Why Your Economic Order Quantities Are Not Very Economic

Originally published by MHD Supply Chain Solutions (May/June 2017):

Economic Order Quantities, the inventory order quantities which minimise annual supply chain carrying and receiving costs, are very useful in supply chain optimisation. Nonetheless, too frequently its key inputs, carrying and receiving cost, are incorrectly calculated yielding unnecessary and wasteful additional supply chain costs. By redefining how the inputs of Economic Order Quantities are determined, your organisation can cut costs while maintaining and improving on all other supply chain performance metrics.

Introduction

There’s a good chance that if your company has a supply chain it is using a derivation of the Economic Order Quantity (EOQ) calculation somewhere in its decision-making process, and if not, it probably should be! EOQ is an order quantity which minimises the total opportunity cost of the business by balancing costs associated with inventory flow and storage, and is used in both distribution and manufacturing industries. Inventory receiving (flow) costs are labour cost associated with placing and receipting orders where carrying (storage) costs are those which increase with inventory on hand. Variations of EOQ calculations have been utilised by organisations in search of reduced inventory costs for at least 100 years, with Harris Ford publishing his paper on EOQ’s titled ‘How Many Parts to Make at Once’ in 1913, and the fundamental benefits offered are still just as relevant today. However, even companies that use EOQs are often unknowingly not minimising the costs associated with flow and holding. This issue stems from the unconscious combination of two very different decision making processes, how to manage fixed costs and how to manage variable costs. This article seeks to address the common misconceptions and flaws in calculating the two primary components of an item’s EOQ; Carrying Cost and Receiving Cost.

The Economic Order Quantity Formula

EOQ calculations are typically used by organisations to determine how much of an item to order. The basis of calculating EOQ assumes that the item will be stocked, it is just a question of what quantity orders should be placed in to minimise their annual supply chain costs. Obtaining this lowest cost order quantity is based on locating the lowest cost point on the inventory cost curve, which is discussed and redefined later in this paper. To date, the most basic form of the EOQ Formula is often represented as follows:

Where Annual Carrying Costs is the cost associated with holding an item of inventory on-hand and is typically represented as a percentage of unit cost. Receiving Cost is the cost per order of an item, represented as a dollar value, and is unrelated to the order quantity. 

Though there are a number of derivations of EOQ, the fundamental inputs, Receiving Cost and Carrying Cost should be the same – but what you may be using could be very different to what you should be using – a quick Google search will show many ways of calculating these fundamental inputs, but which is correct?

The Common Misconception

The common misconception with Receiving and Carrying costs is that they are associated with total annual costs rather than total variable annual costs. The question of whether or not the item should be stocked at all, or whether or not an organisation should even be in a line of business at all, does not and should not come into EOQ calculations.

In most facets of business, total cost is represented as the summation of fixed and variable costs. Supply chain costs are no different and are classified here as:

Total Supply Chain Cost = Fixed Supply Chain Costs + Variable Supply Chain Costs

Making this distinction, and separating out total supply chain cost in this way, makes it easier to see that only varying components of item cost should be considered when deciding how much of something to order and hold.

The majority of physical infrastructure, equipment and employment costs required to do business are “fixed” in the near-term. These costs include most labour, power, amenities and management time cost. Under normal circumstances, fixed costs do not vary significantly throughout the year and are unrelated to the quantity of inventory held at any point in time.

Variable supply chain costs include Carrying Costs and Receiving Costs. Carrying Costs vary depending on inventory levels, they rise as inventory levels increase and fall as inventory levels decrease. Receiving Costs vary with the frequency in which orders are placed and receipted. In general, only a small percentage of physical infrastructure, equipment and employment costs are variable and associated with Receiving and Carrying costs.

When it comes to determining how much to order to minimise operating costs (using the EOQ), fixed costs should not be considered - as the replenishment decision-making process has no effect on the outcome of fixed costs. Fixed costs are sunk and should not influence the day-to-day operating of the business to maximise profit. Even with no stock on hand, fixed costs still need to be paid. Therefore, only the variable cost components of Receiving and Carrying Cost should influence the net inventory position and only these variable costs should be considered when calculating EOQs. For the mathematically inclined, this is explained in further detail at the end of this article.  

Utilising only variable cost components for Carrying and Receiving Cost calculations is the process of separating out two very independent questions, one is strategic, the other is tactical:

1. What supply chain network infrastructure and workforce should I have in place to service my product range? (Fixed Costs)
2. What quantities should I order my stocks in to meet my targeted service levels at minimum cost? (Variable Costs)

By utilising only variable costs in EOQ calculations, it is likely an organisation will achieve lower overall total supply chain cost while maintaining all other present supply chain targets and characteristics. So how do you accurately calculate Receiving and Carrying Costs?

Calculating Carrying Cost

For order quantity decision making, Carrying Costs should be calculated as follows:

As indicated by the equation, Carrying Cost is the summation of every cost which increases with increasing inventory on hand, divided by the average inventory value over the same period. The Weighted Average Cost of Capital (WACC) is then added to account for the incremental business cost required to acquire an extra dollar to hold inventory.

Approach

Theoretically, Carrying Cost could be broken down and determined for every SKUL (Stock Keeping Unit by Location). Practically however, select groupings of Carrying Cost are calculated by aggregating similar items and locations. Often this will include a unique carrying cost for DCs, stores and ‘bulky’ or perishable products, and the groupings can be broken down further wherever there are considerable variations in carrying cost (such as by region). The approach and level of detail to which Carrying Costs are calculated is very organisation specific and will be influenced by available data and accounting methods. 

Weighted Average Cost of Capital (WACC)

WACC is typically in the range of 9-15% and is influenced by the level and rates of debt and equity a company uses to finance its business. WACC is the only component of Carrying Cost which is not related to average on-hand inventory value.

Average On-hand Inventory Value

Average on-hand inventory value is the dollar value of inventory on hand averaged over the period in which the Variable Annual Holding Costs are assessed (typically one year).

Variable Annual Holding Costs

Variable Annual Holding Costs should comprise the following cost components:

Insurance Cost

Total insurance costs for each ‘grouping’ which is directly related to that location’s value of inventory. Other insurance costs such as ‘fixtures and fittings’ insurance should not be included here as they are fixed costs.

Storage Costs

Storage costs include any costs which are attributable to areas which are only required to hold variable stock levels. Storage cost are often subject to miscalculation as companies will sum all their storage costs into the Carrying Cost equation, including those which do not vary with changing inventory levels. This approach dramatically overstates storage costs and results in incorrect EOQ calculations. In order to find the percentage of storage costs which are attributable to varying stock levels, determine the percentage of a location’s variable stock holding area out of the whole location area. 

The variable stock holding area includes:

• Excess storage areas for DCs
• Offsite overflow storage areas
• Miscellaneous store room areas
• Any ‘purely random’ product storage areas.

The variable stock area is often in the ballpark of 15% total location area and should not include:

• Fixed pick/pack stocking locations in DCs (typically, a large portion of DC area)
• Office spaces, cafeterias and amenities
• Stock packing, unloading and shipping areas.

Once the percentage of total storage cost attributable to variable cost is determined, it should then be multiplied by the total annual storage cost for a location to determine the variable storage cost attributable to inventory holding. The total annual storage cost includes:

If there are significant offsite storage areas, it is worth adding the additional Labour time spent managing these areas. This can also include stock stored in ‘difficult to access’ locations – such as over-shelves and in back storage rooms, as there is additional labour and time required to move these items back to their ‘shippable’ locations. Where any warehousing is outsourced, the variable cost component should also be accounted for.

Typically, the variable component of storage costs is about 10-20% total site costs, and includes: 

But what if my company outsources warehousing?

Outsourced warehousing is typically charged on a per pallet basis and for movements (ins and outs) in addition to storage. Therefore, the costs can be taken as is, on a volume basis. Ignore any fixed baseline expenses if applicable.

Calculating Receiving Costs

For order frequency decision making, Receiving Cost should be determined as:

Receiving Costs include labour time costs that are purely associated with the order and receipt process and are typically assessed over a one-year period. As higher order frequencies result in a net increase in processing times, Receiving Cost should be calculated based on the percentage of time various departments spend on activities related to the purchasing of goods. 

Approach

Receiving Costs should include time spent which related to the frequency of order placement, payment and receipt. If the frequency of ordering does not impact employment time usage, it should not be included. Ask the question; if these orders were not being placed, would this time still be required? If so it is a fixed cost and should not be included.

Just like the Carrying Cost calculations, best practice Receiving Cost calculations only observe incremental ordering costs over and above fixed business costs.

Include time costs incurred by the following departments, provided they are involved in the ordering and receipting process. Your organisation may have different names or more touchpoints involved, if so, also include them:

Freight Costs

Freight cost which vary significantly with order frequency can also be added to the Receiving Cost calculation above.

Other Costs

Costs directly associated with completion of receiving processes, such as phone calls and stationary usage can have their relative variable cost percentage added in to the Receiving Cost calculation above.

What if my company outsources logistics?

If your company outsources logistics, the ‘Receipting Team’ costs in the Table above should be replaced by the equivalent annual 3PL fees. Similarly, if the information is available, 3PL freight costs which vary with order frequency can also be included.

Conclusion

Economic Order Quantities are an invaluable tool in optimising supply chains. However, confusing and varying definitions of EOQ mean that many organisations are incurring themselves unnecessary cost. This article has set out to redefine how the key components of EOQ, Carrying and Receiving cost, are determined to maximise the benefit of EOQs. In doing so the derivation of EOQ has been revised to more accurately represent the reality of the replenishment decision making process today. EOQ calculations should only consider the costs to which orders actually affect; variable costs! Though this article has predominantly focused on a distributer’s supply chain, the same overarching logic applies to manufacturers and MROs. By using the above approach, the variable supply chain cost curve can be optimised and subsequently lower total supply chain costs while maintaining all other supply chain performance metrics.

About the Author

Charles Edwards

Charles is a consultant with GRA, based in Melbourne. Charles’ previous clients include the Defence Force, MROs, automotive and ASX listed retail businesses within Australia.

Charles has experience in supply chain strategic, sales and operations planning, inventory optimisation, 3D printing and demand and replenishment planning. He is particularly interested in business strategy, big data and the impacts of disruptive technologies on the supply chain.