Economic Order Quantity (EOQ): Definition, Formula, and Benefits

Every procurement staffer faces a repeated decision about how much to order each time. Order too often, and administrative and shipping costs rise. Order too much, and capital is tied up in the warehouse while storage costs climb. Many decisions still follow habit. Economic order quantity offers a solution through calculation. This article covers the EOQ formula, a worked example, a cost-comparison table, and the assumptions that limit it.

In short, economic order quantity (EOQ) is the order quantity that minimizes total inventory cost by balancing ordering cost and holding cost. The EOQ value is calculated using the square root of 2 times annual demand times cost per order, divided by holding cost per unit. So the order quantity is set from cost data, not habit.

The EOQ Formula and a Worked Example

The EOQ formula uses only three variables. They are annual demand, cost per order, and holding cost per unit per year. The purchase price per unit and lead time, the delivery waiting time, are not part of the basic calculation. The model was introduced by Ford W. Harris in 1913. R. H. Wilson analyzed it, so the formula is often called the Wilson formula.

As a procurement decision within the supply chain management process, EOQ needs three numbers that the inventory team usually already has. The formula stays the same across operations sources, including Corporate Finance Institute.

EOQ = √(2DS ÷ H), where D is annual demand (units), S is cost per order, and H is holding cost per unit per year.

Here is an illustration. A distributor has stable annual demand. Its costs are also well recorded.

1. Gather the three variables. D = 5,000 units per year. S = Rp100,000 per order. H = Rp1,000 per unit per year.
2. Plug into the formula: EOQ = √(2 × 5,000 × 100,000 / 1,000).
3. Compute the numerator. 2 × 5,000 × 100,000 = 1,000,000,000. Then divide by H. ÷ 1,000 = 1,000,000.
4. Take the square root. √1,000,000 = 1,000 units per order.
5. With demand of 5,000 units, the company should order 5 times per year (5,000 ÷ 1,000). Orders are placed about every 73 days.

Why does EOQ produce the lowest total cost?

Two cost components move in opposite directions with order size. As the order quantity grows, annual ordering cost falls because orders are less frequent. But holding cost rises because average stock is higher. EOQ is the point where these two costs are equal, and total cost is lowest. This is the main benefit of EOQ.

The table below uses the same example figures and shows total cost at three order sizes:

At EOQ, ordering cost equals holding cost. Each is Rp500,000. The total cost is Rp1,000,000. That is lower than the Rp1,250,000 at a quantity of 500 or 2,000. This equality of the two costs comes from the EOQ formula. It forms a U-shaped cost curve.

EOQ Assumptions and Limitations You Should Know

The EOQ formula is simple because it relies on assumptions that are rarely fully true in the field. So the EOQ result is best used as a benchmark, not an exact figure. The following four assumptions are often unmet and can affect the optimal quantity if conditions change.

• Demand is fixed and known. If demand fluctuates or is seasonal, EOQ must be checked periodically.
• Ordering and holding costs do not change. If shipping costs or the cost of capital change, the EOQ value changes too.
• No quantity discounts. If a supplier offers volume discounts, the most economical quantity can be larger than EOQ. This needs its own cost analysis.
• Orders are received all at once with no stockouts. The basic model does not account for staged delivery or stockouts.

Because of those limitations, EOQ is used together with safety stock and a reorder point to cover the uncertainty that is not modeled. The division of labor is simple. EOQ determines how much to order, while the reorder point determines when to reorder. All three work within warehouse management that keeps stock levels under control.

EOQ in Modern Inventory Planning Systems

EOQ is not a one-time spreadsheet calculation. Its value changes as demand or cost structure changes. In an ERP system, EOQ becomes a lot-sizing parameter that is recalculated automatically. EOQ is not a fixed number set once and then ignored.

In SAP S/4HANA, EOQ is one of the most efficient lot-sizing procedures for material requirements planning. The system calculates a lot size that lowers ordering cost and holding cost, as long as both costs are recorded in the material data, per the SAP Help Portal. For inventory planning across products and locations, companies use SAP Integrated Business Planning, or SAP IBP.

FAQ (Frequently Asked Questions)

What is the EOQ formula and how do you calculate it?

The EOQ formula is the square root of (2 times annual demand times cost per order) divided by holding cost per unit. Written as EOQ = √(2DS/H). For example, demand of 5,000 units, ordering cost Rp100,000, and holding cost Rp1,000 per unit gives EOQ = √1,000,000. The result is 1,000 units per order.

What is the difference between EOQ and the reorder point (ROP)?

Both are complementary inventory tools. EOQ answers how much to order per order. The result is the quantity per PO. ROP answers when to order. The result is the trigger stock level. EOQ sets the order size. ROP sets the timing. The two are used together in a single replenishment policy.

What are the drawbacks or limitations of the EOQ method?

EOQ assumes demand is always fixed and known. Ordering and holding costs are also fixed. There are no quantity discounts. Goods are received all at once so there are no stockouts. Because these assumptions are rarely fully true, EOQ is used as a benchmark supplemented by safety stock and a reorder point, not as an exact order quantity.

Conclusion

Setting the order quantity by habit can hide the true cost. EOQ turns this into a definite figure. EOQ shows the point where ordering cost and holding cost are balanced, so total cost is at its minimum. This holds as long as the assumptions are met and it is supported by safety stock and a reorder point. As an SAP Platinum Partner through United VARs membership, Soltius has experience since 1998. Soltius helps implement and support SAP supply chain planning, such as SAP IBP, for manufacturing and distribution companies.

To discuss implementing Economic Order Quantity and inventory planning using SAP IBP, visit soltius.co.id.