Optimizing
Economic Order Quantity (EOQ)
By Dave Piasecki
Inventory
models for calculating optimal order quantities and reorder points have been
in existence long before the arrival of the computer. When the first
Model T Fords were rolling off the assembly line, manufacturers were already
reaping the financial benefits of inventory management by determining the most
cost effective answers to the questions of When? and How much?.
Yes long before JIT, TQM, TOC, and MRP, companies were using these same (then
unnamed) concepts in managing their production and inventory. I recently
read Purchasing and Storing, a
textbook that was part of a “Modern Business Course” at the Alexander
Hamilton Institute in New York. The
textbook published in 1931 (that’s right 1931) was essentially a how to book
on inventory management in a manufacturing environment.
If you’re wondering why I would want to read a 70-year-old business
text, my answer would be that the fundamental concepts of managing a business
change very little with time, and reading about these concepts in a vintage
text is a great way to reinforce the value of the fundamentals.
The occasional reference to “The War” (referring to WWI) also keeps
it interesting and the complete absence of acronyms is refreshing.
As
you may have guessed, this 70-year-old book contained a section on Minimum
Cost Quantity, which is what we now refer to as Economic
Order Quantity (EOQ). I can
imagine that in the 1930’s an accountant (or more likely a room full of
accountants) would have calculated EOQ or other inventory related formulas one
item at a time in a dimly lit office using the inventory books, a mechanical
adding machine and a slide rule. Time
consuming as this was, some manufacturers of the time recognized the financial
benefits of taking a scientific approach to making these inventory decisions.
So
why is it that, in these days of advanced information technology, many
companies are still not taking advantage of these fundamental inventory
models? Part of the answer lies in poor results received due to
inaccurate data inputs. Accurate product costs, activity costs,
forecasts, history, and lead times are crucial in making inventory models
work. Ironically, software advancements may also in part to blame. Many ERP
packages come with built in calculations for EOQ which calculate
automatically. Often the users do not understand how it is calculated and
therefore do not understand the data inputs and system setup which controls
the output. When the output appears to be "out of whack" it is
simply ignored. This sometimes creates a situation in which the
executives who had purchased the software incorrectly assume the material
planners and purchasing clerks are ordering based upon the systems
recommendations. I should also note that many operations will find these
built-in EOQ calculations inadequate and in need of modifications to deal with
the diversity of their product groups and processes.
Corporate
goals and strategies may sometimes conflict with EOQ. Measuring
performance solely by inventory turns is one of the most prolific mistakes made in
the name of inventory management. Many companies have achieved
aggressive goals in increasing inventory turns only to find their bottom line
has shrunk due to increased operational costs.
EOQ
is essentially an accounting formula that determines the point at which
the combination of order costs and inventory carrying costs are the
least. The result is the most cost effective quantity to order.
In purchasing this is known as the order quantity, in manufacturing it
is known as the production lot size.
While
EOQ may not apply to every inventory situation, most organizations will find
it beneficial in at least some aspect of their operation.
Anytime you have repetitive purchasing or planning of an item, EOQ
should be considered. Obvious applications for EOQ are purchase-to-stock
distributors and make-to-stock manufacturers, however, make-to-order
manufacturers should also consider EOQ when they have multiple orders or
release dates for the same items and when planning components and
sub-assemblies. Repetitive buy
maintenance, repair, and operating (MRO) inventory is also a good application
for EOQ. Though EOQ is generally
recommended in operations where demand is relatively steady, items with demand
variability such as seasonality can still use the model by going to shorter
time periods for the EOQ calculation. Just
make sure your usage and carrying costs are based on the same time period.
Doesn’t
EOQ conflict with Just-In-Time? While
I don’t want to get into a long discussion on the misconceptions of what
Just-In-Time (JIT) is, I will address the most common misunderstanding in
which JIT is assumed to mean all components should arrive in the exact run
quantities “just in time” for the production run.
JIT is actually a quality initiative with the goal of eliminating
wasted steps, wasted labor, and wasted cost. EOQ should be one of the tools
used to achieve this. EOQ is used to determine which components fit into this
JIT model and what level of JIT is economically advantageous for your
operation. As an example, let us
assume you are a lawn equipment manufacturer and you produce 100 units per day
of a specific model of lawn mower. While
it may be cost effective to have 100 engines arrive on your dock each day, it
would certainly not be cost effective to have 500 screws (1 days supply) used
to mount a plastic housing on the lawn mower shipped to you daily.
To determine the most cost effective quantities of screws or other
components you will need to use the EOQ formula.
The basic Economic Order Quantity (EOQ) formula is as follows:
The Inputs
While
the calculation itself is fairly simple the task of determining the correct
data inputs to accurately represent your inventory and operation is a bit of a
project. Exaggerated order costs and carrying costs are common mistakes
made in EOQ calculations. Using
all costs associated with your purchasing and receiving departments to
calculate order cost or using all costs associated with storage and material
handling to calculate carrying cost will give you highly inflated costs
resulting in inaccurate results from your EOQ calculation.
I also caution against using benchmarks or published industry standards
in calculations. I have
frequently seen references to average purchase order costs of $100 to $150 in
magazine articles and product brochures.
Often these references trace back to studies performed by advocacy
agencies working for business that directly benefit from these exaggerated (my
opinion) costs used in ROI calculations for their products or services.
I am not denying that some operations may have purchase costs in this
range, especially if you are frequently re-sourcing, re-quoting, and/or buying
from overseas vendors. However if your operation is primarily involved with
repetitive buying from domestic vendors
— which is more common
— you’ll likely
see your purchase order costs in the substantially lower $10 to $30 range.
As you prepare to undertake this project keep in mind that even though accuracy is crucial, small variances in the data inputs generally have very little effect on the outputs. The following breaks down the data inputs in more detail and gives insight into the aspects of each.
Annual Usage.
Expressed in units, this is generally the easiest part of the equation. You simply input your forecasted annual usage.
Order Cost.
Also known as purchase cost or set up cost, this is the sum of the fixed costs that are incurred each time an item is ordered. These costs are not associated with the quantity ordered but primarily with physical activities required to process the order.
For
purchased items, these would
include the cost to enter the purchase order and/or requisition, any approval
steps, the cost to process the receipt, incoming inspection, invoice
processing and vendor payment, and in some cases a portion of the inbound
freight may also be included in order cost. It is important to
understand that these are costs associated with the frequency of the orders
and not the quantities ordered. For example, in your receiving department the
time spent checking in the receipt, entering the receipt, and doing any other
related paperwork would be included, while the time spent repacking materials,
unloading trucks, and delivery to other departments would likely not be
included. If you have inbound quality inspection where you inspect a
percentage of the quantity received you would include the time to get the
specs and process the paperwork and not include time spent actually
inspecting, however if you inspect a fixed quantity per receipt you would then
include the entire time including inspecting, repacking, etc. In the
purchasing department you would include all time associated with creating the
purchase order, approval steps, contacting the vendor, expediting, and
reviewing order reports, you would not include time spent reviewing forecasts,
sourcing, getting quotes (unless you get quotes each time you order), and
setting up new items. All time spent dealing with vendor invoices would be
included in order cost.
Associating actual costs to the activities associated with order cost is where many an EOQ formula runs afoul. Do not make a list of all of the activities and then ask the people performing the activities "how long does it take you to do this?" The results of this type of measurement are rarely even close to accurate. I have found it to be more effective to determine the percentage of time within the department consumed performing the specific activities and multiplying this by the total labor costs for a certain time period (usually a month) and then dividing by the line items processed during that same period.
It is extremely difficult to associate inbound freight costs with order costs in an automated EOQ program and I suggest it only if the inbound freight cost has a significant effect on unit cost and its effect on unit cost varies significantly based upon the order quantity.
In manufacturing, the order cost would include the time to initiate the work order, time associated with picking and issuing components excluding time associated with counting and handling specific quantities, all production scheduling time, machine set up time, and inspection time. Production scrap directly associated with the machine setup should also be included in order cost as would be any tooling that is discarded after each production run. There may be times when you want to artificially inflate or deflate set-up costs. If you lack the capacity to meet the production schedule using the EOQ, you may want to artificially increase set-up costs to increase lot sizes and reduce overall set up time. If you have excess capacity you may want to artificially decrease set up costs, this will increase overall set up time and reduce inventory investment. The idea being that if you are paying for the labor and machine overhead anyway it would make sense to take advantage of the savings in reduced inventories.
For the most part, order cost is primarily the labor associated with processing the order, however, you can include the other costs such as the costs of phone calls, faxes, postage, envelopes, etc.
Carrying cost.
Also called Holding cost, carrying cost is the cost associated with having inventory on hand. It is primarily made up of the costs associated with the inventory investment and storage cost. For the purpose of the EOQ calculation, if the cost does not change based upon the quantity of inventory on hand it should not be included in carrying cost. In the EOQ formula, carrying cost is represented as the annual cost per average on hand inventory unit. Below are the primary components of carrying cost.
Interest. If you had to borrow money to pay for your inventory, the interest rate would be part of the carrying cost. If you did not borrow on the inventory, but have loans on other capital items, you can use the interest rate on those loans since a reduction in inventory would free up money that could be used to pay these loans. If by some miracle you are debt free you would need to determine how much you could make if the money was invested.
Insurance. Since insurance costs are directly related to the total value of the inventory, you would include this as part of carrying cost.
Taxes. If you are required to pay any taxes on the value of your inventory they would also be included.
Storage Costs. Mistakes in calculating storage costs are common in EOQ implementations. Generally companies take all costs associated with the warehouse and divide it by the average inventory to determine a storage cost percentage for the EOQ calculation. This tends to include costs that are not directly affected by the inventory levels and does not compensate for storage characteristics. Carrying costs for the purpose of the EOQ calculation should only include costs that are variable based upon inventory levels.
If you are running a pick/pack operation where you have fixed picking locations assigned to each item where the locations are sized for picking efficiency and are not designed to hold the entire inventory, this portion of the warehouse should not be included in carrying cost since changes to inventory levels do not effect costs here. Your overflow storage areas would be included in carrying cost. Operations that use purely random storage for their product would include the entire storage area in the calculation. Areas such as shipping/receiving and staging areas are usually not included in the storage calculations. However. if you have to add an additional warehouse just for overflow inventory then you would include all areas of the second warehouse as well as freight and labor costs associated with moving the material between the warehouses.
Since
storage costs are generally applied as a percentage of the inventory value you
may need to classify your inventory based upon a ratio of storage space
requirements to value in order to assess storage costs accurately. For
example, let's say you have just opened a new E-business called "BobsWeSellEverything.com".
You calculated that overall your annual storage costs were 5% of your average
inventory value, and applied this to your entire inventory in the EOQ
calculation. Your average inventory on a particular piece of software
and on 80 lb. bags of concrete mix both came to $10,000. The EOQ formula
applied a $500 storage cost to the average quantity of each of these items
even though the software actually took up only 1 pallet position while the
concrete mix consumed 75 pallet positions. Categorizing these items
would place the software in a category with minimal storage costs (1% or less)
and the concrete in a category with extreme storage costs (50%) that would
then allow the EOQ formula to work correctly.
There are situations where you may not want to include any storage costs in your EOQ calculation. If your operation has excess storage space of which it has no other uses you may decide not to include storage costs since reducing your inventory does not provide any actual savings in storage costs. As your operation grows near a point at which you would need to expand your physical operations you may then start including storage in the calculation.
A portion of the time spent on cycle counting should also be included in carrying cost, remember to apply costs which change based upon changes to the average inventory level. So with cycle counting, you would include the time spent physically counting and not the time spent filling out paperwork, data entry, and travel time between locations.
Other costs that can be included in carrying cost are risk factors associated with obsolescence, damage, and theft. Do not factor in these costs unless they are a direct result of the inventory levels and are significant enough to change the results of the EOQ equation.
Variations
There are many variations on the basic EOQ model. I have listed the most useful ones below.
· Quantity discount logic can be programmed to work in conjunction with the EOQ formula to determine optimum order quantities. Most systems will require this additional programming.
· Additional logic can be programmed to determine max quantities for items subject to spoilage or to prevent obsolescence on items reaching the end of their product life cycle.
· When used in manufacturing to determine lot sizes where production runs are very long (weeks or months) and finished product is being released to stock and consumed/sold throughout the production run you may need to take into account the ratio of production to consumption to more accurately represent the average inventory level.
· Your safety stock calculation may take into account the order cycle time that is driven by the EOQ. If so, you may need to tie the cost of the change in safety stock levels into the formula.
Implementing EOQ
There are primarily two ways to implement EOQ. Both methods obviously require that you have already determined the associated costs. The simplest method is to set up your calculation in a spreadsheet program, manually calculate EOQ one item at a time, and then manually enter the order quantity into your inventory system. If your inventory has fairly steady demand and costs and you have less than one or two thousand SKUs you can probably get by using this method once per year. If you have more than a couple thousand SKUs and/or higher variability in demand and costs you will need to program the EOQ formula into your existing inventory system. This allows you to quickly re-calculate EOQ automatically as often as needed. You can also use a hybrid of the two systems by downloading your data to a spreadsheet or database program, perform the calculations and then update your inventory system either manually or through a batch program. Whichever method you use you should make sure to follow the following steps:
· Test the formula. Prior to final implementation you must test the programming and setup. Run the EOQ program and then manually check the results using sample items that are representative of the variations of your inventory base.
· Project results. You'll need to run a simulation or use a representative sampling of items to determine the overall short-term and long-term effects the EOQ calculation will have on warehouse space, cash flow, and operations. Dramatic increases in inventory levels may not be immediately feasible, if this is the case you may temporarily adjust the formula until arrangements can be made to handle the additional storage requirements and compensate for the effects on cash flow. If the projection shows inventory levels dropping and order frequency increasing, you may need to evaluate staffing, equipment, and process changes to handle the increased activity.
· Maintain EOQ. The values for Order cost and Carrying cost should be evaluated at least once per year taking into account any changes in interest rates, storage costs, and operational costs.
A
related calculation is the Total Annual Cost calculation.
This calculation can be used to prove the EOQ calculation.
Total Annual Cost = [(annual usage in units)/(order quantity)(order
cost)]+{[.5(order quantity)+(safety stock)]*(annual carrying cost per unit)}.
This formula is also very useful when comparing quotes where vendors
offer different minimum order quantities, price breaks, lead times,
transportation costs.
Use it! The EOQ calculation is "Hard Science", if you have accurate inputs the output is the most cost-effective quantity to order based upon your current operational costs. To further increase inventory turns you will need to reduce the order costs. E-procurement, vendor-managed inventories, bar coding, and vendor certification programs can reduce the costs associated with processing an order. Equipment enhancements and process changes can reduce costs associated with manufacturing set up. Increasing forecast accuracy and reducing lead times which result in the ability to operate with reduced safety stock can also reduce inventory levels.
Also read my article on Calculating Safety Stock
Recommended
Reading:
Richard J, Tersine, Principles of Inventory and Materials Management, PTR Prentice Hall, August 1993
See reviews of above books at the InventoryOps Bookshelf
Inventory Accuracy: People, Processes, & Technology is a comprehensive treatment of Inventory Accuracy and Cycle Counting in distribution, fulfillment, and manufacturing environments. I have long known that many businesses struggle with accuracy and are often unclear as to what they should be doing to improve operations. The interest I have received on the articles I have written related to inventory accuracy inspired me to write what I like to refer to as "the ultimate resource on inventory accuracy." Rather than just writing a little book on cycle counting or bar coding, I decided to write a book that not only comprehensively covers these topics, but also goes beyond bar codes and cycle counts to cover many other key facets of accuracy. For more detailed information, sample pages, and ordering information go to www.accuracybook.com. |
Inventory
Accuracy: People, Processes, & TechnologyDave Piasecki, CPIM is owner/operator of Inventory Operations Consulting LLC, a consulting firm providing services related to inventory management, material handling, and warehouse operations to manufacturers and distributors in Southeast Wisconsin and Northeast Illinois. He has over 15 years experience in warehousing and inventory management and can be reached through his website (http://www.inventoryops.com), where he maintains additional relevant information and links
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