Economic Order Quantity Calculator

by Shaun Snapp on April 10, 2014

What This Article Covers

  • Introduction to Economic Order Quantity
  • The Uses of Economic Order Quantity
  • When EOQ is Applicable
  • Using Economic Order Quantity in Production Systems
  • The Relationship Between the EOQ and the Forecast Error
  • EOQ and Quantity Discounts
  • EOQ and Production Planning and Setup Costs
  • How the Calculation Form Works
  • The Economic Order Quantity Calculator

EOQ

Introduction to Economic Order Quantity

Economic order quantity (EOQ) is one of the oldest formulas in inventory management. It was first developed by Ford W. Harris in 1913 (interestingly, as with the development of MRP, the originator of EOQ was not an academic). EOQ is not an adjustable formula, unlike the dynamic safety stock calculation, it has no ability to account for variability. Some have proposed that this means it cannot be used for more product location combinations (PLCs) with more variable demand history — and this is true — if the data provided to the EOQ is not periodically changed. Therefore, it must be periodically recomputed for the entire database.

Using Economic Order Quantity in Production Systems

After calculation it most often placed into the minimum order quantity field. This sets the minimum order level. However, sometimes other factors such as the larger than this level — such as when products must be purchased in rail car loads. In that case, the no EOQ calculation is necessary. The minimum order quantity is the car load.

While the formula is one of the easiest in supply chain to calculate, many companies do not determine their unconstrained (that is unconstrained by minimum order sizes such as with the example of the car load, or minimum package quantities) products on the basis of EOQ. However, there really is no reason aside from work effort to not do so. The fact is, most companies don’t get around to calculating EOQ or if they do calculate it they do so very infrequently. Students are often told that EOQ is used in industry very frequently — when in fact it isn’t. But this does not mean that it should not be — it certainly adds value and quantifies and then trades off the most important costs for making an ordering decision. That is the truth of how lean the staffing is in supply chain management, they do not have the staffing the apply elementary inventory management techniques that are over 80 years old.

While it would be easy to place this into supply planning systems in the parameters of  the product record, it is generally not done. Software vendors tend to assume that companies will periodically calculate the value externally.

This is the standard relationship between cycle stock and safety stock with a stable order quantity. The inventory is reduced by orders — hopefully only occasionally dipping into safety stock. 

When EOQ is Applicable

EOQ is used in conjunction with reorder point (see this link for the reorder point calculator http://www.scmfocus.com/supplyplanning/2014/04/09/dynamic-reorder-point-calculator/), and it applies under similar circumstances:

  1. The item is replenished in lots or batches, either by purchasing or manufacturing, and is not produced continuously.
  2. Sales or usage rates are uniform and are low compared to the rate at which the item is produced, so a significant amount of inventory results. – Production and Inventory Control: Principles and Techniques

This second point brings up the topic of when the product is perishable. There can be scenarios where the shelf life of the product does not allow for the full EOQ to be ordered. In this case, the EOQ should not be used, and the shelf life time – converted into units, should be used instead. (Silver and Peterson) The same issue applies to products that go through frequent revisions, and ordering the EOQ would or could result in significant obsolescence. EOQ must also be managed versus storage capacity. In general storage capacity is less expensive than accepting increase costs through shorter production runs, but the question becomes more grey for procured items where the costs to be traded off are quantity discounts and order costs. 

Either products with a low ability or high forecast-ability are suitable for using EOQ  and reorder points. http://www.scmfocus.com/demandplanning/2010/06/forecastable-non-forecastable-formula/

Economic Order Quantity and Forecast Error

The higher the forecast error the less use the EOQ value is. This is because was the forecast error increases, the likelihood that the quantity will be consumed declines. However, this is not different from any other supply planning parameter. Supply planning parameters have the highest value when the forecast is most accurate.

EOQ and Quantity Discounts

If there are quantity discounts, the calculation below will not be accurate. For instance, the formula below may propose an EOQ of 184 units. If the price per each at this level is $50 then this is a total cost of (184 * $50) + 45 or $9245. However, if the quantity discount kicks it at 200 units and this discount is 15% then 16 more units could be obtained for $8538. This would be a missed opportunity. This can be easily calculated for an individual item, but this can not really be systematized because supply planning applications do not have EOQ functionality or even step function min lot sizes. Typically this is handled by procurement as they are up to date on the volume discounts and will up the orders to meet the discount.

EOQ and Production Planning

If the item in question is procured than the standard term “ordering cost” which is often used with the EOQ formula is correct. However, if the EOQ is being calculated for an internally produced item, then the order cost becomes the “ordering and setup/changeover cost.” This is the cost of changing the line over to a new product. Unfortunately, few companies have costings for their changeovers. Therefore, this usually takes some time to develop these costs. 

How the Calculation Form Works

This form requires input to provide output. However, it also has default values. You can change any input value and the rest of the formula — the output will change immediately. You can continue making changes and the form will always update without having to press any button or refresh.


This calculator assumes that the location receives the entire order at one time. However, this assumption does not always hold. For the non instantaneous receipt EOQ calculator see this link: http://www.scmfocus.com/supplyplanning/2014/04/20/economic-order-quantity-calculator-noninstantaneous-receipt/

References

Plossl, George W. Production and Inventory Control: Principles and Techniques, Second Edition. Prentice Hall, 1985.

Plossel, George. Orlicky’s Material Requirement’s Planning. Second Edition. McGraw Hill. 1984. (first edition 1975)

Harris. Ford W. How Many Parts to Make at Once. Factory, The Magazine of Management. 1913. 

Silver, Edward A. Peterson, Rein. Decision Systems for Inventory Management and Production Planning. Second Edition. John Wiley and Sons. 1985.  

Shaun Snapp

Shaun Snapp is a long time supply chain planning software consultant, author & as well as the Managing Editor at SCM Focus. He focuses on both SAP APO as well as best of breed applications for demand, supply and production planning.

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