A deterministic inventory formula that gives the order quantity Q* minimizing the steady‑state sum of ordering cost and holding cost per period for constant, known demand D, fixed cost per order S, and constant per‑unit holding cost H, under assumptions of instantaneous replenishment, infinite planning horizon and no stockouts.

Principle

When demand is constant and lead time is deterministic, total annual cost is the sum of ordering cost (S·D/Q) and holding cost (H·Q/2); minimizing this convex cost function yields Q* = sqrt(2·D·S / H), balancing ordering frequency against average inventory.

Demonstration

Illustrative scenario → Situation: A distributor has deterministic annual demand D=10,000 units, order cost S=$50/order, holding cost H=$2/unit·year. → Recognition: Assumptions of constant demand and instantaneous replenishment hold. → Action: Compute Q* = sqrt(2·10,000·50/2) = sqrt(500,000) ≈ 707 units. → Consequence: Ordering ~707 units per order minimizes combined ordering and holding costs under the model assumptions.

Misapplication

Using EOQ unchanged when demand is stochastic, lead time is variable, replenishment is not instantaneous, quantity discounts exist, capacity or lot‑size constraints apply, or stockouts/backordering are permitted; the error is treating EOQ’s deterministic tradeoff as universally optimal.

Consequence

Correct use yields a closed‑form stocking policy that minimizes the modeled tradeoff between ordering frequency and average inventory cost; misapplication can produce suboptimal orders, higher total cost, or service failures because critical factors (variability, constraints, discounts) are omitted.

Reversal

If demand is stochastic, lead times uncertain, or unit price varies with order size, optimal policies shift to (s,S) policies, newsvendor formulations, or quantity‑discount optimization; capacity or minimum‑order constraints discretize or alter the optimum away from the EOQ closed form.

Boundary

Clearly within: constant deterministic demand rate, fixed order cost per replenishment, constant holding cost per unit, instantaneous replenishment, infinite horizon, no shortages. Boundary case: small random demand noise with robust safety stock adjustments—EOQ may remain a useful baseline. Clearly outside: stochastic demand models, fixed periodic review policies, multi‑item joint replenishment problems, or lot‑size discounts without modification.

Semantic Tension

Analytical tractability and closed‑form policy ↔ realism of demand and cost structures (uncertainty, lead‑time variability, discounts, capacity limits); EOQ trades simplicity for limited applicability.

Synthesis

EOQ isolates the pure tradeoff between ordering and holding costs in a deterministic setting; it serves as a tractable baseline and starting point, but practitioners must adapt or replace it when variability, pricing, or constraints materially affect costs or service.