Objectives, Decision Variables, Constraints, and Feasibility › Disadvantages

The model omits details of the world. An optimum can therefore prescribe a poor operational decision when a relevant requirement is missing or a coefficient is wrong. Conversely, an infeasible model may reveal incompatible requirements, rather than a formulation error. Both possibilities require investigation.

Computational difficulty depends on structure as well as size. General mixed-integer linear optimization is NP-hard, although particular instances can be easy. Continuous nonlinear problems may be convex or nonconvex. A local numerical solver can terminate at a stationary point or on a step or objective tolerance; successful termination alone does not establish a global optimum.

Solver statuses must be read with their tolerances. A mixed-integer optimal status generally means the incumbent and search bound meet the requested stopping criteria, using floating-point feasibility and integrality tolerances. It is stronger than merely finding no better plan, but it is not an exact-arithmetic proof. Tolerance settings depend on the solver and options. Scaling and units affect their physical interpretation and how reliably numerical tests can be met; there is no universal $10^{-9}$ rule.

Formulations can go stale. Coefficients that were correct last quarter can become wrong without an obvious warning when costs, capacities, or operating conditions change. If relevant costs change and the inputs are not updated or revalidated, the model can continue recommending plans based on an obsolete cost structure. Periodic reviews and updates require ongoing work for an actively maintained model.