How this calculation works
Balance annual order cost against the holding cost of average cycle stock. Compare feasible quantities either side of the continuous optimum, without automatically rounding upward or assuming a purchase-price discount.
Continuous EOQ = √(2DS/H); compare DS/Q + HQ/2 at adjacent positive pack multiplesA worked example
Demand 12,000 units/year, ₹500 per order and ₹30 annual holding per unit give a continuous EOQ of about 632.455532 units. With unit-sized packs, compare 632 with 633; 632 has the lower modeled annual cost.
Good to know
Deterministic constant demand, full instantaneous replenishment, no shortages and no quantity discounts. Purchase price and safety-stock holding are excluded. Pack rounding is a modeled cost comparison, not a complete order recommendation.
Reference: Reference: model definitions and scope (opens in a new tab) ↗
The continuous optimum is not automatically a feasible order
With annual demand of 12,000 units, ₹500 per replenishment and ₹30 annual holding cost per unit, the continuous optimum is about 632.455532 units. If only whole units can be ordered, the useful comparison is between 632 and 633. Rounding upward by default does not necessarily select the lower modeled cost.
For these inputs, 632 units gives about ₹18,973.670886 of combined annual ordering and cycle-stock holding cost, while 633 gives about ₹18,973.672986. The difference is tiny and can disappear in a two-decimal currency display. The comparison uses unrounded costs, not the rounded figures you happen to see.
The reorder point and inventory position calculator checks a trigger using supplied stock commitments. EOQ instead compares order quantities under a fixed ordering/holding-cost model.
Pack multiples change the feasible choices
With packs of ten, compare 630 and 640 rather than 632 and 633. Their modeled annual combined costs are about ₹18,973.809524 and ₹18,975 respectively. The lower feasible choice is 630 under this particular cost function. If the continuous optimum is below one pack, the minimum feasible quantity is one pack.
Ordering cost falls as the lot gets larger because fewer replenishments are needed. Average cycle stock grows as Q/2, so its holding cost rises. The square-root balance assumes constant demand and full instantaneous replenishment. A change in unit purchase price, a storage cap or a perishable item would alter the decision model.
Order quantity and reorder timing answer different questions
This page addresses lot size. The reorder point and inventory position calculator instead checks when an entered demand/lead/buffer trigger is reached. A statistically modeled safety buffer can be explored in the safety stock calculator, but it is not automatically added to the EOQ cycle-stock calculation.
Use one annual basis for demand and holding cost. The days represented by that year are an entered planning basis used for the cycle-duration figure, not a detected calendar. All monetary inputs must already share one currency. This simple cost minimum does not decide cash availability, supplier reliability, capacity or whether an order should actually be placed.
A few questions, answered
Is holding cost a percentage?
Here it is a currency amount per unit per modeled year. Convert any percentage-based carrying assumption into that compatible amount before entering it.
Why compare both neighboring pack multiples?
The continuous EOQ can lie between feasible quantities. The lower combined ordering-plus-holding cost may be below or above it; automatically rounding upward is not enough.
Are purchase discounts included?
No. Unit purchase price is held constant and its cost does not change the optimum in this model. Quantity discounts require a different cost comparison.
Does the lot size include safety stock?
No. The Q/2 average is cycle stock. Safety-stock level and replenishment timing are separate tasks.