What is a dummy variable in Operations research?

There are various forms.

In linear programming, a dummy variable may be used to convert an inequality into an equation. For example x < 10 can be written as x + u = 10 where u > 0. In this case, it is also called a slack variable.

Dummy variables are used in regression to indicate the presence or absence of a factor, or for binary variables. For example, male/female could be coded numerically as 0/1 where, because the question is binary, the exact coding does not matter.