Optimization is at the core of analytics, allowing you to make the best possible decisions given a set of options and limitations. In any optimization problem, you are trying to find the most favorable outcome—such as maximizing profit or minimizing cost—by carefully selecting certain values, called decision variables, while respecting a set of limitations, known as constraints. The objective is the specific goal you want to achieve, like increasing revenue or reducing delivery time. In analytics, these elements work together to create a structured problem that can be solved with mathematical methods and computational tools.

Structure of an optimization problem in analytics

• Decision variables: what you control. For example, let $x$ represent the number of products to make.

• Objective: what you want to optimize. For instance, maximize profit: $\text{profit} = \text{revenue} - \text{cost}$.

• Constraints: limitations or requirements. For example:

  • $x \leq \text{machine\_capacity}$
  • $x \geq \text{minimum\_order}$

Example mapping:

• $x$: decision variable;
• Maximize profit: objective;
• $\text{machine\_capacity}$, $\text{minimum\_order}$: constraints.