| name | ors-theory-development |
| description | Use when formulating the model and stating results for an Operations Research (OR) manuscript — defining the optimization/stochastic/simulation model, assumptions, and the theorems, propositions, and lemmas that carry the contribution. Builds the mathematical object and its claimed results; it does not prove them in detail (ors-methods) or run the computational study (ors-data-analysis). |
Model & Result Development (ors-theory-development)
When to trigger
- You are turning an OR problem into a precise mathematical model.
- You need to decide what to claim — and as what (theorem vs. proposition vs. conjecture).
- A reviewer will ask whether your assumptions are necessary or merely convenient.
Build the model the OR way
Operations Research rewards a clean mathematical object and provable results.
For the dominant OR/MS methodologies:
- Optimization model: state decision variables, objective, constraints, and the
feasible region precisely. Identify structure (convexity, total unimodularity,
submodularity, conic representability) — structure is what enables theorems and
efficient algorithms.
- Stochastic / probabilistic model: specify the probability space, the process
(Markov chain, queue, MDP), the information/filtration, and the performance measure
(steady-state cost, regret, tail probability). State stability/ergodicity conditions.
- Simulation model: specify the stochastic dynamics and the estimand, and how a
consistent estimator with quantifiable error will be obtained.
- Decision-analytic model: specify the utility/risk measure, the information
structure, and the optimality criterion.
State results at the right strength
| Claim type | Use when |
|---|
| Theorem | A central, fully proved result (optimality, complexity, convergence rate, bound) |
| Proposition | A supporting proved result of lesser scope |
| Lemma | A technical step used inside a proof |
| Corollary | An immediate consequence |
| Conjecture | Stated explicitly as unproven; never disguised as a theorem |
Each formal statement needs explicit hypotheses; tie every assumption to where the
proof uses it (this is what ors-methods will then discharge).
Assumptions discipline
- Justify, don't smuggle. For every assumption, say why it holds in the motivating
application or why it is standard, and whether results degrade gracefully without it.
- Minimality. Reviewers probe whether an assumption is necessary; pre-empt with a
counterexample showing the result fails when it is dropped, or a remark that it can be
relaxed.
- Tightness. Where you prove a bound or rate, indicate whether it is tight (a
matching instance) — tightness is a strong OR contribution.
Frame significance without equations (for the intro)
OR requires an equation-free introduction: articulate the problem, the results,
and their significance in words. Develop the model here, but draft the plain-language
version of each result so the intro can state "we show that ..." without notation.
Model-level pushback patterns and the OR fix
| Referee/AE remark | What it flags | Fix that meets the OR bar |
|---|
| "Model too stylized to matter" | structure stripped to triviality | restore the feature that makes the decision realistic; reprove |
| "Model too general to say anything" | no exploitable structure | impose convexity/submodularity/ergodicity that the application supports |
| "Assumption is convenient, not necessary" | proof-driven hypothesis | add a counterexample showing the result fails without it, or relax it |
| "This is a conjecture, not a theorem" | numerically-supported claim labeled Theorem | downgrade to Conjecture, or supply the proof in ors-methods |
| "Structural result not connected to the application" | theorem floats free of the decision | state which operational policy the structure prescribes |
Because Operations Research is the INFORMS flagship for rigorous OR/MS methodology,
the editorial bar is a clean mathematical object whose structure both enables a
theorem and maps to a decision. A model that admits no theorem reads as
under-specified; one that admits a theorem but no operational reading reads as elegant
but irrelevant — the two failure modes the table above pre-empts.
Worked formulation vignette (illustrative)
Stochastic-inventory control under correlated demand. Model: state = on-hand
inventory; action = order quantity; objective = expected discounted holding + backorder
cost; demand a Markov-modulated process (illustrative). Structure exploited:
K-convexity of the value function under the modulation. Result strength: Theorem 1
states an (s,S)-type policy is optimal (a proved central result); Proposition 1 gives
monotone comparative statics in the modulation rate (supporting); a Conjecture flags the
multi-product extension as unproven. Assumptions discipline: the bounded-demand
hypothesis is justified by capacity limits in the application and shown necessary via a
counterexample where unbounded demand breaks K-convexity. Plain-language for the
intro: "we show the optimal replenishment rule reduces to ordering up to a single
critical level that depends on the demand regime" — no notation, decision-relevant. This
gives ors-methods an explicit theorem-to-machinery handoff and keeps the structure
tethered to the operational policy.
Anti-patterns
- A model so general it admits no theorem, or so special it is uninteresting.
- Assumptions chosen to make a proof easy with no application grounding.
- Calling a numerically supported regularity a "theorem."
- Hiding the key assumption in notation rather than stating it.
Output format
【Model】variables / objective / constraints / process / estimand ...
【Structure exploited】convexity / submodularity / ergodicity / ...
【Results】Thm/Prop/Lemma list with one-line plain-language each
【Assumptions】each justified + necessity noted
【Plain-language for intro】"we show ..." (no notation)
【Next step】ors-methods
