In optimization models, what do binary variables typically represent?

Binary variables are specifically designed to represent two distinct states in optimization models, typically denoting the presence or absence of a decision option. When a binary variable is used, it can take on only two values: 0 or 1. A value of 1 usually indicates that a particular option or decision is selected or active, while a value of 0 implies that the option is not selected or is inactive.

This characteristic of binary variables is particularly useful in various applications, such as project selection, facility location, or any situation where decisions are of an on/off nature. For instance, if a company is deciding whether to launch a new product, a binary variable can succinctly express the choice to launch (1) or not to launch (0).

In contrast, continuous variables are better suited for representing quantities that can take any value within a given range, such as the amount of raw material to produce. Thus, the representation of binary variables aligns perfectly with situations requiring a clear choice of alternatives, making their use integral to forming valid optimization models.