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EOQ Calculator

Balance annual ordering and holding costs with the basic Economic Order Quantity formula and visible model assumptions.

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How to use

  1. 1.Enter annual demand in units per year.
  2. 2.Enter fixed cost per order and annual holding cost per unit using one currency basis.
  3. 3.Calculate EOQ, review assumptions and feasible pack sizes, then copy the metrics if useful.

About EOQ Calculator

EOQ Calculator evaluates the basic Economic Order Quantity model for one inventory item. Enter annual demand D, fixed ordering or setup cost S, and annual holding cost per unit H. The result reports the continuous EOQ, expected orders per year, average days between orders, annual ordering cost, annual holding cost, and their combined relevant cost. Calculation stays in the browser and the metrics can be copied.

The standard formula is Q*=sqrt(2DS/H). It comes from minimizing annual relevant cost TC(Q)=DS/Q+HQ/2. The first term falls as order quantity grows because fewer orders are placed. The second rises because average cycle stock is Q/2. At the continuous optimum those two cost components are equal. University operations-management materials independently state both the square-root formula and the cost balance used here.

All three inputs must share one annual basis. Demand is units per year, ordering cost is currency per order, and holding cost is currency per unit per year. If holding cost is supplied as a percentage of unit price, convert it to an annual currency amount per unit before entry. The calculator does not infer currencies or perform that conversion. Output cost uses whatever consistent currency was entered.

The displayed EOQ can be fractional because it is the mathematical continuous optimum. Real orders may require whole units, cases, pallets, minimum quantities, or supplier pack multiples. Compare feasible quantities immediately below and above the formula result using the total-cost equation before choosing. Blind rounding can be inappropriate when pack constraints are large, although the cost curve is often relatively flat near its minimum.

Basic EOQ assumes constant known demand, constant known ordering and holding costs, instantaneous complete replenishment, no shortages, no safety stock, no quantity discounts, and no capacity or cash constraint. It also assumes unit purchase price does not change with Q, so purchase cost is omitted from relevant-cost comparison. Violating these assumptions can change the best quantity materially.

Lead time is not an EOQ input because EOQ answers how much to order, not when to reorder. A reorder-point model uses demand during lead time plus any justified safety stock. Seasonal demand, uncertain lead time, perishability, obsolescence, production replenishment, discounts, or service-level targets require a different model or an extension.

Eight external golden cases include the university example D=1200, S=5, H=1.2, which gives exactly 100 units, plus fractional costs and a wide range of scales. Tests verify the square-root outputs and the invariant that annual ordering cost equals annual holding cost at EOQ. Zero, negative, non-finite, and excessively large inputs are rejected.

Use this page for coursework, a first inventory baseline, or sensitivity exploration. Do not treat it as an automatic purchasing commitment. Validate demand forecasts, carrying-cost composition, supplier constraints, cash, shelf life, lead-time risk, service levels, and feasible pack sizes with responsible operations staff before ordering.

Sensitivity matters because D, S, and H are estimates rather than timeless facts. Recalculate when forecasts, administration, warehouse cost, insurance, shrinkage, or capital cost changes. Comparing realistic scenarios is more informative than preserving one precise EOQ from stale inputs.

Methodology & sources

Validate positive annual D, S, and H; calculate Q*=sqrt(2DS/H), D/Q orders per year, 365Q/D cycle days, DS/Q ordering cost, HQ/2 holding cost, and their sum. Expose the cost-balance invariant and basic-model assumptions without rounding the optimization internally.

Frequently asked questions

Why can EOQ be fractional?
The formula finds a continuous optimum; compare feasible whole or pack-multiple quantities around it.
Is purchase price included?
Not when unit price is constant; discounts require a quantity-discount model and cost comparison.
Does EOQ tell me when to order?
No. Reorder timing needs demand during lead time and any justified safety stock.
Why are ordering and holding costs equal?
At the basic continuous EOQ, the two variable annual cost terms balance mathematically.

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