Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 22:11:47

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 1), 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: flights.number_of_flights[rid] for each route rid, integer
- Operational parameters align with expected linear objective: maximize total_passengers = ∑(routes.passenger_capacity[rid] × flights.number_of_flights[rid])
- Business configuration includes: Total number of flights available for allocation. (used for Used as a constraint bound in the optimization model.), Maximum number of flights that can be assigned to each route. (used for Used as a constraint bound in the optimization model.)
- 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_4",
  "iteration": 1,
  "business_context": "Optimize the allocation of flights to routes to maximize the total number of passengers transported while respecting capacity constraints and ensuring each route is serviced by at least one flight.",
  "optimization_problem_description": "Determine the optimal number of flights assigned to each route to maximize passenger transport. Each route has a specific capacity, and the airline wants to ensure that all routes are serviced while maximizing the total number of passengers.",
  "optimization_formulation": {
    "objective": "maximize total_passengers = \u2211(routes.passenger_capacity[rid] \u00d7 flights.number_of_flights[rid])",
    "decision_variables": "flights.number_of_flights[rid] for each route rid, integer",
    "constraints": [
      "\u2211(flights.number_of_flights[rid]) \u2264 business_configuration_logic.total_available_flights",
      "flights.number_of_flights[rid] \u2264 business_configuration_logic.max_flights_per_route for each route rid",
      "flights.number_of_flights[rid] \u2265 1 for each route rid"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "passenger_capacity[rid]": {
        "currently_mapped_to": "routes.passenger_capacity",
        "mapping_adequacy": "good",
        "description": "Passenger capacity for each route, used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "total_available_flights": {
        "currently_mapped_to": "business_configuration_logic.total_available_flights",
        "mapping_adequacy": "good",
        "description": "Total number of flights available for allocation"
      },
      "max_flights_per_route": {
        "currently_mapped_to": "business_configuration_logic.max_flights_per_route",
        "mapping_adequacy": "good",
        "description": "Maximum number of flights that can be assigned to each route"
      }
    },
    "decision_variables": {
      "number_of_flights[rid]": {
        "currently_mapped_to": "flights.number_of_flights",
        "mapping_adequacy": "good",
        "description": "Number of flights assigned to each route",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas.

CREATE TABLE routes (
  route_id INTEGER,
  passenger_capacity INTEGER
);

CREATE TABLE flights (
  route_id INTEGER,
  number_of_flights INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical airline operations, ensuring that the number of flights and passenger capacities are realistic for a mid-sized airline.

-- Realistic data for routes
INSERT INTO routes (route_id, passenger_capacity) VALUES (1, 150);
INSERT INTO routes (route_id, passenger_capacity) VALUES (2, 200);
INSERT INTO routes (route_id, passenger_capacity) VALUES (3, 250);

-- Realistic data for flights
INSERT INTO flights (route_id, number_of_flights) VALUES (1, 3);
INSERT INTO flights (route_id, number_of_flights) VALUES (2, 4);
INSERT INTO flights (route_id, number_of_flights) VALUES (3, 5);


```

DATA DICTIONARY:
{
  "tables": {
    "routes": {
      "business_purpose": "Stores route-specific data including passenger capacity.",
      "optimization_role": "business_data",
      "columns": {
        "route_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each route.",
          "optimization_purpose": "Key for linking route data.",
          "sample_values": "1, 2, 3"
        },
        "passenger_capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Passenger capacity for each route.",
          "optimization_purpose": "Coefficient in the objective function.",
          "sample_values": "150, 200, 250"
        }
      }
    },
    "flights": {
      "business_purpose": "Stores the number of flights assigned to each route.",
      "optimization_role": "decision_variables",
      "columns": {
        "route_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier linking to the route.",
          "optimization_purpose": "Key for linking to route data.",
          "sample_values": "1, 2, 3"
        },
        "number_of_flights": {
          "data_type": "INTEGER",
          "business_meaning": "Number of flights assigned to the route.",
          "optimization_purpose": "Primary decision variable.",
          "sample_values": "1, 2, 3"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "total_available_flights": {
    "data_type": "INTEGER",
    "business_meaning": "Total number of flights available for allocation.",
    "optimization_role": "Used as a constraint bound in the optimization model.",
    "configuration_type": "scalar_parameter",
    "value": 12,
    "business_justification": "The airline has a fleet size that allows for a total of 12 flights, balancing operational capacity and demand."
  },
  "max_flights_per_route": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of flights that can be assigned to each route.",
    "optimization_role": "Used as a constraint bound in the optimization model.",
    "configuration_type": "scalar_parameter",
    "value": 5,
    "business_justification": "Operational constraints and demand analysis suggest a maximum of 5 flights per route to optimize resource utilization."
  }
}

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_4

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: flights.number_of_flights[rid] for each route rid, integer
- Operational parameters align with expected linear objective: maximize total_passengers = ∑(routes.passenger_capacity[rid] × flights.number_of_flights[rid])
- Business configuration includes: Total number of flights available for allocation. (used for Used as a constraint bound in the optimization model.), Maximum number of flights that can be assigned to each route. (used for Used as a constraint bound in the optimization model.)
- 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: maximize
- Metric to optimize: maximize total_passengers = ∑(routes.passenger_capacity[rid] × flights.number_of_flights[rid])
- 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: ['∑(flights.number_of_flights[rid]) ≤ business_configuration_logic.total_available_flights', 'flights.number_of_flights[rid] ≤ business_configuration_logic.max_flights_per_route for each route rid', 'flights.number_of_flights[rid] ≥ 1 for each route rid'] (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 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas.

CREATE TABLE routes (
  route_id INTEGER,
  passenger_capacity INTEGER
);

CREATE TABLE flights (
  route_id INTEGER,
  number_of_flights 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 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical airline operations, ensuring that the number of flights and passenger capacities are realistic for a mid-sized airline.

-- Realistic data for routes
INSERT INTO routes (route_id, passenger_capacity) VALUES (1, 150);
INSERT INTO routes (route_id, passenger_capacity) VALUES (2, 200);
INSERT INTO routes (route_id, passenger_capacity) VALUES (3, 250);

-- Realistic data for flights
INSERT INTO flights (route_id, number_of_flights) VALUES (1, 3);
INSERT INTO flights (route_id, number_of_flights) VALUES (2, 4);
INSERT INTO flights (route_id, number_of_flights) VALUES (3, 5);


```

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

Response:
# Complete Optimization Problem and Solution: flight_4

## 1. Problem Context and Goals

### Context  
The airline is focused on optimizing the allocation of its flights across various routes to maximize the total number of passengers transported. Each route has a specific passenger capacity, and the airline aims to ensure that all routes are serviced by at least one flight. The decision variable in this context is the number of flights assigned to each route, which is an integer value. The operational parameters include the total number of flights available for allocation and the maximum number of flights that can be assigned to each route. These parameters are used as constraints in the optimization model. The airline's business configuration specifies that there are a total of 12 flights available for allocation, and no more than 5 flights can be assigned to any single route. This setup ensures that the optimization problem remains linear, focusing on maximizing passenger transport without involving nonlinear relationships.

### Goals  
The primary goal of the optimization is to maximize the total number of passengers transported across all routes. This is achieved by strategically assigning flights to routes based on their passenger capacities. The success of this optimization is measured by the total number of passengers, which is calculated by summing the product of the passenger capacity of each route and the number of flights assigned to that route. The objective is clearly defined in linear terms, focusing on maximizing passenger transport while adhering to the constraints of flight availability and route capacity.

## 2. Constraints    

The optimization problem is subject to several constraints that ensure the solution is feasible and aligns with business requirements:

- The total number of flights assigned across all routes must not exceed the total number of flights available, which is 12.
- Each route can have a maximum of 5 flights assigned to it, ensuring that no single route is over-serviced.
- Every route must have at least one flight assigned to ensure that all routes are operational.

These constraints are expressed in business terms that naturally lead to linear mathematical forms, avoiding any nonlinear relationships such as variable products or divisions.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas.

CREATE TABLE routes (
  route_id INTEGER,
  passenger_capacity INTEGER
);

CREATE TABLE flights (
  route_id INTEGER,
  number_of_flights INTEGER
);
```

### Data Dictionary  
The data dictionary provides a business-oriented mapping of tables and columns to their purposes and roles in the optimization process:

- **Routes Table**: This table stores data specific to each route, including the passenger capacity. The passenger capacity serves as a coefficient in the objective function, representing the potential number of passengers that can be transported on each route.
  - **route_id**: A unique identifier for each route, used to link route data.
  - **passenger_capacity**: The maximum number of passengers that can be accommodated on the route, used as a coefficient in the optimization objective.

- **Flights Table**: This table records the number of flights assigned to each route, which is the primary decision variable in the optimization model.
  - **route_id**: An identifier linking to the route, ensuring that flight assignments are correctly associated with their respective routes.
  - **number_of_flights**: The number of flights assigned to the route, serving as the decision variable in the optimization process.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical airline operations, ensuring that the number of flights and passenger capacities are realistic for a mid-sized airline.

-- Realistic data for routes
INSERT INTO routes (route_id, passenger_capacity) VALUES (1, 150);
INSERT INTO routes (route_id, passenger_capacity) VALUES (2, 200);
INSERT INTO routes (route_id, passenger_capacity) VALUES (3, 250);

-- Realistic data for flights
INSERT INTO flights (route_id, number_of_flights) VALUES (1, 3);
INSERT INTO flights (route_id, number_of_flights) VALUES (2, 4);
INSERT INTO flights (route_id, number_of_flights) VALUES (3, 5);
```
