# Inventory balance equation

### From Glossary

The constraint that says that the amount of
inventory in the next time period must equal the current inventory
plus what is produced or purchased minus what is lost or sold. Let
be the inventory at the beginning of period ,
with given.
Then, the inventory equation is:

where is the level of production (or somehow acquired),
and is the level of sales (or somehow consumed). Typically, ,
but if it is called a *loss factor*, and if it is called
a *gain factor*.

The language used is for the inventory control in the production scheduling problem, but this has become a standard system of equations that appears in many mathematical programs. Thus, the meaning of the variables can be substantially different. One example is the

steel beam assortment problem.