Economic order quantity (EOQ) is an inventory decision model that estimates the replenishment quantity minimizing the combined annual cost of placing orders and holding cycle stock. The basic model balances fewer, larger orders against more average inventory.
EOQ does not determine when to order, how much safety stock to hold, or whether a supplier’s quantity discount is economical. Those decisions require lead-time, demand-risk, service-level, purchase-price, capacity, and cash-flow analysis beyond the basic formula.
Key Takeaways
- Basic EOQ is the square root of twice annual demand times ordering cost, divided by annual holding cost per unit.
- At the theoretical EOQ, annual ordering cost equals annual cycle-stock holding cost.
- EOQ is an order-size decision; the reorder point is a timing decision.
- Safety stock is added for uncertainty and is not part of the basic deterministic EOQ formula.
- Quantity discounts require comparing total purchase, ordering, and holding cost at feasible price breaks.
- The model is most useful for repeatable items with reasonably stable inputs and should be recalculated when those inputs change.
$$
Q^* = \sqrt{\frac{2DS}{H}}
$$
where:
- (Q^*) = economic order quantity in units
- (D) = annual demand in units
- (S) = relevant cost to place and receive one order
- (H) = annual holding cost per unit
The modeled annual relevant cost at order quantity (Q) is:
$$
TC(Q) = \frac{D}{Q}S + \frac{Q}{2}H
$$
The first term is annual ordering cost. The second is annual holding cost for average cycle stock, assuming inventory declines evenly from (Q) to zero and replenishment arrives at once.
If annual holding cost is expressed as a percentage (i) of unit cost (C), then:
$$
H = iC
$$
The holding-rate estimate should include relevant storage, insurance, damage, obsolescence, handling, and cost-of-capital effects without double counting.
Worked Example: Choosing a Replenishment Quantity
A distributor expects annual demand of 24,000 units. Relevant ordering cost is $75 per order, and annual holding cost is $3 per unit.
$$
Q^* = \sqrt{\frac{2 \times 24{,}000 \times \$75}{\$3}} = \sqrt{1{,}200{,}000} \approx 1{,}095\text{ units}
$$
Rounding to a practical order size of about 1,100 units implies roughly:
$$
\frac{24{,}000}{1{,}095} \approx 21.9\text{ orders per year}
$$
At the unrounded EOQ, annual ordering and cycle-stock holding costs are approximately equal:
$$
\frac{24{,}000}{1{,}095} \times \$75 \approx \$1{,}643
$$
$$
\frac{1{,}095}{2} \times \$3 \approx \$1{,}643
$$
The combined modeled relevant cost is about $3,286 per year, excluding purchase cost, safety stock, stockouts, and other constraints. The company may round to a case, pallet, truckload, storage, or supplier minimum after comparing feasible alternatives.
EOQ and Reorder Point Answer Different Questions
EOQ answers how much to order. A reorder point answers when to place the order.
For stable daily demand and lead time:
$$
\text{Reorder Point} = (\text{Demand per Day} \times \text{Lead Time in Days}) + \text{Safety Stock}
$$
If demand is 80 units per day, lead time is five days, and safety stock is 150 units:
$$
(80 \times 5) + 150 = 550\text{ units}
$$
The inventory system would trigger an order near 550 units and order about the selected EOQ, subject to open orders, backorders, seasonality, and operational constraints.
Basic EOQ Assumptions
The standard formula generally assumes:
- known and reasonably constant demand
- known and constant replenishment lead time
- immediate receipt of the full order
- no stockouts in the modeled cycle
- constant unit purchase price
- constant ordering cost per order
- constant holding cost per unit and period
- no binding storage, cash, order-size, or supplier constraints
- independent treatment of the item
Real inventory rarely satisfies every assumption. EOQ can still provide a baseline, but users should model material departures rather than present the output as an exact optimum.
What Belongs in Ordering and Holding Cost
Ordering cost
Include costs that change with the number of orders, such as purchase-order processing, supplier communication, inbound scheduling, receiving setup, inspection setup, and invoice handling. Do not automatically allocate costs that will remain unchanged regardless of order frequency.
Holding cost
Include costs that change with average inventory, potentially including warehouse space, handling, insurance, damage, spoilage, obsolescence, shrinkage, and the financing or opportunity cost of working capital. The relevant amount depends on whether capacity is avoidable and how the decision changes cash use.
Data quality matters more than extra decimal places. An understated holding rate produces orders that are too large; an understated ordering cost produces orders that are too small.
Quantity Discounts and Other Constraints
When unit price changes at order thresholds, the constant-price EOQ is not enough. For each feasible candidate quantity:
$$
\text{Total Annual Cost} = DC + \frac{D}{Q}S + \left(\frac{Q}{2} + SS\right)H
$$
where (C) is purchase cost per unit and (SS) is safety stock. Compare the feasible EOQ for each price tier and the price-break quantities. Also consider tax, expiry, working capital, storage, transport, supplier risk, and demand uncertainty.
Other practical constraints include case packs, truckload economics, shelf life, minimum order quantities, production campaigns, warehouse slots, import cycles, and cash limits. The selected quantity should be the best feasible policy, not blindly the square-root result.
Risks and Limitations
- Demand variability: Average annual demand can hide seasonality, trends, promotions, and intermittent usage.
- Lead-time uncertainty: Late or variable supply affects safety stock and order timing.
- Stockout cost omission: Basic EOQ assumes replenishment without shortages and does not price lost sales or disruption.
- Correlated items: Ordering related items together can change freight and administrative economics.
- Perishable or obsolete stock: Holding cost may rise sharply with age rather than remain linear.
- Capacity and cash: The calculated lot may exceed storage, receiving, production, or financing limits.
- Supplier resilience: Lowest modeled cost may increase dependence on one supplier or route.
- False precision: Input estimates and rounding constraints usually matter more than the last calculated unit.
This page is educational and does not provide accounting, procurement, operations, tax, lending, or investment advice.
FAQs
Does EOQ include safety stock?
The basic EOQ formula does not. Safety stock addresses demand and lead-time uncertainty and affects average inventory and the reorder policy. It should be incorporated in the broader cost and service analysis.
Why are ordering and holding cost equal at EOQ?
Under the basic model, increasing order size reduces ordering cost and increases cycle-stock holding cost. At the mathematical minimum, those two modeled annual cost components are equal.
Should a company order exactly the calculated EOQ?
Not automatically. It should compare nearby feasible quantities and account for packaging, discounts, transport, shelf life, storage, cash, supplier minimums, and service requirements.
Authoritative Sources
- Inventory is the working-capital asset affected by replenishment size and timing.
- Cost Management helps identify which ordering and holding costs are decision-relevant.
- Cash Budget tests whether purchase timing and order size fit liquidity constraints.
- Capacity Utilization Rate helps evaluate receiving, storage, or production constraints.
- Cost of Goods Sold is affected by inventory cost flows but is not minimized directly by the basic EOQ formula.
- Gross Profit Method estimates inventory when a complete count is not available and serves a different purpose from EOQ.