ors-methods
GitHub用于运筹学稿件中证明技术、算法或仿真协议的设计。根据所需结果（如最优性、收敛率等）匹配数学工具，确保算法具有可证明的保证，规范仿真方法论及证明严谨性，以应对同行评审。
Trigger Scenarios
Install
npx skills add brycewang-stanford/Awesome-Journal-Skills --skill ors-methods -g -y
SKILL.md
Frontmatter
{
"name": "ors-methods",
"description": "Use when designing the proof technique, algorithm, or simulation protocol for an Operations Research (OR) manuscript — choosing the right machinery (duality, dynamic programming, probabilistic coupling, convergence analysis, simulation output analysis) to actually establish the claimed results. Establishes the results; it does not state the model (ors-theory-development) or run the experiments (ors-data-analysis)."
}
Proof & Algorithm Methodology (ors-methods)
When to trigger
- The model and claims exist (
ors-theory-development) and now must be proved or guaranteed. - You need to pick a proof strategy or design an algorithm with provable guarantees.
- A reviewer says "the proof of Theorem X has a gap" or "the rate is not established."
Match the machinery to the result
Operations Research is mathematically rigorous: the contribution lives or dies on the soundness and strength of the analysis. Pick technique by methodology:
| Result you need | Typical machinery |
|---|---|
| Optimality / strong duality | LP/conic duality, KKT, polyhedral / total unimodularity, submodularity |
| Approximation guarantee | LP/SDP rounding, primal-dual, greedy + submodular bounds |
| Complexity / hardness | reductions (NP-hardness), oracle lower bounds |
| Convergence & rate | monotonicity/Lyapunov, fixed-point/contraction, first-order analysis |
| Steady-state / stability | Foster-Lyapunov, regenerative arguments, fluid/diffusion limits |
| Stochastic comparison / bounds | coupling, stochastic dominance, martingale/concentration inequalities |
| MDP / dynamic decisions | dynamic programming, value/policy iteration, ADP with error bounds |
| Heavy-traffic / asymptotics | functional CLT, weak convergence, state-space collapse |
Algorithm design with guarantees
- State what the algorithm guarantees: exact/optimal, an approximation factor, an ε-stationary point, or a regret/convergence rate — and under which assumptions.
- Give complexity (time, iterations, oracle calls; per-iteration cost and total).
- Separate the method from its proof of correctness/convergence; a fast heuristic without analysis is not an OR methodological contribution on its own.
Simulation methodology (when the analysis is empirical-stochastic)
- Specify the estimator and argue consistency; quantify error with valid confidence intervals (batch means, regenerative, or replication-based).
- Use variance reduction (common random numbers, control variates) and justify it.
- For ranking-and-selection / simulation optimization, state the statistical guarantee (e.g., probability of correct selection) and the budget rule.
Proof hygiene OR reviewers expect
- Every assumption used is invoked explicitly where the proof needs it.
- Long proofs go to an e-companion (which must not be longer than the manuscript); the main text keeps the key idea and a proof sketch.
- Constants and rates are tracked, not hidden in "O(·)" when tightness is claimed.
Methodology pushback patterns and the OR fix
| Referee remark | Underlying defect | Fix that meets the OR bar |
|---|---|---|
| "Proof of Theorem X has a gap" | an assumption invoked implicitly | name where each hypothesis is used; add a lemma to bridge the step |
| "The rate is asserted, not established" | rate read off numerical curves | prove it analytically (Lyapunov / contraction / first-order) with tracked constants |
| "Algorithm has no guarantee" | a fast heuristic without analysis | attach an approximation factor, ε-stationarity, or regret/convergence bound |
| "Bound may not be tight" | only an upper bound shown | exhibit a matching instance, or reframe explicitly as best-known |
| "Simulation conclusions unreliable" | point estimates, no error control | report CIs (batch-means/regenerative) and variance reduction with the rule |
| "Structural result not connected to the application" | theorem floats free of the decision | show the guarantee changes the operational policy it motivates |
Operations Research, as the INFORMS flagship, lives on soundness and strength of analysis: a heuristic without a guarantee is an INFORMS Journal on Computing artifact, not an OR methodological contribution. The machinery table above exists so each claim is discharged by analysis a referee can verify line by line.
Worked machinery walk-through (illustrative)
Target result: an approximation algorithm for a stochastic-covering problem with a claimed 1.5-factor guarantee (illustrative). Machinery selection from the table: LP-rounding + primal-dual for the factor; concentration (martingale) to control the stochastic constraint; an oracle lower bound to argue the factor cannot be pushed below 1.5 without stronger assumptions. Proof hygiene: each of the three assumptions (bounded second moment, independence across stages, integral demand) is cited exactly where the argument needs it; the full rounding analysis goes to the e-companion, the main text keeps the primal-dual sketch and the tight-instance construction. This produces a theorem-grade result and a tightness statement — the combination OR referees reward over a bare upper bound.
Execution bridge (StatsPAI / Stata MCP)
For the empirical / causal lane, estimate and audit rather than only specify. Full
map: execution-with-mcp. Operations Research is predominantly analytical / optimization / stochastic modeling; use the chain below only for its empirical/causal papers — modeling, optimization, and simulation are outside this causal-inference toolchain.
detect_design→recommend→ fit withas_handle=true→audit_resultto enumerate the checks the design owes.- Panel / staggered DiD:
callaway_santanna/sun_abraham+bacon_decompositionhonest_did_from_result. IV:effective_f_test+anderson_rubin_ci. RDD:rdrobust+mccrary_test.
- Experiments: randomization-based inference and
romano_wolffor the many-outcome family-wise correction reviewers expect.
Match the toolchain to the reviewer pool, and report the effect size the venue wants. A run end-to-end (synthetic data, real returns) is in the JF execution walkthrough.
Anti-patterns
- A "proof" that silently adds an assumption mid-argument.
- Claiming a rate from numerical curves rather than analysis.
- An algorithm with no guarantee presented as the central contribution.
- Simulation conclusions with no confidence intervals or variance control.
Output format
【Result → technique】each Thm/Prop mapped to its machinery
【Algorithm】guarantee (exact/approx/rate) + complexity
【Simulation】estimator, CI method, variance reduction (if used)
【Proof hygiene】assumptions invoked explicitly; e-companion plan
【Open gaps】[...]
【Next step】ors-data-analysis
Version History
- 1839142 Current 2026-07-05 14:08
