Mike $5. Mike uses an annual interest rate of 25 percent to compute his holding cost.
a. Determine the optimal number of oil filters that Mike should purchase, and the optimal time between placement of orders.
b. Determine the level of on-hand inventory at the time a reorder should be placed.
c. Assuming that Mike uses an optimal inventory control policy for oil filters, what is the annual cost of holding and order setup for this item?