Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 21:40:57

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: swimming

```sql
CREATE TABLE swimmer (
  ID NUMBER,
  name TEXT,
  Nationality TEXT,
  meter_100 NUMBER,
  meter_200 TEXT,
  meter_300 TEXT,
  meter_400 TEXT,
  meter_500 TEXT,
  meter_600 TEXT,
  meter_700 TEXT,
  Time TEXT
);
```

```sql
CREATE TABLE stadium (
  ID NUMBER,
  name TEXT,
  Capacity NUMBER,
  City TEXT,
  Country TEXT,
  Opening_year NUMBER
);
```

```sql
CREATE TABLE event (
  ID NUMBER,
  Name TEXT,
  Stadium_ID NUMBER,
  Year TEXT
);
```

```sql
CREATE TABLE record (
  ID NUMBER,
  Result TEXT,
  Swimmer_ID NUMBER,
  Event_ID NUMBER
);
```



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": "swimming",
  "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": "swimming",
  "iteration": 0,
  "business_context": "Optimize the allocation of swimmers to events in a way that maximizes the overall performance score of a swimming competition, considering the capacity of stadiums and the availability of swimmers.",
  "optimization_problem_description": "The goal is to maximize the total performance score of swimmers across multiple events while ensuring that each event does not exceed the stadium capacity and each swimmer participates in a limited number of events.",
  "optimization_formulation": {
    "objective": "maximize total_performance_score = \u2211(performance_score[swimmer_id, event_id] \u00d7 x[swimmer_id, event_id])",
    "decision_variables": "x[swimmer_id, event_id] = 1 if swimmer_id is assigned to event_id, 0 otherwise (binary)",
    "constraints": [
      "\u2211(x[swimmer_id, event_id]) \u2264 max_events_per_swimmer for each swimmer_id",
      "\u2211(x[swimmer_id, event_id]) \u2264 stadium_capacity[event_id] for each event_id",
      "x[swimmer_id, event_id] \u2208 {0, 1} for all swimmer_id, event_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "performance_score[swimmer_id, event_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "the performance score of a swimmer in a specific event"
      }
    },
    "constraint_bounds": {
      "max_events_per_swimmer": {
        "currently_mapped_to": "business_configuration_logic.key",
        "mapping_adequacy": "missing",
        "description": "maximum number of events a swimmer can participate in"
      },
      "stadium_capacity[event_id]": {
        "currently_mapped_to": "stadium.Capacity",
        "mapping_adequacy": "good",
        "description": "the capacity of the stadium hosting the event"
      }
    },
    "decision_variables": {
      "x[swimmer_id, event_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if a swimmer is assigned to an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Performance scores for each swimmer in each event",
    "Maximum number of events a swimmer can participate in"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine performance scores and maximum event participation limits for swimmers"
  }
}
