The economic order quantity (EOQ) tells how much to buy in each order. Ordering often and in small amounts raises ordering costs; ordering rarely and in large amounts raises the money waiting in stock. EOQ is the quantity that minimises the sum of these two costs.

Formula

EOQ = √( 2 × D × S / (c × h) )
Symbol Meaning
D Annual demand (units)
S Fixed cost per order
c Unit cost
h Annual holding rate (share of stock value)

The two costs:

annual ordering cost = (D / Q) × S
annual holding cost  = (Q / 2) × c × h

At the EOQ the two are equal.

Step-by-step example

Annual demand 3,650 units (10 a day), cost per order 500, unit cost 40, holding rate 25%.

annual holding cost per unit = 40 × 0.25                 = 10
EOQ                          = √(2 × 3,650 × 500 / 10)   = 604.2 units
orders per year              = 3,650 / 604.2             = 6.04
days between orders          = 365 / 6.04                = 60.4 days
annual ordering cost         = 6.04 × 500                = 3,020.8
annual holding cost          = 604.2 / 2 × 10            = 3,020.8
total                                                    = 6,041.5

The calculator above opens with this example.

How sensitive is it?

The total cost curve is flat around the EOQ. In the example, ordering 500 or 700 units raises the total cost by only a few percent. So rounding the EOQ to a case size or the supplier’s minimum order quantity is fine, and small errors in the inputs have little effect.

When is it not suitable?

  • If demand is very erratic or seasonal, the annual average can mislead; the order quantity should follow the forecast.
  • For products with a short shelf life, the EOQ must not exceed what can be sold before it spoils.
  • If the ordering cost is unknown, a “target days of cover” rule (for example 30 days of need) is more practical.

In VidiStock

EOQ assumes constant demand, which does not hold for seasonal products. So when a cost per order is entered in Settings, VidiStock uses EOQ’s exact counterpart for period demand instead: the Wagner–Whitin method finds the order schedule with the lowest total cost from the weekly forecast, ordering cost and holding cost. Minimum order quantity, case size, maximum cover and shelf life are part of the calculation. Without an ordering cost, the target days of cover are used. EOQ is shown in the order breakdown for comparison. Unit cost comes from the product card (at the current rate for foreign-currency products), and the holding rate is the sum of the capital, storage, insurance and obsolescence rates. More: Reorder point.