The EOQ Formula and Interpretation

EOQ = √[(2 × D × S) / H]

D = Annual Demand (units)
S = Ordering Cost per order ($)
H = Holding Cost per unit per year ($)

Conceptual Understanding

Why Square-Root Relationship? The square-root in the EOQ formula emerges from the mathematical optimization of opposing cost curves. Total annual ordering cost decreases as order quantity increases because fewer orders are placed. The square-root form arises from minimizing the total inventory cost function using calculus, balancing ordering and holding cost tradeoffs.

Balancing Tradeoffs: At the EOQ level, the total annual ordering cost equals the total annual holding cost, resulting in minimum total inventory cost. Order too frequently, and excessive ordering costs dominate. Order too infrequently, and excessive holding costs dominate. EOQ identifies the economic sweet spot where these costs are balanced.

Constant Demand Assumption: The classic formula assumes constant, continuous demand and fixed lead times. This simplification enables closed-form mathematical solutions but may require adjustment for real-world variability. Advanced models incorporate safety stock and probabilistic demand patterns.

EOQ Model Assumptions

Constant and Predictable Demand

EOQ assumes demand is deterministic and occurs at a known average rate over time. Seasonal patterns, trend growth, or demand spikes weaken this assumption and reduce EOQ accuracy. Seasonal demand weakens EOQ assumptions and often requires periodic recalibration or dynamic lot-sizing methods.

Fixed Ordering Costs

The cost to place each order (processing, shipping, handling) remains constant regardless of order size. No volume discounts on ordering expenses.

Stable Holding Costs

Holding cost per unit (storage, insurance, capital, obsolescence) remains linear and constant. No warehouse capacity constraints or economies of scale in storage.

No Supply Variability

Lead time is constant and known. No supplier delays, quality issues, or transportation disruptions. Supply reliability is assumed perfect.

Instantaneous Replenishment

Instantaneous replenishment assumes inventory is added to stock in a single batch upon arrival, though lead time may still exist before delivery.

No Stockout Costs

Basic model assumes no shortages or lost sales. Backorder costs and stockout penalties are not included in the classical formulation.

Model Limitations

Demand Variability Ignored

EOQ determines economic lot size under deterministic demand assumptions. Demand variability is typically handled separately through safety stock and reorder point calculations. In volatile markets, EOQ calculations may recommend inventory levels that result in stockouts or excess inventory. Stochastic inventory models (newsvendor, base-stock) better handle uncertainty.

Static Pricing Assumptions

EOQ assumes constant unit prices. It does not incorporate dynamic pricing, quantity discounts, or seasonal price variations. Price fluctuations significantly impact optimal order quantities.

Cost Estimate Sensitivity

EOQ is relatively robust to estimation errors because of the square-root structure. Large percentage errors in cost parameters typically produce smaller proportional errors in EOQ estimates.

Not a Replacement for Advanced Models

EOQ provides a baseline optimization but cannot replace advanced inventory models for complex supply chains. Multi-echelon systems, probabilistic demand, and dynamic environments require sophisticated optimization tools.

When NOT to Use EOQ

Highly Variable Demand

EOQ is inappropriate for products with highly seasonal demand, fashion items with short lifecycles, or innovative products with unpredictable adoption rates. Use dynamic lot-sizing methods or stochastic models instead.

Unstable Supply Chains

If suppliers face frequent disruptions, quality issues, or variable lead times, EOQ's assumptions are violated. Probabilistic inventory models with safety stock calculations are more appropriate.

Probabilistic Inventory Needs

When service levels and stockout probabilities are critical, EOQ is insufficient. Use safety stock optimization, service level constraints, and fill-rate models rather than deterministic EOQ.

Multi-Echelon Systems

EOQ optimizes single-stage inventory. For complex supply chains with warehouses, distribution centers, and retailers, use multi-echelon inventory optimization (MEIO) or linear programming approaches.

Calculator Features

Basic EOQ

Classic Wilson EOQ model for instantaneous replenishment and constant demand rate.

Reorder Point

Calculate ROP based on lead time and demand variability. Include safety stock calculations.

Demand Integration: Reorder point integrates average demand during lead time plus safety stock for variability. ROP = (Average daily demand × Lead time days) + Safety stock. This ensures replenishment orders trigger before stockouts occur.

Total Cost Analysis

Visual breakdown of ordering costs vs. holding costs. See total cost curve and optimal zone.

Sensitivity Analysis

What-if scenarios: How does EOQ change if demand increases 20% or ordering costs drop?

Risk Planning: Sensitivity analysis reveals how robust EOQ decisions are to parameter uncertainty. If small demand changes produce large EOQ shifts, consider implementing flexible ordering policies rather than rigid EOQ quantities.

EOQ Variants and Usage Guidance

Production Order Quantity (POQ)

For gradual replenishment (production environments) rather than instantaneous delivery.

Manufacturing Preference: Use POQ when inventory replenishes gradually as units are produced rather than arriving in bulk shipments. The formula adjusts for production rate vs. consumption rate, preventing excessive inventory buildup during production runs.

Quantity Discount Model

Adjust EOQ when suppliers offer price breaks for larger quantities. Compare total costs at price breakpoints.

Economic Benefit: Quantity discounts become economically beneficial when the purchase cost savings outweigh increased holding costs. Calculate total cost (purchase + ordering + holding) at each price breakpoint to determine the true optimal order quantity.

Backorder EOQ

Model allowing planned stockouts when shortage costs are less than holding costs.

Strategic Tradeoff: Backorder models apply when customers accept delays or when products are expensive to hold (luxury goods, specialized components). The model balances holding cost savings against shortage/penalty costs.

Industry Applications

Retail Inventory Replenishment

Optimize reorder quantities for stable, high-volume consumer goods. Determine how frequently to restock shelves while minimizing storage costs and stockout risks.

Manufacturing Raw Materials

Calculate optimal procurement quantities for production inputs. Balance ordering costs (purchase orders, receiving) against warehouse holding costs for materials awaiting production.

Healthcare Medical Supplies

Manage inventory of consumable medical supplies with predictable usage. Ensure critical supplies remain available while minimizing expiration waste and carrying costs.

E-commerce Fulfillment

Optimize inbound inventory from suppliers to fulfillment centers. Determine order quantities that minimize total logistics costs while maintaining service levels for online orders.

Distribution Warehouse

Manage stocking levels for distribution centers supplying retail locations. Balance bulk purchasing advantages against inventory carrying costs and warehouse space constraints.

Beginner's Guide to EOQ

What EOQ Calculates: EOQ determines the ideal order size that minimizes the combined costs of ordering inventory and storing inventory. It answers: "How much should I order each time to spend the least amount possible on inventory management?"

When to Use EOQ: Apply EOQ when you have stable, predictable demand for products, consistent supplier lead times, and measurable ordering and holding costs. Use it for routine replenishment decisions of standard inventory items.

Real-World Example: A hardware store sells 1,200 bags of cement annually. Each order costs $50 to process and ship. Holding cement costs $2 per bag per year (storage + capital). EOQ calculates the optimal order size is 245 bags. Ordering 245 bags approximately 5 times per year costs less than ordering monthly (100 bags) or quarterly (300 bags). The store saves on both ordering fees and warehouse space while maintaining stock availability.

Frequently Asked Questions

What happens if demand is not constant in EOQ?

If demand varies significantly, EOQ produces suboptimal results. For seasonal demand, use dynamic lot-sizing methods (Silver-Meal, least unit cost) or adjust EOQ parameters seasonally. For trend growth, use EOQ with rolling averages or time-varying parameters. In highly uncertain environments, stochastic inventory models (newsvendor, base-stock policies) better handle variability than deterministic EOQ.

What is the difference between EOQ and reorder point?

EOQ answers "How much should I order?" It determines order quantity to minimize costs. Reorder Point (ROP) answers "When should I order?" It determines inventory level that triggers replenishment to avoid stockouts during lead time. EOQ affects inventory cycle patterns; ROP affects timing. Both are needed: order EOQ quantity when inventory hits ROP.

Can EOQ be used for service inventory planning?

Yes, EOQ applies to service industries with "inventory-like" resources: spare parts for maintenance, office supplies, restaurant ingredients, or hospital supplies. Any resource with holding costs (storage, capital) and ordering costs (procurement, delivery) suits EOQ analysis. However, services with perishable capacity (hotel rooms, airline seats) use revenue management or overbooking models rather than EOQ.

How are holding costs calculated in EOQ?

Holding cost (H) includes: (1) Capital costs—opportunity cost of money tied up in inventory (typically 10-20% annually), (2) Storage costs—warehouse space, utilities, insurance, (3) Risk costs—obsolescence, damage, theft, expiration. Calculate as: H = (Unit Cost × Carrying Cost %). For a $10 item with 15% carrying cost, H = $1.50 per unit per year. Accurate H is critical—small errors significantly affect EOQ calculations.

What is the difference between EOQ and POQ?

EOQ (Economic Order Quantity) assumes entire order arrives instantaneously (purchased items, vendor deliveries). POQ (Production Order Quantity) assumes gradual replenishment as items are produced. POQ formula adjusts for production rate (p) vs. demand rate (d): POQ = √[(2DS) / (H(1-d/p))]. Use POQ for manufacturing environments where inventory builds up slowly during production runs; use EOQ for purchased items arriving in bulk shipments.

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