Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:46:28

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: pilot_record

```sql
CREATE TABLE aircraft (
  Aircraft_ID NUMBER,
  Order_Year NUMBER,
  Manufacturer TEXT,
  Model TEXT,
  Fleet_Series TEXT,
  Powertrain TEXT,
  Fuel_Propulsion TEXT
);
```

```sql
CREATE TABLE pilot (
  Pilot_ID NUMBER,
  Pilot_name TEXT,
  Rank NUMBER,
  Age NUMBER,
  Nationality TEXT,
  Position TEXT,
  Join_Year NUMBER,
  Team TEXT
);
```

```sql
CREATE TABLE pilot_record (
  Record_ID NUMBER,
  Pilot_ID NUMBER,
  Aircraft_ID NUMBER,
  Date TEXT
);
```



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": "pilot_record",
  "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": "pilot_record",
  "iteration": 0,
  "business_context": "Optimize pilot assignments to aircraft to minimize operational costs while ensuring pilots are assigned to aircraft they are qualified to fly and respecting pilot availability constraints.",
  "optimization_problem_description": "The goal is to minimize the total operational cost of assigning pilots to aircraft. The cost is influenced by the pilot's rank and the aircraft's fuel efficiency. Constraints include ensuring each pilot is assigned to at most one aircraft per day, each aircraft is assigned exactly one pilot, and pilots are only assigned to aircraft they are qualified to fly based on their rank.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_coefficient[pilot_id, aircraft_id] * assignment[pilot_id, aircraft_id])",
    "decision_variables": "assignment[pilot_id, aircraft_id] (binary: 1 if pilot is assigned to aircraft, 0 otherwise)",
    "constraints": [
      "\u2211(assignment[pilot_id, aircraft_id] for all aircraft_id) \u2264 1 for each pilot_id (each pilot is assigned to at most one aircraft)",
      "\u2211(assignment[pilot_id, aircraft_id] for all pilot_id) = 1 for each aircraft_id (each aircraft is assigned exactly one pilot)",
      "assignment[pilot_id, aircraft_id] \u2264 qualification[pilot_id, aircraft_id] for each pilot_id and aircraft_id (pilots are only assigned to aircraft they are qualified to fly)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_coefficient[pilot_id, aircraft_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "cost of assigning a pilot to an aircraft, based on pilot rank and aircraft fuel efficiency"
      }
    },
    "constraint_bounds": {
      "qualification[pilot_id, aircraft_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary indicator of whether a pilot is qualified to fly a specific aircraft"
      }
    },
    "decision_variables": {
      "assignment[pilot_id, aircraft_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary decision variable indicating if a pilot is assigned to an aircraft",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "cost_coefficient[pilot_id, aircraft_id] (cost of assigning a pilot to an aircraft)",
    "qualification[pilot_id, aircraft_id] (binary indicator of pilot qualification for each aircraft)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define cost coefficients and pilot qualification data to complete the optimization model."
  }
}
