Decision optimization modeling

Decision Optimization Modeling

Translate an operational decision into a falsifiable mathematical model whose recommended solution can be independently checked. Read references/optimization-modeling-method.md before selecting a formulation or solver.

Workflow

1. Define the decision owner, controllable actions, entities, horizon, frequency, latency, downstream effects, baseline policy, and terminal decision artifact. Separate controllable choices from forecasts and facts.
2. Declare sets, indices, parameters, units, sources, timestamps, uncertainty, missingness, and lineage. Reject inputs whose meaning or unit cannot be reconciled.
3. Define decision variables and domains before writing the objective. Include state, recourse, slack, and activation variables only when their operational meaning is explicit.
4. State the objective in business or system units. For multiple objectives, declare priority, lexicographic order, Pareto treatment, or calibrated trade-off weights; never hide policy choices inside arbitrary coefficients.
5. Encode hard constraints separately from soft preferences and penalties. Bind every constraint to its operational rule, source, tolerance, and reason for being hard or relaxable.
6. Choose deterministic, scenario-based stochastic, chance-constrained, or robust treatment according to the uncertainty and decision timing. State distributional and independence assumptions and what happens outside the modeled set.
7. Test feasibility and boundedness before optimization. Exercise empty, minimum, maximum, conflicting, and impossible cases; preserve an explicit diagnostic for infeasibility instead of silently dropping constraints.
8. Solve with reproducible configuration. Record solver, version, formulation, seed where relevant, termination status, objective, bounds, optimality gap, resource limits, and incumbent solution.
9. Independently recompute the objective and every material constraint from the emitted solution. Compare with a current baseline, a simple heuristic, and exhaustive enumeration on a tiny fixture where feasible.
10. Run sensitivity, scenario, stress, and parameter-perturbation analysis. Convert the model into a robust operating policy with fallback behavior, monitoring signals, re-solve triggers, and decision handoff.

Artifact

Produce a Constrained Decision Model:

• decision boundary, horizon, baseline, assumptions, and non-goals;
• sets, parameters, units, provenance, uncertainty, and data-quality rules;
• variables, objective, constraints, tolerances, and mathematical formulation;
• feasibility evidence, solver configuration, result, bounds, gap, and runtime;
• independent solution verification and baseline or heuristic comparison;
• sensitivity, stress cases, robust policy, fallback, monitoring, and re-solve conditions;
• unsupported claims, unresolved model risk, and implementation handoff.

Boundaries

• Use optimization-objective-review for the real outcome, proxy, Goodhart, gaming, and protected-floor contract when an automated optimizer will act on the model. This Skill consumes that contract and owns variables, constraints, solver evidence, and solution verification.
• When both Skills apply but no standalone objective audit was requested, integrate the material objective-contract fields into this Constrained Decision Model rather than emitting a second artifact.
• Use decision-quality-standard when the job is evidence-based qualitative selection among materially distinct options without a mathematical program.
• Use agent-planning-system-review for how an agent decomposes, sequences, observes, and replans work.
• Use probabilistic-forecasting when the primary artifact is a calibrated prediction rather than a controllable decision.
• Use product-experiment-review or causal-inference-analysis to estimate the effect of an intervention. An optimizer may consume those estimates but does not identify them.
• Do not treat solver success as model validity. Feasible nonsense remains nonsense when variables, objectives, constraints, data, or uncertainty do not represent the operational decision.