Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-25 22:38:04

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: {'x_flight[flno]': 'Binary decision variable indicating whether flight flno is operated', 'y_employee[eid]': 'Binary decision variable indicating whether employee eid is assigned to a flight'}
- Operational parameters align with expected linear objective: minimize ∑(price[flno] × x_flight[flno]) + ∑(salary[eid] × y_employee[eid])
- Business configuration includes: Cost of operating flight flno (used for Objective coefficient for flight cost), Salary of employee eid (used for Objective coefficient for employee salary)
- 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_1",
  "iteration": 2,
  "business_context": "An airline aims to minimize the total cost of operating flights while ensuring that all flights are staffed with certified employees and that aircraft are not overutilized. The optimization problem is formulated as a linear programming model to ensure computational efficiency and scalability.",
  "optimization_problem_description": "The airline needs to decide the number of flights to operate between different origins and destinations, considering aircraft availability, employee certifications, and cost constraints. The objective is to minimize the total operational cost, which includes flight costs and employee salaries. The problem is formulated as a linear programming model with linear objective and constraints.",
  "optimization_formulation": {
    "objective": "minimize \u2211(price[flno] \u00d7 x_flight[flno]) + \u2211(salary[eid] \u00d7 y_employee[eid])",
    "decision_variables": {
      "x_flight[flno]": "Binary decision variable indicating whether flight flno is operated",
      "y_employee[eid]": "Binary decision variable indicating whether employee eid is assigned to a flight"
    },
    "constraints": [
      "\u2211(x_flight[flno]) \u2264 max_flights[origin, destination] for all origin, destination pairs",
      "\u2211(y_employee[eid]) \u2265 x_flight[flno] for all flno"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "price[flno]": {
        "currently_mapped_to": "business_configuration_logic.price[flno]",
        "mapping_adequacy": "good",
        "description": "Cost of operating flight flno"
      },
      "salary[eid]": {
        "currently_mapped_to": "business_configuration_logic.salary[eid]",
        "mapping_adequacy": "good",
        "description": "Salary of employee eid"
      }
    },
    "constraint_bounds": {
      "max_flights[origin, destination]": {
        "currently_mapped_to": "aircraft_capacity.max_flights",
        "mapping_adequacy": "good",
        "description": "Maximum number of flights between origin and destination"
      }
    },
    "decision_variables": {
      "x_flight[flno]": {
        "currently_mapped_to": "flight_operation.flno",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether flight flno is operated",
        "variable_type": "binary"
      },
      "y_employee[eid]": {
        "currently_mapped_to": "employee_assignment.eid",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether employee eid is assigned to a flight",
        "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 tables for flight costs and employee salaries to address missing optimization requirements. Business configuration logic updated to include scalar parameters for flight costs and employee salaries.

CREATE TABLE aircraft_capacity (
  origin STRING,
  destination STRING,
  max_flights INTEGER
);

CREATE TABLE employee_assignment (
  eid INTEGER,
  flno INTEGER
);

CREATE TABLE flight_operation (
  flno INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards for flight costs and employee salaries, ensuring they align with typical airline operations. Flight numbers and employee IDs were generated sequentially to maintain consistency.

-- Realistic data for aircraft_capacity
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('JFK', 'LAX', 8);
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('LAX', 'JFK', 8);
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('ORD', 'DFW', 5);

-- Realistic data for employee_assignment
INSERT INTO employee_assignment (eid, flno) VALUES (1, 101);
INSERT INTO employee_assignment (eid, flno) VALUES (2, 102);
INSERT INTO employee_assignment (eid, flno) VALUES (3, 103);

-- Realistic data for flight_operation
INSERT INTO flight_operation (flno) VALUES (101);
INSERT INTO flight_operation (flno) VALUES (102);
INSERT INTO flight_operation (flno) VALUES (103);


```

DATA DICTIONARY:
{
  "tables": {
    "aircraft_capacity": {
      "business_purpose": "Maximum number of flights between origin and destination",
      "optimization_role": "constraint_bounds",
      "columns": {
        "origin": {
          "data_type": "STRING",
          "business_meaning": "Origin airport code",
          "optimization_purpose": "Constraint bound for origin",
          "sample_values": "JFK, LAX"
        },
        "destination": {
          "data_type": "STRING",
          "business_meaning": "Destination airport code",
          "optimization_purpose": "Constraint bound for destination",
          "sample_values": "LAX, JFK"
        },
        "max_flights": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of flights between origin and destination",
          "optimization_purpose": "Constraint bound for aircraft capacity",
          "sample_values": "5, 10"
        }
      }
    },
    "employee_assignment": {
      "business_purpose": "Whether employee is assigned to a flight",
      "optimization_role": "decision_variables",
      "columns": {
        "eid": {
          "data_type": "INTEGER",
          "business_meaning": "Employee ID",
          "optimization_purpose": "Decision variable for employee assignment",
          "sample_values": "1, 2, 3"
        },
        "flno": {
          "data_type": "INTEGER",
          "business_meaning": "Flight number",
          "optimization_purpose": "Decision variable for flight operation",
          "sample_values": "101, 102, 103"
        }
      }
    },
    "flight_operation": {
      "business_purpose": "Whether flight is operated",
      "optimization_role": "decision_variables",
      "columns": {
        "flno": {
          "data_type": "INTEGER",
          "business_meaning": "Flight number",
          "optimization_purpose": "Decision variable for flight operation",
          "sample_values": "101, 102, 103"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "price[flno]": {
    "data_type": "INTEGER",
    "business_meaning": "Cost of operating flight flno",
    "optimization_role": "Objective coefficient for flight cost",
    "configuration_type": "scalar_parameter",
    "value": 7500,
    "business_justification": "Average cost of operating a flight, considering fuel, maintenance, and other expenses"
  },
  "salary[eid]": {
    "data_type": "INTEGER",
    "business_meaning": "Salary of employee eid",
    "optimization_role": "Objective coefficient for employee salary",
    "configuration_type": "scalar_parameter",
    "value": 4000,
    "business_justification": "Average monthly salary for airline employees, including pilots and cabin crew"
  }
}

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_1

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: {'x_flight[flno]': 'Binary decision variable indicating whether flight flno is operated', 'y_employee[eid]': 'Binary decision variable indicating whether employee eid is assigned to a flight'}
- Operational parameters align with expected linear objective: minimize ∑(price[flno] × x_flight[flno]) + ∑(salary[eid] × y_employee[eid])
- Business configuration includes: Cost of operating flight flno (used for Objective coefficient for flight cost), Salary of employee eid (used for Objective coefficient for employee salary)
- 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 ∑(price[flno] × x_flight[flno]) + ∑(salary[eid] × y_employee[eid])
- 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: ['∑(x_flight[flno]) ≤ max_flights[origin, destination] for all origin, destination pairs', '∑(y_employee[eid]) ≥ x_flight[flno] for all flno'] (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 tables for flight costs and employee salaries to address missing optimization requirements. Business configuration logic updated to include scalar parameters for flight costs and employee salaries.

CREATE TABLE aircraft_capacity (
  origin STRING,
  destination STRING,
  max_flights INTEGER
);

CREATE TABLE employee_assignment (
  eid INTEGER,
  flno INTEGER
);

CREATE TABLE flight_operation (
  flno INTEGER
);


```

### 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 costs and employee salaries, ensuring they align with typical airline operations. Flight numbers and employee IDs were generated sequentially to maintain consistency.

-- Realistic data for aircraft_capacity
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('JFK', 'LAX', 8);
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('LAX', 'JFK', 8);
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('ORD', 'DFW', 5);

-- Realistic data for employee_assignment
INSERT INTO employee_assignment (eid, flno) VALUES (1, 101);
INSERT INTO employee_assignment (eid, flno) VALUES (2, 102);
INSERT INTO employee_assignment (eid, flno) VALUES (3, 103);

-- Realistic data for flight_operation
INSERT INTO flight_operation (flno) VALUES (101);
INSERT INTO flight_operation (flno) VALUES (102);
INSERT INTO flight_operation (flno) VALUES (103);


```

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

Response:
# Complete Optimization Problem and Solution: flight_1

## 1. Problem Context and Goals

### Context  
An airline is tasked with optimizing its flight operations to minimize costs while ensuring operational efficiency. The airline must decide which flights to operate and which employees to assign to those flights, considering aircraft availability and employee certifications. Each flight has an associated operational cost, and each employee has a fixed salary. The goal is to minimize the total cost, which includes the sum of flight operational costs and employee salaries.  

The airline operates flights between specific origin and destination pairs, with a maximum number of flights allowed for each pair based on aircraft capacity. Additionally, every flight that is operated must be staffed with certified employees. The operational cost of each flight is determined by factors such as fuel, maintenance, and other expenses, while employee salaries are based on industry standards for pilots and cabin crew.  

The problem is formulated as a linear optimization model to ensure computational efficiency and scalability. The decision variables include whether to operate a specific flight and whether to assign a specific employee to a flight. The objective is to minimize the total cost, which is a linear combination of flight operational costs and employee salaries.  

### Goals  
The primary goal of this optimization problem is to minimize the total operational cost for the airline. This cost includes the sum of the operational costs for all flights that are operated and the salaries of all employees assigned to those flights. Success is measured by achieving the lowest possible total cost while ensuring that all operational constraints, such as aircraft capacity and employee staffing requirements, are satisfied.  

## 2. Constraints  

1. **Flight Capacity Constraint**: The number of flights operated between any origin and destination pair must not exceed the maximum number of flights allowed for that pair. This ensures that aircraft are not overutilized and that operational limits are respected.  

2. **Employee Assignment Constraint**: Every flight that is operated must be staffed with at least one certified employee. This ensures that all flights have the necessary personnel to operate safely and efficiently.  

These constraints are designed to ensure that the airline's operations remain within feasible limits while minimizing costs.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating tables for flight costs and employee salaries to address missing optimization requirements. Business configuration logic updated to include scalar parameters for flight costs and employee salaries.

CREATE TABLE aircraft_capacity (
  origin STRING,
  destination STRING,
  max_flights INTEGER
);

CREATE TABLE employee_assignment (
  eid INTEGER,
  flno INTEGER
);

CREATE TABLE flight_operation (
  flno INTEGER
);
```

### Data Dictionary  
- **aircraft_capacity**:  
  - **Business Purpose**: Specifies the maximum number of flights allowed between origin and destination pairs based on aircraft availability.  
  - **Columns**:  
    - **origin**: The airport code for the origin of the flight.  
    - **destination**: The airport code for the destination of the flight.  
    - **max_flights**: The maximum number of flights allowed between the origin and destination.  

- **employee_assignment**:  
  - **Business Purpose**: Tracks which employees are assigned to which flights.  
  - **Columns**:  
    - **eid**: The unique identifier for an employee.  
    - **flno**: The flight number to which the employee is assigned.  

- **flight_operation**:  
  - **Business Purpose**: Tracks which flights are operated.  
  - **Columns**:  
    - **flno**: The unique identifier for a flight.  

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards for flight costs and employee salaries, ensuring they align with typical airline operations. Flight numbers and employee IDs were generated sequentially to maintain consistency.

-- Realistic data for aircraft_capacity
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('JFK', 'LAX', 8);
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('LAX', 'JFK', 8);
INSERT INTO aircraft_capacity (origin, destination, max_flights) VALUES ('ORD', 'DFW', 5);

-- Realistic data for employee_assignment
INSERT INTO employee_assignment (eid, flno) VALUES (1, 101);
INSERT INTO employee_assignment (eid, flno) VALUES (2, 102);
INSERT INTO employee_assignment (eid, flno) VALUES (3, 103);

-- Realistic data for flight_operation
INSERT INTO flight_operation (flno) VALUES (101);
INSERT INTO flight_operation (flno) VALUES (102);
INSERT INTO flight_operation (flno) VALUES (103);
```
