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赛题分析与建模设计

Competition Problem Analysis and Modeling Design

数学建模规范参考

Reference for Mathematical Modeling Specifications

如需领域判断，读取

../_references/math_modeling_norms.md

中的“赛题理解与子问题识别”“假设与模型建立”和“题型防错速查”小节。该文件只作为规范知识库，不替代本阶段的分析报告结构。

For domain judgment, read the sections "Problem Understanding and Sub-problem Identification", "Hypothesis and Model Establishment", and "Quick Check for Problem Type Error Prevention" in

../_references/math_modeling_norms.md

. This file only serves as a specification knowledge base and does not replace the analysis report structure of this phase.

必须产出

Mandatory Deliverables

在当前工作目录的

reports/

子目录中创建或更新：

```
reports/ANALYSIS_MODELING_REPORT.md
```
：
- 赛题分析、子问题拆解、数据与附件理解、评价标准、关键歧义和假设预检。
- 变量、符号、模型假设、目标函数、约束条件、求解算法、各子问题实现口径、代码阶段任务清单

不要在本阶段写论文正文，不要生成最终

paper/

，不要把图表排版任务提前到这里。

Create or update in the

reports/

subdirectory of the current working directory:

```
reports/ANALYSIS_MODELING_REPORT.md
```
:
- Competition problem analysis, sub-problem decomposition, data and attachment understanding, evaluation criteria, key ambiguities, and hypothesis pre-check.
- Variables, symbols, model assumptions, objective functions, constraint conditions, solution algorithms, implementation specifications for each sub-problem, and code phase task list

Do not write the main body of the paper in this phase, do not generate the final

paper/

, and do not advance the chart typesetting task to this stage.

工作流程

Workflow

Step 1: 子问题拆解

Step 1: Sub-problem Decomposition

只把题面中明确编号的顶层问题当作子问题，例如“问题一/二/三”“Problem 1/2/3”。不要把小问、背景描述、数据说明、提交要求误当成独立子问题。

在

ANALYSIS_MODELING_REPORT.md

开头明确写：

根据题目动态调整问题数量

本赛题共 X 个子问题。

每个子问题要说明：

输入数据和已知条件。
决策变量或预测对象。
目标函数或评价指标。
约束条件。
与其它子问题的依赖关系。
绘制哪些图像或表格来展示结果。

Only treat the top-level problems with clear numbering in the problem statement as sub-problems, such as "Problem 1/2/3" or "Problem 1/2/3". Do not mistake sub-questions, background descriptions, data explanations, or submission requirements as independent sub-problems.

Clearly write at the beginning of

ANALYSIS_MODELING_REPORT.md

Adjust the number of problems dynamically according to the topic

This competition problem has a total of X sub-problems.

Each sub-problem should include explanations of:

Input data and known conditions.
Decision variables or prediction objects.
Objective functions or evaluation indicators.
Constraint conditions.
Dependencies with other sub-problems.
Which graphs or tables to draw to display results.

Step 2: 假设敏感性预检

Step 2: Hypothesis Sensitivity Pre-check

列出关键歧义，不要急着定模型。对影响结果的歧义至少给出两种解释，并用简单验算或逻辑递进判断选择。

必须在

ANALYSIS_MODELING_REPORT.md

中包含：

markdown

undefined

List key ambiguities and do not rush to finalize the model. Provide at least two interpretations for ambiguities that affect results, and judge the selection through simple verification or logical progression.

Must include the following in

ANALYSIS_MODELING_REPORT.md

markdown

undefined

假设敏感性预检

Hypothesis Sensitivity Pre-check

模糊表述及解释

Ambiguous Expressions and Interpretations

...

快速验算与递进性检查

Quick Verification and Progressive Check

...

最终采用的解释

Final Adopted Interpretations

...

绘制的图像和对比表格

Plotted Graphs and Comparison Tables


如果某个假设会让后续问题的新增条件没有边际效果，要回头调整解释.


If a certain assumption makes the new conditions of subsequent problems have no marginal effect, go back to adjust the interpretation.

Step 3: 数据理解与建模路线

Step 3: Data Understanding and Modeling Route

对每份附件做数据理解：

行列规模和字段解释。
缺失、异常、重复、单位不一致。
可直接用于建模的变量。
需要派生的指标。

然后给出总体路线：

text

题面 -> 数据清洗(EDA) -> 子问题一模型 -> 子问题二模型 -> 。。。。 -> 结果检验 -> 论文展示

Conduct data understanding for each attachment:

Row and column scale and field explanations.
Missing values, anomalies, duplicates, and inconsistent units.
Variables that can be directly used for modeling.
Indicators that need to be derived.

Then provide the overall route:

text

Problem Statement -> Data Cleaning(EDA) -> Sub-problem 1 Model -> Sub-problem 2 Model -> 。。。。 -> Result Verification -> Paper Presentation

Step 4: 建模报告

Step 4: Modeling Report

在

ANALYSIS_MODELING_REPORT.md

中写出可交给代码阶段实现的完整方案。

每个子问题至少包含：

问题目标。
符号和变量。
模型假设。
目标函数。
约束条件。
求解方法。
输入输出。
代码实现要点。
结果校验方法。

公式要清楚到代码阶段能直接实现。算法描述要包含核心步骤、停止条件、复杂度或可行性说明。

推荐结构：

markdown

undefined

Write a complete solution in

ANALYSIS_MODELING_REPORT.md

that can be handed over to the code phase for implementation.

Each sub-problem must include at least:

Problem objectives.
Symbols and variables.
Model assumptions.
Objective functions.
Constraint conditions.
Solution methods.
Input and output.
Key points for code implementation.
Result verification methods.

Formulas must be clear enough for direct implementation in the code phase. Algorithm descriptions should include core steps, stop conditions, complexity or feasibility explanations.

Recommended structure:

markdown

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建模报告

Modeling Report

1. 总体建模框架

1. Overall Modeling Framework

2. 数据处理方案

2. Data Processing Scheme

3. 符号说明

3. Symbol Explanation

4. 问题一模型

4. Sub-problem 1 Model

5. 问题二模型

5. Sub-problem 2 Model

6. 问题三模型

6. Sub-problem 3 Model

....

7. 灵敏度分析与检验方案

7. Sensitivity Analysis and Verification Scheme

8. 代码实现任务清单

8. Code Implementation Task List


如果子问题数量不是 3 个，按实际题面调整章节，不要硬凑。


If the number of sub-problems is not 3, adjust the chapters according to the actual problem statement, do not force-fit.

Step 5: 给代码阶段的接口

Step 5: Interface for the Code Phase

在

ANALYSIS_MODELING_REPORT.md

末尾写一个“代码实现任务清单”，格式如下：

markdown

undefined

Write a "Code Implementation Task List" at the end of

ANALYSIS_MODELING_REPORT.md

in the following format:

markdown

undefined

代码实现任务清单

Code Implementation Task List

任务	输入	输出	方法	校验
问题一	...	...	...	...
问题二	...	...	...	...

undefined

Task	Input	Output	Method	Verification
Sub-problem 1	...	...	...	...
Sub-problem 2	...	...	...	...

undefined

质量要求

Quality Requirements

所有结论都能回到题面或数据。
不编造数据字段和数值。
不跳过歧义分析。
模型既要有数学表达，也要能被代码实现。
若数据不足或题面不清，要明确记录风险和替代方案。

All conclusions can be traced back to the problem statement or data.
Do not fabricate data fields or values.
Do not skip ambiguity analysis.
The model should have both mathematical expressions and be implementable by code.
If data is insufficient or the problem statement is unclear, clearly record risks and alternative solutions.