EOQ Calculator (Economic Order Quantity)

EOQ = √(2 × D × S / H). The Wilson formula, published by Ford W. Harris in 1913 and popularized by R.H. Wilson. It finds the order quantity that minimizes total inventory cost — the trade-off between ordering frequently (high order costs) and ordering large batches (high holding costs).

Where:

• D = annual demand (units per year)
• S = setup or order cost per order ($)
• H = holding cost per unit per year ($)

The trade-off the formula solves. Two costs move in opposite directions:

• Ordering cost: small batches mean many orders per year, each with admin overhead, shipping minimums, vendor processing time. Annual ordering cost = (D / Q) × S.
• Holding cost: large batches mean lots of inventory sitting in the warehouse paying rent, insurance, obsolescence, and capital cost. Annual holding cost = (Q / 2) × H.

EOQ is the Q where the two cost curves intersect — total cost minimum.

Worked derivation (the math sanity check).

• Total annual cost = (D / Q) × S + (Q / 2) × H
• Take derivative with respect to Q: -D × S / Q² + H / 2 = 0
• Solve: Q² = 2 × D × S / H
• Q = √(2DS / H)

Holding cost components (H per unit per year):

• Capital cost (cost of money tied up in inventory): typically 10-15% of unit value
• Storage (warehouse rent, utilities, security): 2-5% of unit value
• Insurance and taxes: 1-3%
• Obsolescence and shrinkage: 2-10% (huge for fashion, electronics, food)
• Total H is typically 15-30% of unit value annually

Order cost (S per order):

• Purchase order processing: $50-$200 in admin
• Inbound logistics (receiving, putting away): $20-$100 per order
• Quality inspection: varies
• Vendor minimum charges, freight tier breaks
• Total S typically $50-$500 for routine orders, much higher for capital purchases

Typical EOQ-driven decisions.

• A widget with D = 10,000/year, S = $100, H = $5: EOQ = √(2 × 10,000 × 100 / 5) = √400,000 = 632 units per order. Orders per year = 10,000 / 632 = 15.8 (every ~3.3 weeks).
• A high-value, slow-moving part: D = 50, S = $500, H = $200: EOQ = √(2 × 50 × 500 / 200) = √250 = 16 units per order. Orders per year = 3.

EOQ assumes constant demand and instantaneous replenishment. Both are oversimplifications. The model breaks down for:

• Seasonal demand (Christmas spikes, summer peaks): use period-specific EOQ or different model.
• Stochastic demand: add safety stock above EOQ-based reorder point.
• Quantity discounts: vendor offers price breaks at higher volumes — modify EOQ to consider tiered pricing.
• Backorders allowed: introduces shortage cost as a third variable.

The reorder point. EOQ tells you HOW MUCH to order; reorder point tells you WHEN. ROP = (daily demand × lead time in days) + safety stock. A part with EOQ of 632, daily demand of 27, and 2-week lead time has ROP = 27 × 14 + safety stock.

Sensitivity is forgiving. EOQ uses square root, so a 100% error in D, S, or H only produces a 41% error in EOQ. The model’s smoothness means rough estimates of inputs still give workable answers — one of its enduring strengths.

Where EOQ fails. Just-in-time (JIT) inventory inverts EOQ logic — Toyota’s lean approach minimizes inventory through frequent small orders supported by tight supplier integration. EOQ assumes order cost is fixed; JIT engineers it down to near zero, which would yield a tiny EOQ, which is the JIT philosophy.