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Encyclopedia > Economic order quantity
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Economic order quantity is that level of inventory that minimises 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. Year 1913 (MCMXIII) was a common year starting on Wednesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Tuesday of the 13-day-slower Julian calendar). ...

Contents

Underlying assumptions

  1. The ordering cost is constant.
  2. The annual (or monthly or whatever periodicity you desire, here we will use annual) demand for the item is constant over time and it is known to the firm.
  3. Quantity discounts doesn't exist.
  4. The order is received immediately after placing the order.

The theory of supply and demand describes how prices vary as a result of a balance between product availability at each price (supply) and the desires of those with purchasing power at each price (demand). ... In finance, discounting is the process of finding the current value of an amount of cash at some future date, and along with compounding cash from the basis of time value of money calculations. ...

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 as carrying 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}{dQ}}left(PD + {frac{CD}{Q}} + {frac{HQ}{2}}right)=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 the economic production quantity model (which determines the optimal production quantity) can be determined in a similar fashion. Economic Production Quantity model (also known as the EPQ model) is an extension of the Economic Order Quantity model. ...


See also

The newsvendor (or newsboy) model is a mathematical model in operations management and applied economics used to determine optimal inventory levels. ...

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).

Year 1934 (MCMXXXIV) was a common year starting on Monday (link will display full 1934 calendar) of the Gregorian calendar. ...

Links

http://www.inventoryops.com/economic_order_quantity.htm


  Results from FactBites:
 
Economic Order Quantity (EOQ) (795 words)
The EOQ is used as part of a continuous review inventory system, in which the level of inventory is monitored at all times, and a fixed quantity is ordered each time the inventory level reaches a specific reorder point.
The EOQ model assumes that demand is constant, and that inventory is depleted at a fixed rate until it reaches zero.
The total order cost per year is S multiplied by the number of orders per year, which is equal to the annual demand divided by the number of orders, or D/Q. Finally, PD is constant, regardless of the order quantity.
Economic order quantity - Wikipedia, the free encyclopedia (324 words)
Economic Order Quantity (also known as the Wilson EOQ Model or simply the EOQ Model) is a model that defines the optimal quantity to order that minimizes total variable costs required to order and hold inventory.
The model was originally developed by F. Harris in 1915, though R. Wilson is credited for his early in-depth analysis of the model.
Additionally, the economic order interval can be determined from the EOQ and the economic production quantity model (which determines the optimal production quantity) can be determined in a similar fashion.
  More results at FactBites »

 
 

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