Question

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 itemâs 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.

Answer 1

Answer:

Check the explanation

Explanation:

The Economic Order Quantity EOQ= SQRT(2*D*Co/Ch),

Where Square root, SQRT, D is the annual demand , Co Cost of order and Ch is the cost of holding

Here annual Demand D =20500

Cost of order Co = 50 $

Cost of holding Ch= 20% of Cost of purchasing = 20%*$14 = $2.8

EOQ = SQRT(2*20500*50/2.8) = SQRT(732142.85) = 855 Units

Minimum TAC can be calculated in two ways

1) With Formula , Minimum TAC = SQRT(2*D*Co*Ch) = $2395.83

2) Without Formula , I.e Cost of Oreder+ Cost of Holding

=(20500/855)*$50 + (855/2)*$2.8 = 2395.83

Where 20500/855 is the number of orders, and 855/2 is the average stock

B) If 500 units purchased at a time

Then Number of orders = 20500/500 = 41 orders in year

Total cost ordering = 41*$50 = $2050

Inventory holding cost = Average inventory * holding cost =

= 500/2*$2.8 = 700

the Total/overall annual cost inventory = $2050+$700 = $2750