The Objective Function quantifies the goal to be optimized (maximized or minimized). It maps decision variables to a real value representing cost, profit, distance, time, or other performance measure. In mathematical form: f(x) where x is the vector of decision variables. For linear programs: f(x) = cᵀx; for nonlinear: f(x) can be any differentiable or non-differentiable function. Multi-objective problems have vector-valued objectives f(x) = (f₁(x), f₂(x), ..., fₖ(x)). The objective function selection critically impacts solutions and requires careful modeling to capture true goals. Considerations include: units, scaling, linearization techniques, and handling multiple conflicting objectives through weighting or Pareto optimization.

Operations Research is the application of advanced analytical methods to help make better decisions. It employs techniques from mathematical sciences, statistics, and algorithms to arrive at optimal or near-optimal solutions to complex decision-making problems. OR aims to optimize resource allocation, improve efficiency, and support strategic planning across various industries including manufacturing, logistics, healthcare, and finance.