Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:35:27

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: flight_company

```sql
CREATE TABLE airport (
  id NUMBER,
  City TEXT,
  Country TEXT,
  IATA TEXT,
  ICAO TEXT,
  name TEXT
);
```

```sql
CREATE TABLE operate_company (
  id NUMBER,
  name TEXT,
  Type TEXT,
  Principal_activities TEXT,
  Incorporated_in TEXT,
  Group_Equity_Shareholding NUMBER
);
```

```sql
CREATE TABLE flight (
  id NUMBER,
  Vehicle_Flight_number TEXT,
  Date TEXT,
  Pilot TEXT,
  Velocity NUMBER,
  Altitude NUMBER,
  airport_id NUMBER,
  company_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": "flight_company",
  "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": "flight_company",
  "iteration": 0,
  "business_context": "Optimize flight scheduling to minimize fuel consumption while ensuring all flights are assigned to an airport and operated by a company, respecting operational constraints.",
  "optimization_problem_description": "The goal is to minimize total fuel consumption across all flights by optimizing the assignment of flights to airports and companies, considering velocity and altitude constraints.",
  "optimization_formulation": {
    "objective": "minimize \u2211(fuel_consumption_coefficient \u00d7 flight_assignment_variable)",
    "decision_variables": "flight_assignment_variable[flight_id, airport_id, company_id] (binary)",
    "constraints": [
      "Each flight must be assigned to exactly one airport: \u2211(flight_assignment_variable[flight_id, airport_id, company_id]) = 1 for each flight_id",
      "Each flight must be assigned to exactly one company: \u2211(flight_assignment_variable[flight_id, airport_id, company_id]) = 1 for each flight_id",
      "Velocity of each flight must be within a specified range: velocity_min \u2264 Velocity \u2264 velocity_max for each flight_id",
      "Altitude of each flight must be within a specified range: altitude_min \u2264 Altitude \u2264 altitude_max for each flight_id",
      "Total number of flights assigned to each airport must not exceed airport capacity: \u2211(flight_assignment_variable[flight_id, airport_id, company_id]) \u2264 airport_capacity for each airport_id",
      "Total number of flights assigned to each company must not exceed company capacity: \u2211(flight_assignment_variable[flight_id, airport_id, company_id]) \u2264 company_capacity for each company_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "fuel_consumption_coefficient[flight_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Fuel consumption coefficient for each flight"
      }
    },
    "constraint_bounds": {
      "velocity_min[flight_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum velocity constraint for each flight"
      },
      "velocity_max[flight_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum velocity constraint for each flight"
      },
      "altitude_min[flight_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum altitude constraint for each flight"
      },
      "altitude_max[flight_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum altitude constraint for each flight"
      },
      "airport_capacity[airport_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Capacity constraint for each airport"
      },
      "company_capacity[company_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Capacity constraint for each company"
      }
    },
    "decision_variables": {
      "flight_assignment_variable[flight_id, airport_id, company_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if a flight is assigned to an airport and company",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Fuel consumption coefficients for each flight",
    "Minimum and maximum velocity constraints for each flight",
    "Minimum and maximum altitude constraints for each flight",
    "Capacity constraints for each airport",
    "Capacity constraints for each company"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "low",
    "next_focus": "Define and map fuel consumption coefficients and operational constraints"
  }
}
