# Fixed charge

### From Glossary

A cost that is some value, say , regardless of the level as long as the level is positive; otherwise the fixed charge is zero. This is represented by , where is a binary variable. If , the fixed charge is 0; if
, the fixed charge is . An example is whether to open a plant
or not . To apply this fixed charge to the non-negative variable , the constraint is added to the mathematical program, where is a very large value, known to exceed any feasible value of . Then, if (e.g., not opening the plant that is needed for
), is forced by
the upper bound constraint. If (e.g., plant is open), is a redundant upper bound. *Fixed charge problems* are mathematical programs with fixed charges.
(See
Myths and Counterexamples in Mathematical Programming
to avoid a misconception.)