Due to different rates for different ordering quantities, we need to compare inv

Question

Due to different rates for different ordering quantities, we need to compare inventory cost for quantities at various levels.

First lets calculate EOQ for quantity < 25 :

EOQ = (2 * Annual Demand * Cost per order)/ (Cost per unit * Holding cost)

EOQ = (2 * 140 * 30)/ (350 * 0.18) = 11.54 12 units

Hence, we see that according to this calculations, the EOQ is 51 units.

This is also logically sound as this is the least amount we need to order to qualify for most discount and any additional quantity in an order would only increase holding costs and total inventory cost.

Order Quantity (q) 12   26 51 No. of Orders (O=140/q) 11.66 5.38 2.74 OC = Ordering Cost (O*30) 349.8 161.4 82.2 HC = Holding Cost (0.18*RespectivePrice*q/2) 378 737.1 1308.15 CP = Cost of Purchase (RespectivePrice*140) 49000 44100 39900 TOTAL INVENTORY COST (OC+HC+CP) 49727.8 44998.5 41290.35

Explanation / Answer

Exercise 10: Parasol Systems sells motherboards for personal computers. For quantities up through 25, the firm charges $350 per board; for quantities between 26 and 50, it charges $315 for each board purchased beyond 25; and it charges $285 each for the additional quantities over 50. A large communications firm expects to require these motherboards for the next ten years at a rate of at least 140 per year Order setup costs are $30 and holding costs are based on an 18 percent annual interest rate. What should be the size of the standing order?

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