# Formulas and Equations¶

The formal expression of the formulas and equations used in the library are detailed here.

## Standard Deviation of Lead-time demand¶

\[\sigma_{LTD} = \sqrt{LT \times \sigma_{D}^2 + D^2 \times \sigma_{LT}^2}\]

- where:
sigma_{LTD} = Standard deviation of lead-time demand

LT = Lead-time

D = Demand

## Reorder Level¶

The formula used for calculating the reorder level is:

\[RL = LT \times D + Z \times \sigma \times \sqrt{LT}\]

- where:
Z = service level

LT = Lead-time

D = Demand

## Safety Stock¶

The formula used for safety stock is:

\[SS = Z \times \sigma \times \sqrt{LT}\]

- where:
SS = Safety Stock

Z = service level

LT = Lead-time

## Economic Order Quantity (eoq)¶

The economic order quantity is calculated using:

\[eoq_{0} = \sqrt \frac{2 \times R \times D}{HC}\]

- where:
R = Reorder Cost

D = Demand

HC = Holding Cost