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MasterMath

Economic Order Quantity Calculator

The economic order quantity, or Wilson formula: how many units to order each time so that ordering cost plus holding cost adds up to the smallest possible total.

Currency and number format for

Optimal order size

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Optimal order size—
Orders per year—
Days between orders—
Annual ordering cost—
Annual holding cost—
Total inventory cost—

How this was worked out

    The formula

    EOQ = √(2 × demand × ordering cost / holding cost)

    What it means

    Two costs pull in opposite directions. Ordering a lot at once makes ordering cheap, because you do it less often, but it fills the warehouse and pushes holding costs up. Ordering little and often does the reverse. The total cost curve is the sum of the two and it has a minimum, and that minimum is the economic order quantity. At it — and this is what serves as a check — the two annual costs come out exactly equal.

    How to work it out by hand

    1. Note the annual demand, what one order costs to place, and what holding one unit for a year costs
    2. Multiply the demand by the ordering cost and by two
    3. Divide by the holding cost
    4. Take the square root: that is the optimal order size

    What is worth knowing

    The formula assumes constant demand, a fixed lead time and no volume discounts, and in practice none of the three quite holds. Its value lies elsewhere: the cost curve is very flat around the optimum, so being twenty per cent off on the order size raises the total by barely two per cent. That means there is no need to be precise, and any reasonably close order size will do. If the supplier offers quantity discounts, compare total cost at each price break.

    Frequently asked questions

    Why do the two costs match at the optimum?

    It is a property of the formula: the minimum of the sum falls exactly where the two curves cross. It works as a check on the arithmetic.

    What if my supplier gives volume discounts?

    Then work out total cost at each price break and compare. The EOQ is only the starting point.

    What goes into the ordering cost?

    Everything that does not depend on order size: administration, fixed transport, receiving and quality control.

    And into the holding cost?

    Warehousing, insurance, obsolescence and above all the financial cost of tied-up money, which is usually the largest.

    Does getting the order size wrong matter much?

    Little. The curve is very flat near the optimum: a 20 % error in order size raises the total by around 2 %.