- Economic order quantity
**Economic order quantity**is that level of inventory that minimizes the total of inventory holding cost and ordering cost. The framework used to determine this order quantity is also known as**Wilson EOQ Model**. The model was developed by F. W. Harris in 1913. But still R. H. Wilson is given credit for his early in-depth analysis of the model.**Underlying assumptions**# The ordering cost is constant.

# The rate of demand is constant**Variables***$Q$ = order quantity

*$Q^*$ = optimal order quantity

*$D$ = annual demand quantity of the product

*$P$ = purchase cost per unit

*$C$ = fixed cost per order ("not" per unit, in addition to unit cost)

*$H$ = annual holding cost per unit (also known ascarrying cost ) (warehouse space, refrigeration, insurance, etc. usually not related to the unit cost)**The Total Cost function**The single-item EOQ formula finds the minimum point of the following cost function:

Total Cost = purchase cost + ordering cost + holding cost

- Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P×D

- Ordering cost: This is the cost of placing orders: each order has a fixed cost C, and we need to order D/Q times per year. This is C × D/Q

- Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is H × Q/2

$TC\; =\; PD\; +\; \{frac\{CD\}\{Q\; +\; \{frac\{HQ\}\{2$.

In order to determine the minimum point of the total cost curve, set its derivative equal to zero:

$\{frac\{dTC(Q)\}\{dQ\; =\; \{frac\{d\}\{dQleft(PD\; +\; \{frac\{CD\}\{Q\; +\; \{frac\{HQ\}\{2\; ight)=0$.

The result of this derivation is:

$-\{frac\{CD\}\{Q^2\; +\; \{frac\{H\}\{2=0$.

Solving for Q gives Q* (the optimal order quantity):

$\{frac\{H\}\{2=\{frac\{CD\}\{Q^2$

$Q^2=\{frac\{2CD\}\{H$

Therefore: $Q^*\; =\; sqrt\{frac\{2CD\}\{H$.

Note that interestingly, Q* is independent of P, it is a function of only C, D, H.

**Extensions**Several extensions can be made to the EOQ model, including backordering costs and multiple items. Additionally, the

economic order interval can be determined from the EOQ and theeconomic production quantity model (which determines the optimal production quantity) can be determined in a similar fashion.**See also*** Classical Newsvendor model:

Newsvendor **References***Harris, F.W. "How Many Parts To Make At Once" Factory, The Magazine of Management, 10(2), 135-136, 152 (1913).

*Harris, F. W. "Operations Cost" (Factory Management Series), Chicago: Shaw (1915).

*Wilson, R. H. "A Scientific Routine for Stock Control" Harvard Business Review, 13, 116-128 (1934).**Links**http://www.inventoryops.com/economic_order_quantity.htm

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**Economic Order Quantity**— Saltar a navegación, búsqueda El Economic Order Quantity, o EOQ, constituye actualmente uno de los sistemas de administración de inventarios. Creado a principios del siglo XX, el EOQ es un método que, tomando en cuenta la demanda, el costo por… … Wikipedia Español**economic order quantity**— ( EOQ) The order quantity that minimizes total inventory costs. Bloomberg Financial Dictionary * * * economic order quantity economic order quantity ➔ quantity * * * economic order quantity UK US noun [C or U] (ABBREVIATION … Financial and business terms**Economic Order Quantity**— Die klassische Losformel oder Andler Formel (engl. Economic Order Quantity, EOQ Formel) ist eine im deutschen Sprachraum 1929 von Kurt Andler bekanntgemachte Methode[1][2] zur Ermittlung der optimalen Losgröße im Rahmen von einstufiger,… … Deutsch Wikipedia**economic order quantity**— EOQ A decision model, based on differential calculus, that determines the optimum order size for purchasing (sometimes called the economic purchase quantity) or manufacturing (economic manufacturing quantity) an item of stock. The optimum order… … Accounting dictionary**economic order quantity**— EOQ A decision model, based on differential calculus, that determines the optimum order size for purchasing (sometimes called the economic purchase quantity) or manufacturing (economic manufacturing quantity) an item of stock. The optimum order… … Big dictionary of business and management**economic order quantity**— That quantity derived from a mathematical technique used to determine the optimum (lowest) total variable costs required to order and hold inventory … Military dictionary**economic order quantity**— /ˌi:kənɒmɪk ɔ:də ˌkwɒntɪti/ noun the quantity of stocks which a company should hold, calculated on the basis of the costs of warehousing, of lower unit costs because of higher quantities purchased, the rate at which stocks are used and the time… … Marketing dictionary in english**economic order quantity**— EOQ A volume of inventory intended to minimize *inventory related administrative, holding, and transport costs. An optimal EOQ can be calculated through either differential calculus or subjective estimation … Auditor's dictionary**Economic Order Quantity - EOQ**— An inventory related equation that determines the optimum order quantity that a company should hold in its inventory given a set cost of production, demand rate and other variables. This is done to minimize variable inventory costs. The full… … Investment dictionary**Economic order quantity (EOQ)**— The order quantity that minimizes total inventory costs. The New York Times Financial Glossary … Financial and business terms