Economic Order Quantity (EOQ)
Also known as: Wilson EOQ Model, Harris-Wilson Model, Optimal Lot Size Model, Ekonomik Sipariş Miktarı
The Economic Order Quantity (EOQ) is a classic deterministic inventory model that identifies the order quantity minimizing the sum of annual ordering and holding costs. Introduced by Ford W. Harris in 1913 and later popularized by R. H. Wilson, EOQ assumes constant demand, fixed cost parameters, and instantaneous replenishment. It remains the foundational benchmark for inventory management in manufacturing, retail, and supply chain contexts where demand is relatively stable and costs are well-characterized.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
EOQ is appropriate when demand is approximately constant and known, ordering and holding costs are stable and well-estimated, lead times are predictable, and items are managed independently. It is best suited for high-volume, steady-demand SKUs. EOQ is less appropriate when demand is seasonal, highly variable, or lumpy; when supplier constraints force minimum or maximum order quantities; or when perishability, obsolescence, or quantity discounts are significant. In such cases, consider the newsvendor model, periodic review policies, or dynamic lot-sizing methods.
Strengths & limitations
- Provides a closed-form, analytically derived optimal solution with minimal computational effort.
- Equally useful as a managerial decision rule and as a benchmark for evaluating more complex policies.
- Robust to moderate parameter errors: total cost is relatively flat near Q*, so small deviations from the true optimum incur little extra cost.
- Easily extended to account for quantity discounts, finite production rates, or backorder allowances.
- Assumes constant, deterministic demand — inapplicable when demand is stochastic, seasonal, or trend-driven.
- Ignores stockout risk; no safety stock is incorporated in the basic model.
- Treats ordering and holding costs as fixed and linear, which may not reflect volume-dependent or step-function cost structures.
- Assumes instantaneous replenishment; the production order quantity (POQ) extension is needed when goods arrive gradually.
Frequently asked
What happens to EOQ if demand doubles?
Because Q* is proportional to the square root of demand (Q* = sqrt(2DS/H)), doubling D increases the optimal order quantity by a factor of sqrt(2), roughly 41%. Total minimum cost also increases by sqrt(2). This square-root relationship means EOQ is relatively insensitive to moderate demand changes, which partly explains its practical robustness.
Does EOQ work when there are quantity discounts?
The basic EOQ formula does not account for quantity discounts. The standard extension evaluates total cost — including purchase price — at the EOQ for each price break and at each minimum quantity threshold that activates a lower price. The feasible solution with the lowest total annual cost (ordering + holding + purchase) is then selected as the optimal order quantity.
How is EOQ different from the Economic Production Quantity (EPQ)?
EOQ assumes instantaneous batch delivery, so average inventory is Q/2. The Economic Production Quantity (EPQ) model relaxes this by assuming goods arrive gradually at a finite production rate p. Average inventory becomes Q/2 * (1 - d/p), where d is demand rate. EPQ always yields a larger optimal batch size than EOQ for the same cost parameters, reflecting the lower average inventory during the production run.
Sources
- Harris, F. W. (1913/1990). How many parts to make at once. Operations Research, 38(6), 947–950 (reprint). DOI: 10.1287/opre.38.6.947 ↗
How to cite this page
ScholarGate. (2026, June 2). Economic Order Quantity (EOQ). ScholarGate. https://scholargate.app/en/operations-research/economic-order-quantity
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ABC AnalysisOperations Research↔ compare
- Newsvendor ModelOperations Research↔ compare
- Safety StockOperations Research↔ compare