The Central Hydraulic Supply Company is a distributor of hydraulic supplies in Central California. 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. Central stocks parts that are used in the maintenance of large construction equipment. The company operates 52 weeks per year, 6 days per week.
Central has grown from a small two-person operation to a $75-million per year business in a span 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 21,840 of these fittings per year (each fitting is purchased for $14 and is sold 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 the supplier has a 4 day lead time and that the standard deviation of daily demand is 15 units. What is the necessary reorder point to achieve a 96% service level?