Question

Dolce & Gabanna manufactures a special product, which requires 0.001 grams of copper per unit. The entity sells 50 million units of this item annually. The product is sold for $125 which includes a 20% mark-up by management. The cost of planning and placing an order is $7.50 per hour which usually takes 5 hours. The annual holding cost is 10% of unit cost of the special product and the purchase price for one gram of copper is $60. Currently, the entity orders twenty times per year. However, management was advised that if the current lot size was doubled, the entity would receive a discount of 2 ½%. If the current lot size was four times more a discount of 5% would be granted, meanwhile a 10% discount would be offered for increasing the current lot size by five times.

Required:

(a) Calculate the economic order quantity (EOQ).

(b) Calculate the total cost of the raw material at EOQ.

(c) Calculate the total cost for the alternative order policy (including the current lot size).

(d) Indicate to management the optimal order quantity.

(e) Give three reasons why it is important that management do not overstock.

(f) Define the terms reorder level, inventory and buffer stock.

Answer 1

The annual demand of product = 50 MM units. Each unit requires 0.001 gms of Copper. Hence Annual demand for copper = A = 0.001 * 50,000,000 = 50,000 gms. Ordering cost = S = 7.5*5 = $37.5. Holding Cost = c = 10% of unit cost. Unit cost = 125*100/120 as the product is sold at a markup of 20% at $125

EOQ = Q = Sqrt(2*A*S/c) = 600 gms

At EOQ The total inventory cost is twice the average inventory holding cost = Q*c = 2*3125 = 6250

Currently there are 20 orders in the year. This results in an order quantity of 50000/20 = 2500 gms. Hence total costs = 20*37.5 [Ordering Costs] + 2500*0.1*100*125/(120*2) = 13770.83

The optimal order quantity is 600 gms. Any increase from this would cause an increase in inverntory costs and hence should not be considered as it would not be enough to offset the costs at these percentages being offered.