## Executive Summary

- We cover the Economic Order Quantity formula and the applicability of the Economic Order Quantity and EOQ and perishability and quantity discounts.
- EOQ can be calculated for both production and procured products.

## Introduction: The Origins of the 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. Since its introduction, EOQ has been one of the most important and most durable formulas in inventory management. You will learn about the calculation of EOQ, reorder points and the other factors which are included into the calcuation of EOQ.

## What is the Reorder Point?

The reorder point tells the system when to reorder, while the economic order quantity tells the system how much to order; as such they are necessarily highly integrated values. EOQ is one method for performing what is generally known as lot sizing. The lot size is the quantity in which the item is produced or procured and therefore it is set at the production location combination in the product master.

## Common Methods of Lot Sizing

Common methods of calculating the lot size are the following:

*Lot for Lot:*This is confusingly named because lot for lot is simply a lot size based upon the net requirements in a particular period. Therefore it is essentially no lot size. Using lot for lot sizing would be considered Lean as the company is only producing or procuring what it absolutely knows that it needs.*Economic Order Quantity:*This bases the lot size on a financial calculation.*Periodic Order Quantity:*This is simply the economic order quantity, but stated in terms of a reorder frequency.

## The Applicability of the Economic Order Quantity

Some have proposed that because EOQ does not automatically adjust with the variability of its inputs, it cannot be used for more product location combinations (PLC’s) 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 product location database. It would be relatively easy to make the EOQ formula continuously altered based upon changes on its inputs, but I have yet to see this functionality in any supply planning application.

## Validity and Applicability of EOQ

EOQ was originally developed for a production lot sizing. However, the book Factory Physics states the following with respect to EOQ:

“For example, in 1913, Harris published his original EOQ paper and established a precise mathematical standard for efficiency research with his famous “square root formula” for the lot size problem. While elegant, this formula relied on assumptions that – for manyreal worldproduction systems – were highly questionable.”

- A fixed, known setup cost
- Constant deterministic demand
- Instantaneous delivery (infinite capacity)
- A single product or no product interactions

“Because of these assumptions, EOQ makes much more sense applied to purchasing environments than to the production environment for which Harris intended it. In a purchasing environment, setups (i.e. purchase orders) may adequately be characterized with constant costs. However in manufacturing systems, setup costs cause all kinds of other problems (e.g., product mix implications, capacity effects, variability effects). The assumptions of EOQ completely gloss over these important issues.”

*This is the very well-known sawtooth pattern, which is a feature of the stocking level rising to its highest point when a new procurement order is received or a new production order is completed, and with the stocking level declining to its lowest point right before the procurement order is received or right before a new production order is scheduled. The minimum stock level should be the safety stock, which the inventory level may consume due to variability in demand or supply.*

EOQ actually has a number of slight adjustments to the formula used to account for different requirements, like the calculator included at this **article** which calculates an EOQ in the case where the company wants to build inventory.

## EOQ and Perishability

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 formula 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, where 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 increased costs through shorter production runs. However, this does not seem to have much influence with companies because they cannot quantify how their production costs change from changing the length of production runs.

Therefore, philosophy rather than facts tends to rule the day with a much greater focus being placed in inventory and storage costs rather than production costs. Although, this greatly depends upon the company. Some companies work exactly the opposite, focusing very little on reducing inventory and being primarily focused on minimizing procurement costs through buying in very large and uneconomic quantities. The question becomes quite a bit more grey for procured items where the costs to be traded off are quantity discounts and order costs.

## Using Economic Order Quantity Formula in Live Systems

After EOQ’s calculation, it is most often placed into the minimum order quantity field which all supply planning systems have. This sets the minimum order level. However, sometimes other factors that are larger than this – such as when products must be purchased in rail carloads, set the actual minimum order level. In that case, no EOQ calculation is necessary. The minimum order quantity is the carload.

While the formula is one of the easiest in supply chain to calculate, many companies do not determine their unconstrained products (that is unconstrained by minimum order sizes such as with the example of the carload, or minimum package quantities) on the basis of EOQ. However, there really is no reason aside from work effort to not do so – and in fact, the work effort is quite low.

## Economic Order Quantity and Forecast Error

The higher the forecast error, the less use the EOQ value is. This is because as the forecast error increases, the likelihood that the quantity will be consumed declines. However, this is no 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 $9,245. However, if the quantity discount kicks in at 200 units and this discount is 15%, then 16 more units could be obtained for $8,538. This would be a missed opportunity. This can be easily calculated for an individual item, but this cannot 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 increase the orders to meet the discount.

## How Often is EOQ Actually Calculated?

For whatever reason, most companies don’t get around to calculating EOQ or, if they do calculate it, they do so very infrequently. Students at university are often told that EOQ is frequently used in industry, when in fact it isn’t (this is just one of the misrepresentations of supply chain management on the part of college courses and supply chain textbooks). But this does not mean that it should not be used. EOQ certainly adds value and quantifies and then trades off the most important costs for making an ordering decision. That is the truth of how understaffed supply chain management departments are. They often do not have the staffing to apply elementary inventory management techniques that are over 80 years old.

## Deriving EOQ Order Cost or Cost Per Order

If the item in question is procured than the standard term order cost or cost per order which is often used with the EOQ formula is correct.

## EOQ For Procured Items

EOQ is often first introduced to people as the order cost or cost per order from a supplier. If you discuss this topic with companies, you will often hear order costs around $12 discussed. In fact, there are many web pages that estimate the ordering cost in the low teens. This is inaccurate and does not show appreciation for what the EOQ formula represents.

The order cost or cost per order for EOQ is supposed to moderate the number of orders that companies place, which means that the order cost or cost per order includes all the costs of placing the order. This includes not only the cost of placing the order in the system (which is the lowest cost portion of the order) but also the cost of receiving the order. The cost of moving the order into stock. The cost of tracking the order and following up if the order is not delivered, etc.. For this reason, once all the total ordering cost is considered, that is the cost of the initial order.

That is all the way to put away, an order cost of between $60 to $75 seems reasonable for many items. However, certain items can be much higher than this. Larger, more difficult items to manage should receive greater economies of scale in receipt and put away than smaller items. Once you move to ordering extremely large units, such as industrial equipment, the order cost or cost per order rises again. But on the other hand, as a percentage of the cost of the item, the order cost or cost per order cost may decline.

## EOQ Internally Produced Items

If the EOQ is being calculated for an internally produced item, then the order cost or cost per order 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.

## EOQ and Production Planning

If the item in question is procured, then 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. This is because what is called the ordering cost is really just the total costs for initiating the replenishment. Unfortunately, few companies have realistic costings for their changeovers. Therefore, it usually takes some time to develop these costs.

## Conclusion

Order cost or cost per order estimation is tricky, and no one can say exactly what an ordering cost is for a particular item. Companies can use variable order cost or cost per order to change depending on the product.

One thing for certain is that the order cost or cost per order that is often presented on websites on the topic does not represent what the EOQ is meant to represent regarding the total order cost or cost per order.

To calculate the EOQ formula online, see our EOQ Calculator at this** article.**

Also, learn about the limitations of EOQ at this **article.**

### Brightwork MRP & S&OP Explorer

## References

### Lean and Reorder Point Planning Book

## Lean and Reorder Point Planning: Implementing the Approach the Right Way in Software

### A Lost Art of Reorder Point Setting?

Setting reorder points is a bit of a lost art as company after company over-rely upon advanced supply planning methods to create the supply plan. Proponents of Lean are often in companies trying to get a movement to Lean. However, how does one implement Lean in software?

### Implementing Lean in Software

All supply planning applications have “Lean” controls built within them. And there are in fact some situations where reorder points will provide a superior output. With supply planning, even within a single company, it is not one size fits all. The trick is understanding when to deploy each of the approaches available in software that companies already own.

### Are Reorder Points Too Simple?

Reorder points are often considered to be simplistic, but under the exact circumstances, they work quite well.

There are simply a great number of misunderstandings regarding reorder points – misunderstandings that this book helps clear up.

Rather than **“picking a side,”** this book shows the advantages and disadvantages of each.

- Understand the Lean Versus the MRP debate.
- How Lean relates to reordering points.
- Understand when to use reorder points.
- When to use reorder points versus MRP.
- The relationship between forecastability and reorder points.
- How to mix Lean/re-order points and MRP to more efficiently perform supply planning.

### Chapters

- Chapter 1: Introduction
- Chapter 2: The Lean versus MRP Debate.
- Chapter 3: Where Supply Planning Fits Within The Supply Plan
- Chapter 4: Reorder Point Planning
- Chapter 5: Lean Planning.
- Chapter 6: Where Lean and Reorder Points are Applicable
- Chapter 7: Determining When to use Lean Versus MRP
- Chapter 8: Mixing Lean and Reorder Points with MRP-Type Planning

EOQ is calculated in supply planning systems.