Home Depot purchases shovels made by a supplier in China. Home Depot’s stores in the United States sell 200,000 units of shovels each year. Assume a constant demand rate. Each unit costs $10 and the company has an annual holding cost of 20% of the unit cost per unit. Placing a replenishment order incurs clerical costs of $500/order. The shipping company charges $5,000 as a fixed cost per shipment.
a. What is the optimal order size for Home Depot? How many orders per year does Home Depot place?
b. What is the annual cost of each type for the optimal policy (ordering (set up) cost, holding cost, and purchasing costs)? What is the annual total cost for the optimal policy?
c. Suppose they want to decrease their lot size to 25,000 units in order to decrease inventories. By how much should they reduce their fixed order cost (clerical costs plus fixed transportation cost) for an order size of 25,000 units to be optimal?