Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-25 22:35:27

Prompt:
You are a business analyst creating structured optimization problem documentation.

DATA SOURCES EXPLANATION:
- FINAL OR ANALYSIS: Final converged optimization problem from alternating process (iteration 2), contains business context and schema mapping evaluation
- DATABASE SCHEMA: Current database structure after iterative adjustments  
- DATA DICTIONARY: Business meanings and optimization roles of tables and columns
- CURRENT STORED VALUES: Realistic business data generated by triple expert (business + data + optimization)
- BUSINESS CONFIGURATION: Scalar parameters and business logic formulas separated from table data

CRITICAL REQUIREMENTS: 
- Ensure problem description naturally leads to LINEAR or MIXED-INTEGER optimization formulation
- Make business context consistent with the intended decision variables and objectives
- Align constraint descriptions with expected mathematical constraints
- Ensure data descriptions map clearly to expected coefficient sources
- Maintain business authenticity while fixing mathematical consistency issues
- Avoid business scenarios that would naturally require nonlinear relationships (variable products, divisions, etc.)

AUTO-EXTRACTED CONTEXT REQUIREMENTS:
- Business decisions match expected decision variables: flight_assignment_variable[flight_id, airport_id, company_id] (binary)
- Operational parameters align with expected linear objective: minimize ∑(fuel_consumption_coefficient[flight_id] × flight_assignment_variable[flight_id, airport_id, company_id])
- Business configuration includes: Minimum velocity constraint for each flight (used for Used in velocity constraint), Maximum velocity constraint for each flight (used for Used in velocity constraint), Minimum altitude constraint for each flight (used for Used in altitude constraint), Maximum altitude constraint for each flight (used for Used in altitude constraint)
- Business logic formulas to express in natural language: Fuel consumption calculation for each flight (calculation method for Used in objective function)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate

FINAL OR ANALYSIS:
{
  "database_id": "flight_company",
  "iteration": 2,
  "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 such as velocity, altitude, and capacity limits.",
  "optimization_problem_description": "Minimize total fuel consumption across all flights by optimizing the assignment of flights to airports and companies, subject to velocity, altitude, and capacity constraints.",
  "optimization_formulation": {
    "objective": "minimize \u2211(fuel_consumption_coefficient[flight_id] \u00d7 flight_assignment_variable[flight_id, airport_id, company_id])",
    "decision_variables": "flight_assignment_variable[flight_id, airport_id, company_id] (binary)",
    "constraints": "1. \u2211(flight_assignment_variable[flight_id, airport_id, company_id]) = 1 for each flight_id (each flight must be assigned to exactly one airport and company), 2. \u2211(flight_assignment_variable[flight_id, airport_id, company_id]) \u2264 airport_capacity[airport_id] for each airport_id (airport capacity constraint), 3. \u2211(flight_assignment_variable[flight_id, airport_id, company_id]) \u2264 company_capacity[company_id] for each company_id (company capacity constraint), 4. velocity_min[flight_id] \u2264 velocity[flight_id] \u2264 velocity_max[flight_id] for each flight_id (velocity constraint), 5. altitude_min[flight_id] \u2264 altitude[flight_id] \u2264 altitude_max[flight_id] for each flight_id (altitude constraint)"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "fuel_consumption_coefficient[flight_id]": {
        "currently_mapped_to": "fuel_consumption_coefficients.coefficient",
        "mapping_adequacy": "good",
        "description": "Fuel consumption coefficient for each flight"
      }
    },
    "constraint_bounds": {
      "velocity_min[flight_id]": {
        "currently_mapped_to": "velocity_constraints.velocity_min",
        "mapping_adequacy": "good",
        "description": "Minimum velocity constraint for each flight"
      },
      "velocity_max[flight_id]": {
        "currently_mapped_to": "velocity_constraints.velocity_max",
        "mapping_adequacy": "good",
        "description": "Maximum velocity constraint for each flight"
      },
      "altitude_min[flight_id]": {
        "currently_mapped_to": "altitude_constraints.altitude_min",
        "mapping_adequacy": "good",
        "description": "Minimum altitude constraint for each flight"
      },
      "altitude_max[flight_id]": {
        "currently_mapped_to": "altitude_constraints.altitude_max",
        "mapping_adequacy": "good",
        "description": "Maximum altitude constraint for each flight"
      },
      "airport_capacity[airport_id]": {
        "currently_mapped_to": "airport_capacities.capacity",
        "mapping_adequacy": "good",
        "description": "Capacity constraint for each airport"
      },
      "company_capacity[company_id]": {
        "currently_mapped_to": "company_capacities.capacity",
        "mapping_adequacy": "good",
        "description": "Capacity constraint for each company"
      }
    },
    "decision_variables": {
      "flight_assignment_variable[flight_id, airport_id, company_id]": {
        "currently_mapped_to": "flight_assignments.assignment",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if a flight is assigned to an airport and company",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a table for flight assignments to address the missing decision variable. Configuration logic updates include scalar parameters for velocity and altitude constraints and formulas for fuel consumption calculations.

CREATE TABLE fuel_consumption_coefficients (
  flight_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE velocity_constraints (
  flight_id INTEGER,
  velocity_min INTEGER,
  velocity_max INTEGER
);

CREATE TABLE altitude_constraints (
  flight_id INTEGER,
  altitude_min INTEGER,
  altitude_max INTEGER
);

CREATE TABLE airport_capacities (
  airport_id INTEGER,
  capacity INTEGER
);

CREATE TABLE company_capacities (
  company_id INTEGER,
  capacity INTEGER
);

CREATE TABLE flight_assignments (
  flight_id INTEGER,
  airport_id INTEGER,
  company_id INTEGER,
  assignment BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards for flight operations, ensuring realistic velocity, altitude, and capacity constraints. Fuel consumption coefficients were derived from typical aircraft performance data.

-- Realistic data for fuel_consumption_coefficients
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (1, 0.5);
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (2, 0.6);
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (3, 0.7);

-- Realistic data for velocity_constraints
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (1, 500, 900);
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (2, 550, 950);
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (3, 600, 1000);

-- Realistic data for altitude_constraints
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (1, 30000, 40000);
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (2, 31000, 41000);
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (3, 32000, 42000);

-- Realistic data for airport_capacities
INSERT INTO airport_capacities (airport_id, capacity) VALUES (1, 10);
INSERT INTO airport_capacities (airport_id, capacity) VALUES (2, 15);
INSERT INTO airport_capacities (airport_id, capacity) VALUES (3, 20);

-- Realistic data for company_capacities
INSERT INTO company_capacities (company_id, capacity) VALUES (1, 5);
INSERT INTO company_capacities (company_id, capacity) VALUES (2, 10);
INSERT INTO company_capacities (company_id, capacity) VALUES (3, 15);

-- Realistic data for flight_assignments
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (1, 1, 1, True);
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (2, 2, 2, True);
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (3, 3, 3, True);


```

DATA DICTIONARY:
{
  "tables": {
    "fuel_consumption_coefficients": {
      "business_purpose": "Fuel consumption coefficients for each flight",
      "optimization_role": "objective_coefficients",
      "columns": {
        "flight_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each flight",
          "optimization_purpose": "Index for fuel consumption coefficient",
          "sample_values": "1, 2, 3"
        },
        "coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Fuel consumption coefficient for the flight",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.5, 0.6, 0.7"
        }
      }
    },
    "velocity_constraints": {
      "business_purpose": "Minimum and maximum velocity constraints for each flight",
      "optimization_role": "constraint_bounds",
      "columns": {
        "flight_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each flight",
          "optimization_purpose": "Index for velocity constraints",
          "sample_values": "1, 2, 3"
        },
        "velocity_min": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum velocity constraint for the flight",
          "optimization_purpose": "Used in velocity constraint",
          "sample_values": "500, 550, 600"
        },
        "velocity_max": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum velocity constraint for the flight",
          "optimization_purpose": "Used in velocity constraint",
          "sample_values": "900, 950, 1000"
        }
      }
    },
    "altitude_constraints": {
      "business_purpose": "Minimum and maximum altitude constraints for each flight",
      "optimization_role": "constraint_bounds",
      "columns": {
        "flight_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each flight",
          "optimization_purpose": "Index for altitude constraints",
          "sample_values": "1, 2, 3"
        },
        "altitude_min": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum altitude constraint for the flight",
          "optimization_purpose": "Used in altitude constraint",
          "sample_values": "30000, 31000, 32000"
        },
        "altitude_max": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum altitude constraint for the flight",
          "optimization_purpose": "Used in altitude constraint",
          "sample_values": "40000, 41000, 42000"
        }
      }
    },
    "airport_capacities": {
      "business_purpose": "Capacity constraints for each airport",
      "optimization_role": "constraint_bounds",
      "columns": {
        "airport_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each airport",
          "optimization_purpose": "Index for airport capacity",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of flights the airport can handle",
          "optimization_purpose": "Used in airport capacity constraint",
          "sample_values": "10, 15, 20"
        }
      }
    },
    "company_capacities": {
      "business_purpose": "Capacity constraints for each company",
      "optimization_role": "constraint_bounds",
      "columns": {
        "company_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each company",
          "optimization_purpose": "Index for company capacity",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of flights the company can handle",
          "optimization_purpose": "Used in company capacity constraint",
          "sample_values": "5, 10, 15"
        }
      }
    },
    "flight_assignments": {
      "business_purpose": "Binary decision variable indicating if a flight is assigned to an airport and company",
      "optimization_role": "decision_variables",
      "columns": {
        "flight_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each flight",
          "optimization_purpose": "Index for flight assignment",
          "sample_values": "1, 2, 3"
        },
        "airport_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each airport",
          "optimization_purpose": "Index for flight assignment",
          "sample_values": "1, 2, 3"
        },
        "company_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each company",
          "optimization_purpose": "Index for flight assignment",
          "sample_values": "1, 2, 3"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary variable indicating if flight is assigned to airport and company",
          "optimization_purpose": "Used in decision variable",
          "sample_values": "true, false"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "velocity_min": {
    "data_type": "INTEGER",
    "business_meaning": "Minimum velocity constraint for each flight",
    "optimization_role": "Used in velocity constraint",
    "configuration_type": "scalar_parameter",
    "value": 500,
    "business_justification": "Minimum velocity for commercial flights to ensure safety and efficiency."
  },
  "velocity_max": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum velocity constraint for each flight",
    "optimization_role": "Used in velocity constraint",
    "configuration_type": "scalar_parameter",
    "value": 900,
    "business_justification": "Maximum velocity for commercial flights to balance speed and fuel consumption."
  },
  "altitude_min": {
    "data_type": "INTEGER",
    "business_meaning": "Minimum altitude constraint for each flight",
    "optimization_role": "Used in altitude constraint",
    "configuration_type": "scalar_parameter",
    "value": 30000,
    "business_justification": "Minimum altitude for commercial flights to ensure safety and efficiency."
  },
  "altitude_max": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum altitude constraint for each flight",
    "optimization_role": "Used in altitude constraint",
    "configuration_type": "scalar_parameter",
    "value": 40000,
    "business_justification": "Maximum altitude for commercial flights to balance fuel efficiency and airspace constraints."
  },
  "fuel_consumption_formula": {
    "data_type": "STRING",
    "business_meaning": "Fuel consumption calculation for each flight",
    "optimization_role": "Used in objective function",
    "configuration_type": "business_logic_formula",
    "formula_expression": "fuel_consumption_coefficient * distance"
  }
}

Business Configuration Design: 
Our system separates business logic design from value determination:
- Configuration Logic (business_configuration_logic.json): Templates designed by data engineers with sample_value for scalars and actual formulas for business logic
- Configuration Values (business_configuration.json): Realistic values determined by domain experts for scalar parameters only
- Design Rationale: Ensures business logic consistency while allowing flexible parameter tuning


TASK: Create structured markdown documentation for SECTIONS 1-3 ONLY (Problem Description).

EXACT MARKDOWN STRUCTURE TO FOLLOW:

# Complete Optimization Problem and Solution: flight_company

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: flight_assignment_variable[flight_id, airport_id, company_id] (binary)
- Operational parameters align with expected linear objective: minimize ∑(fuel_consumption_coefficient[flight_id] × flight_assignment_variable[flight_id, airport_id, company_id])
- Business configuration includes: Minimum velocity constraint for each flight (used for Used in velocity constraint), Maximum velocity constraint for each flight (used for Used in velocity constraint), Minimum altitude constraint for each flight (used for Used in altitude constraint), Maximum altitude constraint for each flight (used for Used in altitude constraint)
- Business logic formulas to express in natural language: Fuel consumption calculation for each flight (calculation method for Used in objective function)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate
- CRITICAL: Include ALL business configuration information (scalar parameters AND business logic formulas) in natural business language

### Goals  
[Regenerate goals that clearly lead to LINEAR mathematical objective:]
- Optimization goal: minimize
- Metric to optimize: minimize ∑(fuel_consumption_coefficient[flight_id] × flight_assignment_variable[flight_id, airport_id, company_id])
- Success measurement aligned with expected coefficient sources
- Use natural language to precisely describe linear optimization goal
- NO mathematical formulas, equations, or symbolic notation

## 2. Constraints    

[Regenerate constraints that directly match expected LINEAR mathematical constraints:]
- Expected constraint: 1. ∑(flight_assignment_variable[flight_id, airport_id, company_id]) = 1 for each flight_id (each flight must be assigned to exactly one airport and company), 2. ∑(flight_assignment_variable[flight_id, airport_id, company_id]) ≤ airport_capacity[airport_id] for each airport_id (airport capacity constraint), 3. ∑(flight_assignment_variable[flight_id, airport_id, company_id]) ≤ company_capacity[company_id] for each company_id (company capacity constraint), 4. velocity_min[flight_id] ≤ velocity[flight_id] ≤ velocity_max[flight_id] for each flight_id (velocity constraint), 5. altitude_min[flight_id] ≤ altitude[flight_id] ≤ altitude_max[flight_id] for each flight_id (altitude constraint) (Form: Standard constraint form based on business requirements)

[Each constraint should be described in business terms that naturally lead to LINEAR mathematical forms (no variable products or divisions)]

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a table for flight assignments to address the missing decision variable. Configuration logic updates include scalar parameters for velocity and altitude constraints and formulas for fuel consumption calculations.

CREATE TABLE fuel_consumption_coefficients (
  flight_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE velocity_constraints (
  flight_id INTEGER,
  velocity_min INTEGER,
  velocity_max INTEGER
);

CREATE TABLE altitude_constraints (
  flight_id INTEGER,
  altitude_min INTEGER,
  altitude_max INTEGER
);

CREATE TABLE airport_capacities (
  airport_id INTEGER,
  capacity INTEGER
);

CREATE TABLE company_capacities (
  company_id INTEGER,
  capacity INTEGER
);

CREATE TABLE flight_assignments (
  flight_id INTEGER,
  airport_id INTEGER,
  company_id INTEGER,
  assignment BOOLEAN
);


```

### Data Dictionary  
[Create comprehensive business-oriented data dictionary mapping tables and columns to their business purposes and optimization roles - NOT technical database terms. Base this on the data_dictionary provided but rewrite in business language that clearly connects to the expected linear mathematical formulation]

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards for flight operations, ensuring realistic velocity, altitude, and capacity constraints. Fuel consumption coefficients were derived from typical aircraft performance data.

-- Realistic data for fuel_consumption_coefficients
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (1, 0.5);
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (2, 0.6);
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (3, 0.7);

-- Realistic data for velocity_constraints
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (1, 500, 900);
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (2, 550, 950);
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (3, 600, 1000);

-- Realistic data for altitude_constraints
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (1, 30000, 40000);
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (2, 31000, 41000);
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (3, 32000, 42000);

-- Realistic data for airport_capacities
INSERT INTO airport_capacities (airport_id, capacity) VALUES (1, 10);
INSERT INTO airport_capacities (airport_id, capacity) VALUES (2, 15);
INSERT INTO airport_capacities (airport_id, capacity) VALUES (3, 20);

-- Realistic data for company_capacities
INSERT INTO company_capacities (company_id, capacity) VALUES (1, 5);
INSERT INTO company_capacities (company_id, capacity) VALUES (2, 10);
INSERT INTO company_capacities (company_id, capacity) VALUES (3, 15);

-- Realistic data for flight_assignments
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (1, 1, 1, True);
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (2, 2, 2, True);
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (3, 3, 3, True);


```

STOP HERE - Do not include section 4 (Mathematical Optimization Formulation).

Response:
# Complete Optimization Problem and Solution: flight_company

## 1. Problem Context and Goals

### Context  
The flight scheduling optimization problem focuses on minimizing total fuel consumption across all flights by assigning each flight to an airport and a company. The decision involves determining whether a specific flight is assigned to a particular airport and company, represented as a binary decision variable. The fuel consumption for each flight is calculated using a predefined coefficient that reflects the fuel efficiency of the flight under specific operational conditions.  

Operational constraints include ensuring that each flight is assigned to exactly one airport and one company, respecting the capacity limits of both airports and companies. Additionally, flights must operate within predefined velocity and altitude ranges to ensure safety and efficiency. The minimum and maximum velocity constraints are set to balance speed and fuel consumption, while the altitude constraints ensure flights operate within safe and efficient airspace levels.  

The fuel consumption calculation is based on a linear relationship between the fuel consumption coefficient and the distance traveled, ensuring the objective function remains linear. This approach avoids nonlinear relationships, such as variable products or divisions, which would complicate the optimization process.  

### Goals  
The primary goal of this optimization problem is to minimize the total fuel consumption across all flights. This is achieved by optimizing the assignment of flights to airports and companies, ensuring that each flight is assigned to exactly one airport and one company while respecting operational constraints.  

Success is measured by the reduction in total fuel consumption, which is directly influenced by the fuel consumption coefficients and the assignment decisions. The optimization process ensures that the fuel consumption coefficients are used effectively to achieve the lowest possible fuel consumption while maintaining operational feasibility.  

## 2. Constraints  

The optimization problem is subject to the following constraints:  

1. **Flight Assignment Constraint**: Each flight must be assigned to exactly one airport and one company. This ensures that all flights are scheduled and no flight is left unassigned.  

2. **Airport Capacity Constraint**: The total number of flights assigned to an airport cannot exceed the airport's capacity. This ensures that airports are not overloaded and can handle the assigned flights efficiently.  

3. **Company Capacity Constraint**: The total number of flights assigned to a company cannot exceed the company's capacity. This ensures that companies can manage the assigned flights without exceeding their operational limits.  

4. **Velocity Constraint**: Each flight must operate within its predefined minimum and maximum velocity limits. This ensures that flights maintain safe and efficient speeds, balancing fuel consumption and travel time.  

5. **Altitude Constraint**: Each flight must operate within its predefined minimum and maximum altitude limits. This ensures that flights operate within safe and efficient airspace levels, avoiding conflicts with other air traffic and optimizing fuel efficiency.  

These constraints are designed to ensure that the optimization problem remains linear and feasible, avoiding any nonlinear relationships that could complicate the solution process.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a table for flight assignments to address the missing decision variable. Configuration logic updates include scalar parameters for velocity and altitude constraints and formulas for fuel consumption calculations.

CREATE TABLE fuel_consumption_coefficients (
  flight_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE velocity_constraints (
  flight_id INTEGER,
  velocity_min INTEGER,
  velocity_max INTEGER
);

CREATE TABLE altitude_constraints (
  flight_id INTEGER,
  altitude_min INTEGER,
  altitude_max INTEGER
);

CREATE TABLE airport_capacities (
  airport_id INTEGER,
  capacity INTEGER
);

CREATE TABLE company_capacities (
  company_id INTEGER,
  capacity INTEGER
);

CREATE TABLE flight_assignments (
  flight_id INTEGER,
  airport_id INTEGER,
  company_id INTEGER,
  assignment BOOLEAN
);
```

### Data Dictionary  
- **fuel_consumption_coefficients**: Contains the fuel consumption coefficients for each flight, which are used to calculate the total fuel consumption in the objective function.  
  - *flight_id*: Unique identifier for each flight.  
  - *coefficient*: Fuel consumption coefficient for the flight, used in the objective function.  

- **velocity_constraints**: Defines the minimum and maximum velocity constraints for each flight, ensuring flights operate within safe and efficient speed limits.  
  - *flight_id*: Unique identifier for each flight.  
  - *velocity_min*: Minimum velocity constraint for the flight.  
  - *velocity_max*: Maximum velocity constraint for the flight.  

- **altitude_constraints**: Defines the minimum and maximum altitude constraints for each flight, ensuring flights operate within safe and efficient airspace levels.  
  - *flight_id*: Unique identifier for each flight.  
  - *altitude_min*: Minimum altitude constraint for the flight.  
  - *altitude_max*: Maximum altitude constraint for the flight.  

- **airport_capacities**: Specifies the maximum number of flights each airport can handle, ensuring airports are not overloaded.  
  - *airport_id*: Unique identifier for each airport.  
  - *capacity*: Maximum number of flights the airport can handle.  

- **company_capacities**: Specifies the maximum number of flights each company can handle, ensuring companies can manage their assigned flights.  
  - *company_id*: Unique identifier for each company.  
  - *capacity*: Maximum number of flights the company can handle.  

- **flight_assignments**: Represents the binary decision variable indicating whether a flight is assigned to an airport and a company.  
  - *flight_id*: Unique identifier for each flight.  
  - *airport_id*: Unique identifier for each airport.  
  - *company_id*: Unique identifier for each company.  
  - *assignment*: Binary variable indicating if the flight is assigned to the airport and company.  

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards for flight operations, ensuring realistic velocity, altitude, and capacity constraints. Fuel consumption coefficients were derived from typical aircraft performance data.

-- Realistic data for fuel_consumption_coefficients
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (1, 0.5);
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (2, 0.6);
INSERT INTO fuel_consumption_coefficients (flight_id, coefficient) VALUES (3, 0.7);

-- Realistic data for velocity_constraints
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (1, 500, 900);
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (2, 550, 950);
INSERT INTO velocity_constraints (flight_id, velocity_min, velocity_max) VALUES (3, 600, 1000);

-- Realistic data for altitude_constraints
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (1, 30000, 40000);
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (2, 31000, 41000);
INSERT INTO altitude_constraints (flight_id, altitude_min, altitude_max) VALUES (3, 32000, 42000);

-- Realistic data for airport_capacities
INSERT INTO airport_capacities (airport_id, capacity) VALUES (1, 10);
INSERT INTO airport_capacities (airport_id, capacity) VALUES (2, 15);
INSERT INTO airport_capacities (airport_id, capacity) VALUES (3, 20);

-- Realistic data for company_capacities
INSERT INTO company_capacities (company_id, capacity) VALUES (1, 5);
INSERT INTO company_capacities (company_id, capacity) VALUES (2, 10);
INSERT INTO company_capacities (company_id, capacity) VALUES (3, 15);

-- Realistic data for flight_assignments
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (1, 1, 1, True);
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (2, 2, 2, True);
INSERT INTO flight_assignments (flight_id, airport_id, company_id, assignment) VALUES (3, 3, 3, True);
```
