EOQ with Quantity Discounts


Demand per year


Cost of placing an order, per order


Annual Inventory Holding Cost: as percentage of item cost


Per Unit Cost of Item


EOQ With Quantity Discount Solution

EOQ =  

EOQ with Quantity Discount Formula

The economic order quantity formula is:

EOQ = √ (2DS) / (IC)


D is the Demand of the product per unit of time

S is the cost of placing the order

I represents annual inventory holding cost as percent of item total cost

C is unit cost of the item

**Note that D and H must be for the same period of time (i.e. months, years, etc).

What is Economic Order Quantity with Quantity Discounts

When considering quantity discounts to determine the EOQ, it is essentially the same formula, but rather than H (holding cost) you evaluate the cost of the item (C) and multiply it by the inventory holding cost of the item as a percent of the cost on an annual basis.

Quick Reference

EOQ Epiphany
December 20, 2013

What is Economic Order Quantity?

Economic Order Quantity is also often referred to as EOQ. It is the optimal number of units to purchase when taking into consideration how many units are sold in a given period of time and the cost to order each unit with holding costs. One important assumption with this model is it assumes a constant rate of demand with no stockouts (stockouts are lost profit and lost sales!). Demand is fairly easy to establish, as we look at the number of past sales in a given period of time, and this is our projection for future demand (there are more complex formula's for forecasting demand and we will touch on them in later articles). The cost of placing an order is determined based on how much time is invested in placing the order; employee time making the order, doing the research, etc. Holding cost, also referred to as carrying cost, is based on how much it costs the company to hold unsold units in inventory. Holding costs include the space the product takes up on the shelves, in the warehouse, money spent and tied up in buying the goods (with interest charges), shrink loss, damage, etc. While there are a large number of industries that use the EOQ model for purchasing decisions, the model is more accurate for some than others.

The Sandbox for Solving Problems

Sample Problem

ABC Pipe buys many pipe fittings and they all have a fairly stable demand, with an average demand for 2" couplings per a year being 2,400 units. The manufacturer charges ABC Pipe $3 per unit delivered to their facility (FOB destination). When the inventory of these 2" couplings reaches the reorder point, the purchasing department must place a new order. The estimated cost to place the order is $1.25; which takes into consideration the processing, receiving, and distribution costs. ABC Pipe has determined that the holding cost of the couplings is $0.60 per unit. What is the EOQ for this problem?
D: 2,400
S: $1.25
H: $0.60
*Note: The $3 figure was just put in there to throw you off!...
In this problem, the EOQ is 100 units. This actually works out perfect because the couplings are sold in 100 unit boxes, so the vendor doesn't have to break up a box... another factor to consider when making EOQ purchases. Some vendors will charge for breaking a box, and some will give order discounts for purchasing box quantities. This simple EOQ model doesn't take into consideration these factors, but they will be addressed in another article and have a different calculator and formula.


Sample EOQ Problem

The Stapler Co.

The Stapler Co. wants to find the optimum order point for the screw they use to complete their manufacturing process. They manufacture approximately 830,000 staplers per a year, and one screw is required per stapler. Demand is fairly stable. When inventory of these screws reaches the reorder point, the purchasing department must place a new order. The estimated cost to place the order is $26.50; which takes into consideration the cost of time to process the order, receive the screws and stock them in the warehouse. The holding cost of the screws is $0.03 per unit. What is the EOQ for this problem?

D: 830,000
S: $26.50
H: $0.03

In this problem, the EOQ is 38,292 screws.