1. The unit price of a product is $20. A manufacturer who needs this product has an inventory carrying cost of 30% of unit value per unit per year, and its ordering cost is $10. Annual demand is 450 units with no variability. How many units should this manufacturer purchase each time? What is the time interval between two consecutive purchases (re-order interval)? What is the frequency of ordering (how many times does it order every year)?
2. Quarter-inch stainless-steel bolts are consumed in a factory at a fairly steady rate of 60 per week. There are 52 weeks per year. The bolts cost the plant two cents each. It costs the plant $12 to initiate an order, and holding costs are based on an annual interest rate of 25%. There is no lead-time (instant receipt of orders).
a. Determine the optimal number of bolts for the plant to purchase and the time between orders.
b. What is the annual holding cost and setup (ordering) cost for this item? What is the total cost (holding + setup)?
c. Now, assume that the plant can only order batches of 60 bolts (that is, the order quantity has to be divisible by 60. Determine the minimal total (holding + setup) cost in such case.
d. Compared what you have in (b) and (c), what does this tell you about the EOQ model? Hint: is there a big increase in total cost?
3. Rocky Mountain Tire Center sells 2,000 go-cart tires per year. The ordering cost for each order is $20, and the holding cost is 35% of the purchase price of the tires per year. The purchase price is $20 per tire if fewer than 100 tires are ordered, $16.20 per tire if 100 or more – but fewer than 1,000 – tires are ordered, and $15.50 per tire if 1,000 or more tires are ordered.
a. How many tires should Rocky Mountain order each time it places an order?
b. What is purchase price it gets from the vendor at this order quantity?
c. What is the total cost under this order policy? (Hint: don’t forget the purchase cost).