Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:47:17

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: debate

```sql
CREATE TABLE people (
  People_ID NUMBER,
  District TEXT,
  Name TEXT,
  Party TEXT,
  Age NUMBER
);
```

```sql
CREATE TABLE debate (
  Debate_ID NUMBER,
  Date TEXT,
  Venue TEXT,
  Num_of_Audience NUMBER
);
```

```sql
CREATE TABLE debate_people (
  Debate_ID NUMBER,
  Affirmative NUMBER,
  Negative NUMBER,
  If_Affirmative_Win OTHERS
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "debate",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing", 
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "debate",
  "iteration": 0,
  "business_context": "A debate organization wants to maximize the total audience engagement across multiple debates by strategically assigning participants from different districts and parties, ensuring diversity and fairness in representation.",
  "optimization_problem_description": "The goal is to maximize the total audience engagement by assigning participants to debates in a way that ensures diversity in district and party representation, while respecting constraints on the number of debates each participant can join and the balance between affirmative and negative sides.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Audience_Engagement[Debate_ID] \u00d7 Num_of_Audience[Debate_ID])",
    "decision_variables": "x[Debate_ID, People_ID, Side] (binary: 1 if participant is assigned to a debate on a specific side, 0 otherwise)",
    "constraints": [
      "Each participant can be assigned to at most 3 debates: \u2211(x[Debate_ID, People_ID, Side]) \u2264 3 for all People_ID",
      "Each debate must have exactly one affirmative and one negative participant: \u2211(x[Debate_ID, People_ID, 'Affirmative']) = 1 and \u2211(x[Debate_ID, People_ID, 'Negative']) = 1 for all Debate_ID",
      "Participants from the same district cannot be on opposing sides in the same debate: x[Debate_ID, People_ID1, 'Affirmative'] + x[Debate_ID, People_ID2, 'Negative'] \u2264 1 for all Debate_ID, People_ID1, People_ID2 where District[People_ID1] = District[People_ID2]",
      "Participants from the same party cannot be on opposing sides in the same debate: x[Debate_ID, People_ID1, 'Affirmative'] + x[Debate_ID, People_ID2, 'Negative'] \u2264 1 for all Debate_ID, People_ID1, People_ID2 where Party[People_ID1] = Party[People_ID2]",
      "The total number of debates a participant can join is limited by their age: \u2211(x[Debate_ID, People_ID, Side]) \u2264 Age[People_ID] / 20 for all People_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Audience_Engagement[Debate_ID]": {
        "currently_mapped_to": "debate.Num_of_Audience",
        "mapping_adequacy": "good",
        "description": "Represents the audience size for each debate, used to weight the engagement metric."
      }
    },
    "constraint_bounds": {
      "District_Constraint[Debate_ID, People_ID1, People_ID2]": {
        "currently_mapped_to": "people.District",
        "mapping_adequacy": "good",
        "description": "Ensures participants from the same district are not on opposing sides."
      },
      "Party_Constraint[Debate_ID, People_ID1, People_ID2]": {
        "currently_mapped_to": "people.Party",
        "mapping_adequacy": "good",
        "description": "Ensures participants from the same party are not on opposing sides."
      },
      "Age_Constraint[People_ID]": {
        "currently_mapped_to": "people.Age",
        "mapping_adequacy": "good",
        "description": "Limits the number of debates a participant can join based on their age."
      }
    },
    "decision_variables": {
      "x[Debate_ID, People_ID, Side]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating if a participant is assigned to a debate on a specific side.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Audience engagement metric per debate",
    "Binary decision variables for participant assignment"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints to ensure diversity and fairness in participant assignments."
  }
}
