The classic EOQ analysis assumes that demand, ordering, and inventory carrying costs are all constant. It also assumes that there are no restrictions on order sizes, and that you do not have to place unusual orders to assure availability.

### Inputs:

This model will accept unit inputs for annual demand and unit cost. It gives the corresponding EOQ recommendation in units and dollars. See the EOQ Input Instruction page for more details.

Input an inventory carrying cost rate. This includes the financial and physical costs of supporting an inventory. This model addresses the “cycle stock”. When the demand forecast is accurate, the cycle inventory peaks just after a receipt and is sold down to zero just before the next receipt. The average cycle inventory investment is one-half the value of the quantity ordered, and that is what is used in this model. Your firm will likely also carry some safety stock inventory, and some systems vary the amount of safety stock for different order cycle times. That variation is not included in this model. The carrying cost may also include allowances for obsolescence, spoilage or damage. There are a number of articles on the Internet for estimating carrying costs. Typical distribution and retail firms use 25-50% of the average annual inventory investment as a carrying cost rate.

Input an order handling cost. This should include all the variable costs of processing one order and shipment, including purchasing, receiving, stocking, accounting, and paying for the order. Some of these costs occur each time your firm creates a purchase order / shipment whether it has one or many skus on it. That might be $10-$50 per order. Additional “per line item” costs are incurred for each additional sku on that order. That might be as low as $1 or so. If you are analyzing just one sku to determine a unit economic order quantity, then use the “per line item” cost. Enter the appropriate amount based on your situation.

### EOQ with Quantity Discounts:

The classic EOQ model does not provide for situations where a quantity discount or other savings are possible. This model has been enhanced to include that. If your firm can earn a discount or have other savings by ordering in a specific amount, enter the amount required to achieve the discount and either the discounted item cost or discount percent. In some cases, this might be a discount provided by a vendor for ordering a specific amount. You should also examine your own costs for potential savings. In our auto parts distribution company, it was more efficient to receive the most popular skus in full pallets. Even though there was no purchase price reduction, our shipment processing costs were lower if we placed a full pallet of one sku into a pallet picking location versus stocking multiple units onto a shelf. A popular air filter or brake rotor might have 100 units on a pallet. We felt we saved about $5 in receiving cost when we received a full pallet of one sku. That effectively reduced our cost by $.05 per unit. The Sample Project is an analysis of this situation, and it shows even this modest savings is enough to suggest purchasing the sample sku in pallet quantities.

Also note that you may choose whether the discount applies only to multiples of the quantity or to all units on an order greater than the quantity.

In the sample case, our savings occurs only when exact pallet quantity orders are handled. For example, if exactly 100 units are a pallet, and we ordered 120, we would only achieve the handling cost savings on the 100 units on the pallet, and we would pay full price and incur full handling cost on the other 20 units. If your situation is like this example, input “Y” in the quantity box.

On the other hand, if a vendor gives a quantity discount for all units on any order over 100 units, then that discount would apply to all units. Input “N” in this box. If you order 120, you’ll achieve the lower cost on all units.

### Output:

The analysis will return the suggested EOQ and a chart of the ordering, carrying, and combined costs. The suggested EOQ can be used as a guideline for ordering.

As you will see from the graphs, the total cost curve is fairly flat around the minimum, so you can (and should) round the exact quantity if a convenient order quantity is close to the exact EOQ.

And, remember that some vendors may require minimum order quantities on some orders. You can still use this model to determine whether the required minimums are greater than your EOQ. You’ll still have to meet your vendor’s restrictions, but this model might give you some ammunition to ask for a vendor concession.

The model computes the “classic” EOQ costs and also the costs and savings including the quantity discount. It will output the lowest cost order size each way and suggest the best. If the quantity savings are sufficient, it will suggest ordering in quantities to achieve those savings.

### Cautions:

This analysis only provides a guideline. You may need to run a number of simulations to determine if your firm can process and handle inventory and shipments based on EOQ ordering.

### Additions:

A number of extensions of the EOQ model have been proposed from time to time. For example, Chuck LaMacchia published an article, “Sizing it up” in the January, 2003 APICS Journal. He cited examples from the office supply industry where the inventory carrying cost should be split into a financial carrying cost and a physical carrying cost. His example contrasted printer cartridges with office chairs. Each might cost about $100, but the carrying cost for the chairs is likely to be higher, as they require much more warehouse space. Others have suggested variations for items with variations in demand or other factors.

If you would like to see models with additional features, or models for other inventory management topics, please contact us with your suggestions.