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Form of an Economic Order Quantity (EOQ) model that takes into account quantity discounts. Quantity discounts are price reductions designed to induce large orders. If quantity discounts are offered, the buyer must weigh the potential benefits of reduced purchase price and fewer orders against the increase in carrying costs caused by higher average inventories.

Hence, the buyer’s goal in this case is to select the order quantity that will minimize total costs, where total cost is the sum of carrying cost, ordering cost, and purchase cost:  

Total Cost = Carrying Cost + Ordering Cost + Purchase Cost
  = C ×(Q/2)+ O(D/Q)+ PD

where C= carrying cost per unit, O= ordering cost per order, D= annual demand, P= unit price, and Q= order quantity.

The Quantity Discount Model takes into consideration of the fact that the purchase cost of an item can vary with the order size. There are two types of quantity discounts: those given on an incremental basisand those given for all units.

With the incremental approach, the quantity discount only applies to those units above a certain level. For example, the cost of a product is $65 per unit for quantities between 1 and 100 and $60 per unit for quantities over 100 units. We determinate that we want to buy this product in quantities of 250 units at a time.

With the incremental approach, we would pay $65 for the first 100 units and $60 for rest of the 150 units.

But, with the all units approach, we would pay $60 a piece for all the 250 units. Thus, the unit cost is determined by the size of the purchase order.

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