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# Economic production quantity

Economic Production Quantity model (also known as the EPQ model) is an extension of the Economic Order Quantity model. The EPQ model was developed by E.W. Taft in 1918. The difference being that the EPQ model assumes orders are received incrementally during the production process. The function of this model is to balance the inventory holding cost and the average fixed ordering cost.

## Variables

• K = setup cost
• D = demand rate
• F = holding cost
• T = cycle length
• P = production rate
• $x = frac \left\{D\right\}\left\{P\right\}$

## Formula

$EPQ = sqrt \left\{frac \left\{2KD\right\}\left\{F\right\}\right\} sqrt \left\{frac \left\{1\right\} \left\{1-x\right\}\right\}$

## Relevant Formulas

Average holding cost per unit time:

$frac\left\{1\right\} \left\{2\right\} FD\left(1-x\right)*T$

Average ordering and holding cost as a function of time:

$x\left(T\right) = frac \left\{1\right\} \left\{2\right\} FD\left(1-x\right)T+ frac \left\{K\right\} \left\{T\right\}$