Problem Formulation

Optimization · Axiom Academy

Learn how to translate real-world problems into mathematical optimization problems The first step in problem formulation is identifying what we're trying to decide. These are the decision variables - the quantities we have control over. Key Question: What choices or actions can we make? The objective function quantifies what we're trying to achieve. It maps our decision variables to a single value we want to maximize or minimize. Key Question: What are we trying to optimize? Maximize profit? Minimize cost? Minimize time? Constraints represent the limitations or requirements that our solution must satisfy. They define the feasible region - the set of all possible solutions. Key Question: What limits our choices? What requirements must be met? Resource constraints: 2x₁ + 3x₂ ≤ 100 (hours available) Non-negativity: x₁ ≥ 0, x₂ ≥ 0 Once we've identified our decision variables, objective, and constraints, we assemble them into the standard form of an optimization problem. 5. Common Pitfalls in Formulation Even experienced practitioners can make mistakes when formulating optimization problems. Here are the most common pitfalls to avoid:

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