## Executive Summary

- The Economic Order Quantity (EOQ) is normally not analyzed before using it.
- We cover the limitations to EOQ.

## Introduction to the Standard EOQ Formula

The EOQ formula is used to determine order batching. You will learn about the assumptions of the EOQ formula and when it is applicable.

## What is the Standard EOQ Formula?

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.

- Since its introduction, EOQ has been one of the most important and most durable formulas in inventory management.
- It contains some important assumptions of EOQ model that are often undiscussed, but important to using the formula properly.

## George Plossl on the Assumptions of Economic Order Quantity

Economic order quantity is discussed as an important consumption based parameter to set. George Plossl points out in the book *Production and Inventory Control*; there are some important assumptions of economic order quantity which make the use of EOQ valid.

This quotation related to economic order quantity assumptions is listed below:

“The right quantity to order is that which best balances the costs related to the number of orders placed against the costs related to the size of the orders placed. When these costs have been balanced properly, the total cost is minimized. The resulting ordering quantity is called the economic lot-size, or economic ordering quantity (EOQ). The EOQ concept applies under the following conditions: The item is replenished in lots or batches, either by purchasing or manufacturing, and is not produced continuously. Sales or usage rates are uniform and are low compared to the rate at which he item is normally produced, so that a significant amount of inventory results. The EOQ concept does not apply to all items produced for inventory. In a refinery or on an assembly line, for example, production is continuous and there are no lot-sizes as such. The bulk of the jobs in a make-to-order plant are made lot-sizes ordered by the customer. Limited tool life, short shelf life, economical price of raw material and other constraints override the application of EOQ techniques. Nevertheless, the concept has broad application in industry, since most production is not continuous and individual lots of material are being taken from one inventory, processed and then delivered to another inventory.”–George Plossl

## Assumptions of EOQ Model

- EOQ assumptions are critical in determining the applicability of EOQ to a scenario.
- The assumptions of EOQ model are that costs can be traded off. With the standard EOQ formula, the assumptions EOQ model is that holding costs and ordering costs are the costs to be used.

## How to Use the EOQ Formula for Pull Forward or Stock Building

Economic order quantity is one of the oldest formulas in inventory management. However, **it is not an adjustable formula**; unlike the dynamic safety stock calculation, it cannot account for variability.

Therefore, it must be periodically recomputed for the entire product location database.

## When is the EOQ Formula Applicable?

EOQ is used in conjunction with reorder point (see this link for the **Reorder Point Calculator**, and it applies under similar circumstances:

The item is replenished in lots or batches, either by purchasing or manufacturing and is

not produced continuously.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

However, economic order quantity can be used in circumstances where sales vary over the year by changing the EOQ value. This is another reason why it is good to perform an external calculation of supply parameter values in a way that can be adjusted and then uploaded to a system.

## How the EOQ Formula Can be Adjusted before High Periods to Build Inventory

Companies often receive a disproportionate amount of demand in one reoccurring period. The EOQ value can be adjusted and then uploaded to the supply planning system in advance of this increased demand to build inventory to the right level more economically. There are two differences regarding doing this versus using the standard EOQ calculation.

- The timing must be right – that is the larger economic order quantity formula must be calculated sufficiently ahead of the demand increase.
- Add the percent increase to the calculator.

## How the Economic Order Quantity Formula 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 **article.**

## What Economic Order Quantity Can’t Consider

EOQ is designed for stable demand situations. What will follow is a list of scenarios that are anything but steady state, however, EOQ is not the only approach to inventory planning that has difficulty in managing these situations.

## Item 1: Seasonal Production

Many products have a seasonal sales pattern. It is not unusual to see much of the anticipated requirements produced well before the season to keep production fairly level throughout the year. During this inventory building, the inventory that is being added is anticipation inventory, not lot size inventory, and the regular EOQ model does not apply.

Instead of balancing ordering costs against inventory the company is now trying to store man hours. For this reason, many seasonal items are produced in one lot size per year.

## Item 2: Assembly Lot Sizes

Another typical situation encountered in real life is the problem of determining lot sizes for assemblies and their components, and once again the extreme situations present the clearest examples. An assembly composed of unique components not used on other assemblies should have its lot size calculated taking into account all setup costs for the components of the assembly, **and most of the components should be manufactured in the same lot sizes as the assembly**.

## Item 3: Die Life

Costs associated with limitations, such as the life of a die set used in a blanking press, are seldom included in the EOQ formula. The calculated EOQ for an item might indicate that 20,000 units were the most economical lot size, whereas the normal die life might be 30,000 units. Because of the high cost of regrinding, refitting and setting up a die, it is almost always practical to tie the economic lot sizes into the die life.

In this case, the calculated lot size would probably be increased by 50,000 units.

## Item 4: Space Costs

There is no specific allowance in the simple EOQ formula for the fact that the space cost for different items can be very different indeed. Shipping cartons usually have a low unit value, a very attractive discount schedule and take up great amounts of storage space.

On the other hand, electronic components have a very high unit cost and take up very little storage space. Especially with bulky items, an estimate of total space requirements resulting from EOQ calculations is essential.

## Item 5: Actual Run vs. Order Quantities

It has been the author’s experience that ordering quantities indicate on records and the ordering quantities used in the factory can frequently be quite different. Any comparison of new lot sizes with the present order quantities to determine the effects and economies of change should be based on the actual lot amount being processed in the plant, not the amount requested by the production control department.

## Item 6: Hold Points

“Many items are dealt with by a sequence of operations. The ordering cost must then include the sum of the setup costs for all operations. If set up on one of the early operations is a highly substantial proportion of total setup costs, it may be economical to establish an inventory called a hold point beyond this high setup operation.”– Production and Inventory Control: Principles and Techniques

On pulling production forward, this same emphasis is covered with a procedure rather than with EOQ in this **link.**

## How to Best Use the EOQ Calculator with Non-Instantaneous Receipt

There are actually **many EOQ formulas or EOQ model** — each for a different environment and different problem. However, this is the EOQ model that is used in most supply planning systems — although it does not necessarily make it the right EOQ model to use for your business or for different segments of the product location database.

George Plossl brings up this point well in the following quotation:

“Frequently, for example, the entire lot size is not received into stock at once. The manufacturing rate may be such that it takes several days or even weeks for the complete lot to be made and delivered into stock. While production is going on, partial deliveries to stock are made, but withdrawals are also made during the period. Consequently, the average lot size inventory will not equal one half of the lot size, as it does where all the lot is received at once. This situation, given the rather formidable name of non-instantaneous receipt, can be handled by using a modification to the basic EOQ formula.”– Production and Inventory Control: Principles and Techniques

The EOQ model he is referring to replaced the denominator of the inventory carry cost with the inventory carrying cost (as a decimal fraction per dollar of average inventory * (1-the usage rate, in the same units as the production rate divided by the production rate), which is emulated in the form below.

- This modified formulas is not available within any supply planning system I am aware of.
- This is why we have been promoting the concept of calculating EOQ outside of the systems through supply planning parameter optimization and then uploading this to the system as a stored rather than calculated value. This is how to arrive at an optimal order quantity calculator.

## How the EOQ Model Calculation Form, Optimal Order Quantity Calculator 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.

## Specific Problems with Lot Sizes

Specific problems with lot sizes come down to first — determining the exact factors to use, which as described by the previous quotation — is always a question.

Secondly, the factors that are used are not stable as the quantities change. This is explained by George Plossl in the following quotation.

“The use of formulas to calculate “economic” order quantities poses several significant problems. The assumption made in the formula derivations that inventory carrying costs and ordering costs vary uniformly with lot size are generally not valid. These costs cannot be assigned a specific, constant value over a range of lot sizes;this value will vary with the total inventory. Either too large an increase in inventory or too many orders being generated can result from application of the formula.”

Therefore, while ordering costs (and if the item is produced, it is ordering costs setup or changeover costs) are considered the same regardless of the quantities involved. When does this not hold in reality?

To further this point, the estimation of precise changeover costs is quite difficult because it depends on what product is being transitioned to. For instance, observe the following changeover matrix.

## Changeover Table

Product Being Moved From | Product Being Moved To | Changeover Cost |
---|---|---|

Product A | Product B | $250 |

Product B | Product A | $600 |

Product C | Product A | $1200 |

Product A | Product C | $300 |

*Notice that the changeover value depends upon what value is being changed over from and to. However, lot sizing must be set up without knowledge as to what the from and to products are (unless the lot size is computed each time manually). Using an average will not help, although it sounds appealing, as in most situations the average value to too far off of the actual value. *

The following quotation goes a step further and critiques the benefits of dynamic order quantities.

## Dynamic Order Quantities

A dynamic order quantity is just allowing the system to change the quantities ordered rather than ordering the same amount for each order. Dynamic order quantities are most definitely the status quo in how MRP is run in companies.

“Dynamic order quantitiesare a mixed blessing in an MRP environment. While they reflect the most up to date version of the materials plan, they change frequently the item’s component requirements and thus also their planned coverage. A re-computation of a parent planned order quantity will often cause MRP to reschedule component item released orders, in addition to revising planned order quantities and schedules in future periods.

While some nervousness inevitably arises in normal operations, it can be greatly amplified by lot sizing techniques recomputinglot sizes automatically. This can and should be avoided. Many users of MRP systems freeze quantities of planned orders within the span of the cumulative product lead time, so that these orders cannot change gross requirements on lower levels that may be covered by replenishment orders already released.”

## Advice on Enjoying the EOQ Quiz

To see the full screen just select the lower right-hand corner and expand. Trust us, expanding makes the experience a whole lot more fun.

## Conclusion

These are interesting observations that are not brought up with much frequency. George Plossl, one of the deepest thinkers on the topic of MRP and inventory management, apparently placed a high emphasis on reducing nervousness in the plan. I have found it very difficult to get my clients to take this position — whenever possible the preference seems to be to update as frequently as possible.

The history of the development of economic order quantity turns out to be interesting. It’s a story of how a high school educated engineer made of the most enduring contribution to inventory management. But most companies that use EOQ are unaware of the EOQ assumptions of economic order quantity. This leads to things like applying order costs which are too low and reducing EOQ’s overall usefulness.

There are in fact many economic order quantity formulas to choose from each with different EOQ assumptions. Therefore, if one does not fit the EOQ assumptions of the requirements, another EOQ formula can be used.

The vast majority of applications only provide a small number of economic order quantity formulas to choose from, but any EOQ formula can be calculated outside the system and imported.

- EOQ can only see the fundamental trade-off between inventory cost and order cost — therefore to account for different scenarios, it must be adjusted.
- A common misperception is that these issues listed above are handled by more sophisticated methods. In a few cases (such as with seasonality & space costs) this can be true — but in actual live systems, it is almost always not the case. In fact, it can be easier and more straightforward to account for these factors through parameter calculation as is explained our application the Brightwork Explorer.

## Being Part of the Solution: Our Evolution of Thinking on Maintaining Inventory Parameters

Maintaining inventory parameters like rounding values and lot size in systems in comes with a number of negatives that tend to not be discussed. One issue is that when using ERP systems, inventory parameters are typically managed on a “one by one” basis. This leads to individual planners entering values without any consideration for how inventory parameters are set across the supply network. After years we have given up managing safety stock or other inventory parameters in we now calculate inventory parameters in our application, the **Brightwork Explorer**, and then simply upload the data into the ERP system. See our link below. We have developed a SaaS application that sets the inventory parameters that allows for simulations to be created very quickly. These parameters can then be easily exported and it allows for far more control over the parameters. In our testing, the approach, which is within the Brightwork Explorer is one of the most effective methods for managing planning in any system. This approach is laid out in the book **How to Repair Your MRP System**.

This allows EOQ to be calculated along with **other inventory parameters**, and for the overall values to be calculated as part of the overall product location database, and to be consistent with either service levels or days of supply settings, which are set at a strategic level and that apply per product location. See the link below.

### Brightwork MRP & S&OP Explorer for Order Optimization

## Order Sizing and Optimization

Order optimization is necessary in order to get the predicted value from ERP and other supply planning applications. The Brightwork MRP & S&OP Explorer does exactly this, and it is free to use in the beginning until it sees “serious usage.” It is permanently free to academics and students. See by clicking the image below:

### What We Do and Research Access

## Using the Diagram

Hover over each bullet or plus sign to see more explanation. To move to a different bullet point, just “hover off” and then hover over the new bullet.

## References

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

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

I cover EOQ and other consumption settings in the following book.

### 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