What is Economic Order Quantity (EOQ)?

In this article, learn about:

• What EOQ (Economic Order Quantity) is

• Why retailers and suppliers use EOQ

• Key factors affecting EOQ calculation

• How to calculate EOQ using the EOQ formula

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How do retailers determine the optimal amount of goods to order to minimize costs? What is the ideal inventory level that reduces expenses like ordering and holding costs? The answer lies in the Economic Order Quantity (EOQ).

What is Economic Order Quantity (EOQ)?

EOQ is a formula that helps replenishment managers (RMs) and buyers calculate the ideal order quantity to minimize costs while ensuring regular production. It enables them to know the best time and amount to place an order, reducing inventory costs and maximizing efficiency.

Mathematically, EOQ occurs where the ordering cost equals the holding cost, as illustrated in the graph below:

The EOQ is the lowest point of the Total Cost curve.

Why Retailers Should Use EOQ

Inventory can be a huge cost factor for retailers. Whether it's raw materials, work in progress (WIP), or finished products, EOQ helps businesses avoid overstocking or understocking by providing a reliable inventory management benchmark. Retailers who fail to order the right quantity risk high holding costs or worse, stockouts that disrupt sales.

Calculating EOQ allows companies to:

• Minimize storage and holding costs

• Avoid surplus stock

• Maintain a steady cash flow

• Plan orders efficiently to meet customer demand

Other inventory control methods like Reorder Points or Period of Supply may complement the use of EOQ in an overall inventory management strategy.

Related Reading: Replenishment 101: What is Replenishment?

Factors to Consider When Calculating EOQ

According to most demand planners or supply chain managers, the ideal way to administer inventory is to get the optimum EOQ for every item in stock. However, retailers need to consider several factors before defining the EOQ for each product:

1. Purchasing Cycles

When using EOQ, it's essential to consider the practicality of purchasing cycles. For instance, if EOQ calculations suggest placing toy orders 17 times a year---more than once a month---this might minimize costs. However, it raises important questions: Do the stores and their workforce have the capacity to handle such frequent orders? Can retailers realistically place more frequent orders without overburdening their suppliers? Moreover, will this increased frequency lead to bottlenecks or disruptions in the supply chain? While EOQ aims to optimize cost efficiency, ensuring it aligns with operational capacity is crucial for seamless execution.

2. On-hand and In-pipe Stock

Fluctuating demand or varying needs across stores can complicate reordering based solely on EOQ. If products are already "in-pipe" (en route or in stock but not yet sold), blindly following EOQ may lead to an inefficient allocation of resources. Instead of reordering, redistributing existing stock to locations with higher demand can be a more cost-effective solution. This approach ensures that products are moved from low-demand areas, freeing up shelf space for higher-value items.

Related Reading: Replenishment 201: Monitoring Store-Level Inventory

3. Lower Demand vs. Capacity Loss

Ordering the EOQ for every product, regardless of its sales value, can lead to capacity issues, particularly for higher-value items. Valuable storage space may be wasted on lower-demand goods that don't need to be consistently stocked. Prioritizing products with higher demand and greater value ensures optimal use of storage space. ABC analysis can help identify high-value SKUs and allocate resources more efficiently.

4. Minimum Order Quantity

With more frequent smaller batch orders, inventory managers have more flexibility to match purchasing behavior with actual customer demand. However, many suppliers must have a minimum order quantity (MOQ) before shipping an order. If orders are received without a MOQ, the suppliers' profit margins per unit dip low, and shipping costs increase. Even though this isn't a comprehensive list of what to consider when deciding EOQ and placing orders with suppliers, these points indicate that EOQ alone is insufficient to manage inventory accurately.

Changes in the EOQ

In a scenario where both the cost per commodity and demand for each commodity are constant, and the number of commodities is small, determining and maintaining the EOQ is relatively straightforward. However, as products progress through their lifecycle and demand fluctuates, calculating the EOQ can become complex, especially when dealing with hundreds of SKUs. In such cases, finding and managing the EOQ becomes a tedious and time-consuming task.

As demand per year is an essential part of the EOQ, it becomes even more challenging to calculate the EOQ with fluctuating products' market. The EOQ for each item must be re-established consistently to absorb alterations.

It's essential to recognize that product demand is rarely constant throughout the year. Retailers and replenishment managers must consider seasonal fluctuations in demand, as well as potential downturns in the market for certain items. If a significant number of low-demand products are stocked during off-peak periods, holding costs can escalate, and valuable inventory space can be wasted.

Related Reading: What is Demand Planning?

How to Calculate EOQ

To maintain optimal inventory levels, retailers must order the right quantity at the right time, factoring in product depreciation and costs. The Economic Order Quantity (EOQ) formula helps calculate the ideal number of units to order, ensuring the most cost-effective transactions while minimizing excess stock.

EOQ calculation begins with three key factors: the product's annual demand, the cost per order, and the holding cost for each unit of inventory. Several assumptions underpin the EOQ formula, including:

• Constant and known lead times

• Constant and predictable product demand

• No quantity discounts

• No stock-outs or shortages

• On-time, in-full receipt of orders

By adhering to these conditions, retailers can determine the most economical order size to balance inventory costs with demand.

The Ad Hoc EOQ formula

The ad hoc EOQ formula consists of several key components: holding cost, ordering cost, annual ordering cost, annual holding cost, and total cost. These elements work together to determine the most cost-efficient order quantity.

Holding cost

Holding cost refers to the expense of storing inventory. It helps assess whether it's more cost-effective to keep a product in stock or transfer it elsewhere, assuming constant demand.

The formula for holding cost is:

H = I * C

Formula definitions:

H = Holding cost

I = Carrying cost

C = Unit cost

In this case, demand is constant, inventory will reduce with use until it reaches zero, and the retailer will order the item again.

Ordering cost

Ordering cost accounts for the expense incurred each time a retailer places an order. To calculate the number of orders needed annually, use the formula:

N = D / Q

Formula definitions:

N = Number of orders

D = Quantity demanded per year

Q = Volume per order

Annual ordering cost

Annual ordering cost is the cost of ordering inventory over the course of a year. To calculate the yearly order cost, multiply the number of orders by the ordering costs using this formula:

AO = (D * S) / Q

Formula definitions:

AO = Annual ordering cost

D = Quantity demanded per year

S = Ordering cost

Q = Volume per order

Annual holding cost

Annual holding cost represents the expense of storing inventory throughout the year. It is calculated by multiplying the order volume by the holding cost, then dividing by two:

AH = (Q * H) / 2

Formula definitions:

AH = Annual holding cost

Q = Volume per order

H = Holding cost

Total cost

The total cost combines annual ordering and holding costs, giving the total yearly cost of managing inventory. Use the following equation:

Total cost = [ (D * S) / Q ] + [ (Q * H) / 2 ]

To find the EOQ, differentiate the total cost by the volume per order:

Wilson's Formula

Though often associated with Mr. R.H. Wilson, Wilson's Formula was originally developed by Ford Whitman Harris. Harris introduced the mathematical concept, while Wilson, an industrial consultant specializing in inventory management, popularized and applied it to optimize inventory.

Wilson's Formula calculates the Economic Order Quantity (EOQ) by recognizing that inventory costs are directly tied to the amount of stock---more inventory means higher costs. This formula balances the trade-off between ordering and holding costs. For example, if a retailer needs 1,000 units, placing a single order for all units is more cost-effective than making 1,000 smaller orders.

Wilson's Formula has three benchmarks:

1. Demand or consumption (D)

2. Order placement cost (CO)

3. Stock ownership cost (SC)

To calculate Wilson's Formula, take the square root of twice the demand multiplied by the order placement cost (or ordering cost) divided by the stock ownership cost (or holding cost).

In the case of retail or wholesale, the ad hoc EOQ formula (above, utilizing the total cost) is the most appropriate and lucrative compared to the Wilson Formula. As for manufacturers, it can depend on the situation, especially if the order calls for a new production. If so, there is a chance of substantial ordering costs (production configuration) and minimum or zero benefits in marginal unit cost subsequently. These are the circumstances when the Wilson Formula is better suited.

Methodologies for Inventory Management

Retailers looking to base their reordering process entirely on the EOQ should ensure that:

• EOQ calculations for all products are consistently tracked and updated,

• Warehouses and suppliers can efficiently handle frequent reorders, and

• Minimum Order Quantities (MOQ) are met, with priority given to the most profitable products to maximize returns.

However, manually calculating EOQ for thousands of SKUs is time-consuming and prone to errors. Relying solely on EOQ can also result in missed opportunities or stock imbalances. To truly optimize inventory management, retailers need to continuously monitor order quantities, reorder levels, demand fluctuations, emergency supply needs, lead times, supplier timelines, and more.

Inventory optimization ensures suppliers and retailers trim inventory to release capital and maximize margins while retaining superior service quality. Small and medium firms use this technique to establish themselves in their industry. However, consistently monitoring and analyzing all factors that form inventory optimization is crucial. The best way to do so is to automate this process.

Inventory optimization helps bring down inventory levels, meet MOQ when placing orders with suppliers, reorder the exact quantities to fill the demand with lead time explained, and perform timely deliveries to customers, among other things.

Ultimately, EOQ is a mathematical approach to determining the ideal quantity of materials to order, balancing demand, production, and inventory costs. In short, it helps businesses identify the optimal order size at the right time.

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