Economic Order Quantity: EOQ Guide

By Ryan O'Connell, CFA, FRM Published November 5, 2026

Ordering a year’s inventory at once saves purchasing work but ties up cash and warehouse space. Ordering a few units at a time reverses that trade-off. Economic order quantity (EOQ) identifies the replenishment batch that minimizes a particular combination of ordering and holding costs. It gives the inventory decision a useful starting point before managers account for supplier terms, uncertainty and operating constraints.

EOQ connects day-to-day purchasing with working capital management. To use it well, distinguish three questions: how much to order, when to place the order, and how much protection to hold against uncertainty.

What Is Economic Order Quantity?

Economic order quantity is the order size that minimizes annual ordering cost plus annual cycle-stock holding cost in the basic inventory model. A larger batch means fewer orders but more inventory sitting between deliveries. A smaller batch means less average inventory but more frequent ordering.^[1]

The basic model assumes one item with known, constant demand; a constant unit purchase price; a fixed cost per order; a constant holding cost per unit per year; and no stockouts. Each replenishment lot becomes available all at once. A known delivery lead time can be accommodated by ordering earlier; instantaneous receipt of the lot does not require zero time between placing and receiving an order.^[1][2]

This is an operating model. Inventory valuation methods address a different task: assigning inventory costs between assets and cost of goods sold. Choosing FIFO or weighted average does not itself determine an economical replenishment batch.

The Economic Order Quantity Formula

Use a consistent annual time basis and define the inputs before calculating:

Ordering cost can include an incremental processing charge, receiving work or a fixed delivery fee incurred each time an order is placed. Holding cost can include the opportunity cost of inventory capital, variable storage charges, insurance and expected deterioration. Include costs that change with the decision; allocating an unchanged purchasing manager’s annual salary across orders does not make that salary avoidable.^[1]

If holding cost is modeled as an annual carrying rate i times purchase price, then H = iC. For example, an assumed 20% annual carrying rate on a $20 item gives H = 0.20 × $20 = $4 per unit per year. That 20% is an illustrative combined carrying rate, not a universal industry percentage or necessarily the firm’s borrowing rate.

Deriving EOQ from the Two Costs

Over a repeated steady cycle, annual demand requires D/Q orders. Multiplying by S gives annual ordering cost. Inventory declines evenly from Q to zero, so its time average is Q/2; multiplying by H gives annual cycle-stock holding cost.

The derivative is dRC/dQ = −DS/Q² + H/2. Setting it equal to zero gives DS/Q² = H/2, so Q² = 2DS/H and Q* = (2DS/H)^1/2. Because the second derivative is 2DS/Q³, which is positive for positive inputs and Q, this stationary point is a minimum.

At that unconstrained optimum, DS/Q* = HQ*/2: annual ordering and cycle holding costs are equal. This equality need not survive a minimum order, case-size adjustment or quantity discount. It is also an equality of annual costs, not of order cost S and holding cost H, which have different units.

Why Purchase Cost Sometimes Disappears

At a constant unit price, annual purchase expenditure is DC regardless of the batch size. Adding it gives the modeled annual total TC(Q) = DC + DS/Q + HQ/2. Since DC is constant, it does not change the minimizing Q. It still matters for budgeting. When the unit price changes with order quantity, purchase cost must return to the comparison.^[3]

EOQ Example: Compare Feasible Order Sizes

Consider a hypothetical distributor selling one product at a constant 100 units per calendar day, including weekends, throughout a 365-day year. Annual demand is therefore 36,500 units. Assume S = $20 per order, C = $20 per unit and H = $4 per unit per year. There is initially no safety stock, no spoilage or shortage, and replenishment arrives as a complete lot.

To see the trade-off, keep this distributor’s annual demand of 36,500 units, $20 order cost and $4 annual unit holding cost fixed while varying Q. The supplier sells only in cases of 100 units, so the following cost schedules show feasible case multiples around the continuous optimum.

Ordering cost falls as batches grow, while holding cost rises. At 600 units their sum is $2,416.67 a year; at 1,200 units it is $3,008.33. The curve is relatively flat near its minimum, so operationally convenient quantities can be economical without matching the square-root result exactly.

Check the Cases on Either Side

The continuous answer, 604.15, is not an available case multiple. Because the basic cost function decreases up to its optimum and increases afterward, compare the neighboring feasible quantities, 600 and 700, rather than automatically rounding upward.

Choose 600 units under these assumptions. Its annual cost is about six cents above the unrounded continuous minimum. Annual purchase expenditure is still 36,500 × $20 = $730,000, so modeled purchase, ordering and holding costs total $732,416.67. Because holding cost includes an opportunity-cost allowance, that economic total need not equal cash paid out or expenses recognized in financial statements.

EOQ, Working Capital and Days Inventory Outstanding

Continue the same hypothetical distributor, using the feasible 600-unit policy. Assume it pays for stock when received, owns no stock in transit, and values merchandise flowing into COGS at its constant $20 unit cost. There are no other inventory costs in this simplified COGS measure. Compare a 600-unit batch with a 1,200-unit batch while annual demand remains 36,500 units.

For the 600-unit policy, DIO = ($6,000 / $730,000) × 365 = 3 days. This is half the six-day receipt cycle because average stock is half a batch and merchandise moves at a constant rate. DIO is an average residence measure, not the number of days until the next delivery. The ratio follows the inventory-turnover relationship discussed in financial ratio analysis.^[6]

Orders per year are long-run rates. An actual year’s records contain a whole number of orders, depending on inventory at the beginning and end of the year. A beginning-and-ending balance average can also misrepresent the true time-average stock if both snapshots happen at similar points in the ordering cycle.

Moving from 1,200 to 600 units lowers average inventory investment by $6,000 and modeled annual relevant cost by $591.67, calculated from unrounded costs. The first amount is capital released during the transition; it is not another $6,000 saving every year. Supplier credit, receivables and other balances determine the change in total net working capital. The treatment of working-capital investment in free cash flow keeps that asset release separate from recurring operating savings.

Here demand flows evenly over 365 calendar days, so cycle length and DIO use that same basis. If demand instead occurs on business days, use demand per business day with business-day lead time. Do not multiply it by a calendar-day lead time without accounting for the operating calendar.

EOQ vs. Reorder Point vs. Safety Stock

Order size, order timing and uncertainty protection are related decisions, but they are not interchangeable.

Reorder Point: Demand During Lead Time

In a continuously reviewed system, a common reorder-point expression is:

For the distributor’s constant 100 units per calendar day and a fixed two-calendar-day lead time, the no-buffer reorder point is 100 × 2 = 200 units. Ordering at the correct time lets demand use those 200 units while the 600-unit shipment is on its way. A known positive lead time changes timing without changing the basic EOQ cost trade-off.

Suppose management separately chooses an illustrative 50-unit safety buffer. Its reorder threshold becomes 200 + 50 = 250 units. This calculation shows how a chosen buffer enters the trigger; it does not demonstrate that 50 is optimal or delivers any stated service level.

Trigger on Inventory Position, Not Just Shelf Stock

The continuous-review rule places the replenishment order when inventory position reaches or falls below R, subject to the policy’s order-size rules. Placing an order immediately increases inventory position, even though on-hand inventory does not increase until delivery. This prevents repeated orders for demand that an outstanding shipment already covers.^[4]

Use the 600-unit order policy and the illustrative 250-unit threshold above. The following snapshots show why a low shelf count does not necessarily require another order. There are no backorders in these examples.

On receipt, 600 units move from the on-order record to on-hand stock; receipt alone does not change inventory position. If the inventory system separately tracks allocated commitments, define available stock consistently so that the same customer obligation is not deducted twice.

What Safety Stock Can and Cannot Establish

Safety-stock decisions require evidence about demand during the replenishment lead time and the consequences of shortages. A chosen buffer trades additional carrying cost against shortage exposure; basic deterministic EOQ does not solve that problem.^[5]

At H = $4, holding an additional 50 units intact would cost 50 × $4 = $200 per year. If that buffer sits untouched beneath the distributor’s deterministic cycle, average stock becomes 600/2 + 50 = 350 units. Under genuinely variable demand, actual average on-hand stock and shortages require a model of that variability; the simple addition is not an exact forecast for every system.

A service target must also specify its measure. A cycle service level concerns avoiding a stockout during a replenishment cycle; a fill rate concerns the share of demand supplied immediately. A 95% cycle service level does not mean 95% of units are filled immediately. Neither percentage follows merely from adding a 50-unit buffer.^[4]

EOQ with Quantity Discounts

A discount can make a larger order worthwhile, but the lowest unit price does not necessarily give the lowest annual cost. For an all-units discount, every unit in an order receives the price associated with that order’s size. Within price bracket j, compare:

Calculate the continuous EOQ at each price, then find that bracket’s best available quantity. If the root lies inside the bracket, compare its neighboring allowed units or case multiples. If it lies below the bracket, use the lowest allowed quantity there. If it lies above a finite bracket, its highest allowed quantity is the bracket candidate. Finally compare total annual costs across the feasible bracket minima.^[3]

A Hypothetical Discount That Is Worth Taking Only So Far

Return to D = 36,500 units per year, S = $20 per order and 100-unit cases. Now replace the constant $20 price with the all-units schedule below. Keep the assumed annual carrying rate at 20%, so holding cost changes with the price. Set aside cash, warehouse and shelf-life constraints for this comparison.

Both discounted-price roots lie below their qualifying thresholds. Once inside either of those brackets, increasing Q further raises that bracket’s ordering-plus-holding total. Its lowest qualifying case quantity is therefore the candidate, not an infeasible order of roughly 607 units.

For example, TC(1,000) = 36,500 × $19.80 + (36,500 × $20 / 1,000) + ($3.96 × 1,000 / 2) = $725,410. The 1,000-unit order wins. Moving to 2,000 saves $730 in annual purchases and $365 in ordering, but adds $1,976 in holding cost, increasing total cost by $881 a year.

All-Units and Incremental Discounts Differ

An incremental discount applies a lower price only to units above its threshold. Under a separate hypothetical incremental offer charging $20 for the first 1,000 units and $19.80 for the next units, a 1,200-unit order costs 1,000 × $20 + 200 × $19.80 = $23,960. Pricing all 1,200 at $19.80 would instead give $23,760, which the incremental offer does not permit.^[2]

That different purchase-cost structure requires its own total-cost calculation and appropriate inventory-value holding assumption. Do not apply the all-units comparison unchanged or assume the lowest marginal price applies to all annual demand.

Limitations of EOQ and the Role of Just-in-Time

Demand and supply variability. Seasonal demand, promotions and erratic delivery make identical cycles unrealistic. Safety stock and reorder timing need their own evidence. A fixed review schedule also creates a different exposure period from the continuously reviewed policy illustrated here.

Capacity, cash and perishability. Minimum orders, truckloads, shelf life and available funding restrict feasible quantities. Storage costs can jump when another warehouse is needed rather than increase smoothly per unit. A large theoretical optimum for a perishable product may require a different model altogether.

Replenishment and coordination. Production that supplies units gradually needs a finite-replenishment model. Shared freight or coordinated orders across many products can change the relevant order cost, so optimizing each item independently can miss the combined decision.^[2]

Just-in-time (JIT). JIT seeks coordinated flow and replenishment tied to need. Toyota’s own description includes advance stocks of the minimum needed parts, rather than a blanket rule of zero inventory.^[7] In EOQ terms, reducing the real cost per replenishment S lowers the economical batch size. Simply forcing Q downward while S, demand and reliability remain unchanged can increase ordering expense or shortage exposure.

How to Evaluate an EOQ Policy

1. Define the item and demand pattern. Establish a forecast, time basis and whether the repeated steady-cycle approximation is reasonable.
2. Estimate relevant costs. Separate incremental order charges, unit holding costs and purchase price; avoid double-counting freight, financing or unchanged overhead.
3. Compute and constrain the batch. Compare nearby allowed cases, minimum orders, capacity limits and feasible discount-bracket candidates.
4. Set the trigger separately. Use consistent lead-time demand and an inventory-position record that includes outstanding orders.
5. Choose and justify uncertainty protection. Specify the service measure or shortage-cost objective; do not infer it from EOQ.
6. Check the cash and service consequences. Use financial forecasts to assess funding needs, then monitor actual costs, stockouts and forecast errors as conditions change.

Common Mistakes When Using EOQ

1. Mixing demand and holding-cost periods. Monthly demand with annual H gives the wrong quantity. Convert one so both refer to the same period, and keep daily demand and delivery lead time on matching calendars.

2. Substituting a percentage for H. If the carrying rate is 20%, H is not 0.20 dollars. Multiply that annual rate by the appropriate unit value and add any separate relevant holding charges.

3. Ordering again whenever shelf stock looks low. A pending shipment already raises inventory position. Ignoring it can create duplicate orders, even when the reorder-point arithmetic is correct.

4. Treating EOQ as safety-stock optimization. Constant-demand EOQ has no demand distribution or service target. Adding a buffer without those inputs cannot establish a stockout probability.

5. Accepting an unavailable discounted EOQ. A price requiring 1,000 units is unavailable on a 607-unit order. Recompute holding cost when price-dependent, enforce each bracket and compare annual costs including purchases.

6. Confusing an asset reduction with annual profit. Releasing inventory capital is a transition cash-flow effect. Recurring holding and ordering savings are annual cost effects; adding both as annual savings overstates the benefit.

Sources

Sources consulted November 5, 2026. All distributor inputs, price schedules and calculations are hypothetical. The article uses a U.S.-oriented educational finance context and does not prescribe inventory accounting treatment.

1. ACCA, Inventory control; EOQ, relevant costs and consistent units, bulk discounts, reorder levels and buffer inventory. No publication date displayed.
2. MIT OpenCourseWare, Inventory and EOQ Models, ESD.273J, Fall 2009; basic model, sensitivity, finite replenishment and quantity discounts.
3. Manuel Rossetti, Analysis of Inventory Systems, Chapter 3: Deterministic Lot Sizing; Sections 3.5.4, 3.7 and 3.8, especially the bracket cost function in equation 3.23. Author’s instructional text; no publication date displayed.
4. Manuel Rossetti, Analysis of Inventory Systems, Chapter 1: Introduction to Inventory Systems; review timing, inventory states, inventory position and service measures. No publication date displayed.
5. Food and Agriculture Organization of the United Nations, Agricultural and Food Marketing Management, Chapter 9; inventory-model limitations, order cycles and safety-stock trade-offs.
6. OpenStax, Introduction to Business 2e, 14.7: Analyzing Financial Statements, published April 22, 2026; Table 14.4 and Activity Ratios, inventory turnover using average inventory and conversion to days.
7. Toyota Motor Corporation, Toyota Production System; Just-in-Time, synchronized production and minimum advance parts stocks. No publication date displayed.