The Central Hydraulic Supply Company is a distributor of hydraulic supplies in the Midwest. Central handles standard fittings, tubing, and similar items. Generally Central carries an entire product line for each manufacturer it represents providing local stock for rapid delivery to customers. The parts that Central stocks are mainly used in the maintenance of large construction equipment. The company operates 52 weeks per year.

Central has grown from a small two-person operation to a $75-million per year business in a si of 25 years. From its inception Central has been a profitable business in sound financial condition. Despite the continued growth of profits in absolute terms, however, Central found that profits as a percentage of sales have declined. When management became aware of the seriousness of the problem, it was decided to undertake a thorough review of policies and procedures in the area of inventory management.

One of the first items the company reviewed was the cost of preparing and processing a requisition, preparing a purchase order, and making necessary record changes. This was estimated to be $50 per order.

One of the typical items of inventory analyzed in detail was a small hydraulic fitting. Central sells about 20,500 of these fittings per year (the fitting is purchases for $14 and sells for $19). The manufacturer from whom Central buys the fitting does not offer any quantity discount. The manufacturer is located about 1,500 miles away and the fittings are shipped to Central by truck.   They all arrive at once.

The annual per unit inventory holding cost is 20% of the item’s value.

A) What is the order quantity that minimizes total annual cost of inventory (TAC)? What is the minimum TAC?

B) Suppose that the supplier of the fittings only has the capacity to deliver the fittings at the rate of 500 per week. Recalculate the optimum order quantity and the minimum TAC.