What is Economic Order Quantity? Definition & Manufacturing Examples

What is Economic Order Quantity?

Economic Order Quantity (EOQ) is the optimal order or production batch quantity that minimizes the total cost of inventory by balancing two opposing cost components: ordering costs and carrying costs. As order quantity increases, the number of orders per year decreases (reducing ordering costs), but the average inventory level increases (raising carrying costs). EOQ finds the sweet spot where the sum of both costs is at its minimum.

The EOQ model was first developed by Ford Whitman Harris in 1913 and later popularized by R.H. Wilson, which is why it is sometimes called the Wilson formula. Despite being over a century old, EOQ remains one of the most widely used inventory management tools because it provides a straightforward, mathematically optimal answer to the question: "How much should we order at a time?"

The basic EOQ formula is: EOQ = √(2DS / H)

Where:

• D = Annual demand (units per year)
• S = Ordering cost per order (or setup cost per production run)
• H = Annual carrying cost per unit

How EOQ Works in Manufacturing

In a manufacturing context, EOQ applies to both purchasing decisions (how much raw material to order) and production batch sizing (how many units to produce per run).

For purchasing decisions, the ordering cost (S) includes the administrative cost of placing a purchase order, receiving and inspecting the delivery, processing the invoice, and any shipping costs that are fixed per order. The carrying cost (H) includes capital costs, storage, insurance, and obsolescence risk.

For production batch sizing, the ordering cost is replaced by the setup cost — the labor, machine downtime, tooling changes, and first-article inspection associated with each production run changeover. Higher setup costs favor larger batches; lower setup costs enable smaller, more frequent runs.

The total annual cost at EOQ is minimized, and importantly, the total cost curve is relatively flat near the EOQ point. This means ordering 10-20% above or below EOQ has minimal cost impact — providing flexibility to adjust for practical constraints like package sizes, truck loads, or production shift lengths.

EOQ also determines the optimal number of orders per year (D / EOQ) and the reorder cycle time (EOQ / D × 365 days).

EOQ Example

A manufacturer of precision gears uses 12,000 steel blanks per year. The relevant costs are:

• Annual demand (D) = 12,000 blanks
• Cost per order (S) = $150 (purchasing, receiving, inspection)
• Annual carrying cost per unit (H) = $8.75 (25% of the $35 unit cost)

EOQ = √(2 × 12,000 × 150 / 8.75) = √(3,600,000 / 8.75) = √411,429 = 641 blanks

At EOQ of 641:

• Orders per year: 12,000 / 641 = 18.7 (approximately 19 orders)
• Average inventory: 641 / 2 = 321 blanks ($11,218)
• Annual ordering cost: 19 × $150 = $2,850
• Annual carrying cost: 321 × $8.75 = $2,809
• Total annual cost: $5,659

Compare this to the previous practice of ordering 2,000 blanks per order (6 orders per year):

• Annual ordering cost: 6 × $150 = $900
• Annual carrying cost: 1,000 × $8.75 = $8,750
• Total annual cost: $9,650

Switching from 2,000-unit orders to the EOQ of 641 saves $3,991 per year on this single item — primarily from reduced carrying costs. The trade-off is more frequent ordering (19 vs. 6 times per year), but the savings far exceed the additional ordering cost.

Why EOQ Matters for Production Scheduling

EOQ directly affects production scheduling because batch sizes determine how frequently the scheduler must plan changeovers. Larger batches mean fewer setups but more inventory. Smaller batches mean more setups but faster response to demand changes and lower inventory levels.

When EOQ is applied to production batch sizing, the setup cost becomes the critical variable. Manufacturers practicing lean manufacturing actively work to reduce setup times (SMED), which reduces S in the EOQ formula and enables smaller economically justified batches. Smaller batches give schedulers more flexibility to respond to changing customer priorities.

Production scheduling software like Resource Manager DB helps planners implement EOQ-based batch sizing while considering real-world constraints such as machine availability, operator schedules, and material delivery timing.

EOQ also interacts with safety stock decisions. The reorder point determines when to order; EOQ determines how much to order. Together, they form the foundation of an inventory replenishment system.

Related Terms

• Carrying Cost — one of the two cost components balanced by EOQ
• Reorder Point — the inventory level that triggers a new order of the EOQ quantity
• Safety Stock — buffer inventory held in addition to the EOQ cycle stock

FAQ

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This term is part of our Manufacturing & Production Scheduling Glossary. Learn more about inventory management, scheduling, and manufacturing terminology.