The Economic Order Quantity (EOQ) formula is EOQ = √((2 × D × S) / H), where D = annual demand (units), S = ordering cost per order ($), and H = holding cost per unit per year ($).

This formula finds the "sweet spot" order quantity that minimizes total inventory costs.

For example, if your annual demand is 10,000 units, ordering cost is $50 per order, and holding cost is $5 per unit per year, then EOQ = √((2 × 10,000 × 50) / 5) = √(1,000,000 / 5) = √200,000 ≈ 447 units.

This means you should order 447 units at a time, resulting in 10,000 ÷ 447 ≈ 22 orders per year (every 16-17 days).

At this quantity, your ordering costs ((10,000 ÷ 447) × $50 = $1,119) equal your holding costs ((447 ÷ 2) × $5 = $1,118), achieving the minimum total cost of $2,237.

The square root relationship means doubling demand only increases EOQ by 41% (√2 ≈ 1.41), not 100%, creating economies of scale.

Ordering cost (S) includes all fixed costs per order: purchase order processing labor ($20-$100), shipping/freight charges (can vary $10-$500+), quality inspection time, invoice processing, and receiving labor.

For example, if your purchasing department spends 2 hours per order ($30/hour labor) and average shipping is $25, your ordering cost is $85 per order.

Holding cost (H) per unit per year includes: warehouse space rent (e.g., $5/sq ft × 0.5 sq ft per unit = $2.50), insurance (typically 1-3% of item value), obsolescence/spoilage risk (5-10% for tech products, 1-2% for stable goods), and capital cost (interest on money tied up in inventory, e.g., 5% of $50 item value = $2.50).

Total holding cost might be $2.50 space + $1 insurance + $2 obsolescence + $2.50 capital = $8 per unit per year.

A common rule of thumb: holding cost ≈ 20-30% of unit cost annually.

For a $50 item, that's $10-$15/year.

Track your actual warehouse invoices and labor hours to refine these estimates—accurate costs lead to better EOQ decisions.

Reorder point (ROP) is the inventory level that triggers a new order, calculated as ROP = (Average Daily Demand × Lead Time in Days) + Safety Stock.

For example, if you sell 27 units/day (10,000 annual ÷ 365) and lead time is 7 days, base ROP = 27 × 7 = 189 units.

However, demand fluctuates—safety stock protects against stockouts during lead time.

If demand standard deviation is 500 units/year (daily σ ≈ 500 ÷ √365 ≈ 26 units) and you want 95% service level (Z-score = 1.65), safety stock = 1.65 × 26 × √7 ≈ 113 units.

Total ROP = 189 + 113 = 302 units.

When inventory drops to 302 units, place your next order for EOQ (447 units).

This 95% service level means you'll meet demand from stock 95% of the time; the remaining 5% may require backorders or expedited shipping.

Increasing service level to 99% (Z = 2.33) raises safety stock to 160 units but reduces costly stockout penalties.

Safety stock costs (160 × $5 holding cost = $800/year) must be weighed against stockout costs (lost sales, expediting fees, customer dissatisfaction).

The classic EOQ model assumes: (1) constant, known demand rate (10,000 units/year spread evenly), (2) fixed ordering and holding costs, (3) instantaneous replenishment (no gradual delivery), (4) no quantity discounts, (5) independent items (no bundling), and (6) infinite planning horizon.

In reality, demand is seasonal (holiday spikes), lead times vary (supplier delays), and suppliers offer volume discounts (buy 1,000+ for 10% off) that may justify larger orders than EOQ.

The model also ignores warehouse capacity constraints (you may lack space for EOQ), working capital limits (cash flow may prevent large orders), and item perishability (food/pharma have shelf lives).

For seasonal products, use adjusted EOQ with peak/off-peak demand rates.

For quantity discounts, calculate total cost at each price break: if buying 1,000 units (vs EOQ 447) drops unit price from $50 to $45, the $5,000 savings may exceed the extra holding cost of 553 units.

Despite limitations, EOQ provides a solid baseline—then adjust for real-world factors like supplier minimums, truck-load quantities, or cash flow cycles.

Service level represents the probability of NOT stocking out during lead time.

A 95% service level means you'll have stock available 95% of replenishment cycles; 5% of the time you may backorder or lose sales.

A 99% service level reduces stockout risk to 1% but requires more safety stock.

The choice depends on stockout cost vs holding cost: (1) High stockout cost items (critical components halting production, high-margin products, customer contracts with penalties) warrant 99%+ service levels.

Example: A $1,000 stockout penalty (expedited shipping + lost customer goodwill) vs $50 extra annual holding cost for higher safety stock → choose 99%. (2) Low stockout cost items (commodity products with substitutes, low-margin goods, build-to-order items) can use 90-95% service levels.

Example: Customer accepts 3-day delay with no penalty → 95% sufficient. (3) Calculate break-even: If stockout costs $500 and occurs 5% of time (95% SL) = $25 expected annual cost.

Raising SL to 99% (1% stockout) = $5 expected cost, saving $20/year.

If extra safety stock holding cost is only $10/year, 99% is justified.

Industry benchmarks: automotive parts 99%+, retail fashion 85-90% (fast obsolescence), grocery staples 98%+, electronics components 95-99%.

EOQ and JIT represent opposite philosophies: EOQ optimizes order quantity to minimize costs while holding inventory, whereas JIT aims to eliminate inventory entirely by synchronizing production with demand.

EOQ calculates an economic batch size (e.g., 447 units every 16 days), accepting holding costs as unavoidable.

JIT orders small frequent batches (even daily), pushing ordering costs onto suppliers through long-term contracts, EDI systems, and supplier-managed inventory (reducing per-order processing to near-zero).

Example comparison: EOQ approach for 10,000 annual demand → 447 unit orders, 22 orders/year, $1,118 holding cost, $1,119 ordering cost, total $2,237.

JIT approach → 38 unit daily deliveries, 263 orders/year, $95 holding cost (38 ÷ 2 × $5), but requires low ordering cost (if still $50/order, costs skyrocket to $13,150).

JIT works when: suppliers are nearby (short lead time), demand is stable (automotive assembly lines), and ordering costs are streamlined (automated systems).

EOQ works when: suppliers are distant (international shipping), demand is lumpy (seasonal products), or ordering involves fixed costs (ocean freight minimum charges).

Many companies use hybrid approaches: JIT for high-volume A-items with reliable suppliers, EOQ for B/C-items with less frequent replenishment.