Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-25 22:45:14

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: assign_airline_route[alid, rid]: binary variable indicating if airline alid is assigned to route rid
- Operational parameters align with expected linear objective: minimize ∑(cost_airline_route[alid, rid] × assign_airline_route[alid, rid])
- Business configuration includes: threshold for operational efficiency (used for used in evaluating airline performance)
- Business logic formulas to express in natural language: formula to calculate total operational cost for a flight (calculation method for used in the 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_4",
  "iteration": 2,
  "business_context": "Optimizing airline route assignments to minimize total operational costs while ensuring coverage of all required destinations and respecting airline capacities.",
  "optimization_problem_description": "Minimize the total operational cost of assigning airlines to routes, ensuring all routes are covered and no airline exceeds its capacity.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_airline_route[alid, rid] \u00d7 assign_airline_route[alid, rid])",
    "decision_variables": "assign_airline_route[alid, rid]: binary variable indicating if airline alid is assigned to route rid",
    "constraints": [
      "\u2211(assign_airline_route[alid, rid] for all alid) = 1 for all rid (each route must be covered by exactly one airline)",
      "\u2211(assign_airline_route[alid, rid] for all rid) \u2264 capacity_airline[alid] for all alid (no airline exceeds its capacity)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_airline_route[alid, rid]": {
        "currently_mapped_to": "cost_airline_route.cost",
        "mapping_adequacy": "good",
        "description": "cost of assigning airline alid to route rid"
      }
    },
    "constraint_bounds": {
      "capacity_airline[alid]": {
        "currently_mapped_to": "capacity_airline.capacity",
        "mapping_adequacy": "good",
        "description": "maximum number of routes airline alid can handle"
      }
    },
    "decision_variables": {
      "assign_airline_route[alid, rid]": {
        "currently_mapped_to": "assign_airline_route.assign",
        "mapping_adequacy": "good",
        "description": "binary decision variable indicating if airline alid is assigned to route rid",
        "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: Added decision variable table assign_airline_route to address missing optimization requirement. Updated business configuration logic with additional scalar parameters and formulas.

CREATE TABLE cost_airline_route (
  alid INTEGER,
  rid INTEGER,
  cost FLOAT
);

CREATE TABLE capacity_airline (
  alid INTEGER,
  capacity INTEGER
);

CREATE TABLE assign_airline_route (
  alid INTEGER,
  rid INTEGER,
  assign BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards, realistic operational costs, and airline capacities. The data ensures that the optimization problem is meaningful and solvable by maintaining logical relationships between tables and respecting business configuration logic.

-- Realistic data for cost_airline_route
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 1, 1200.0);
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 2, 1800.0);
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 3, 2500.0);

-- Realistic data for capacity_airline
INSERT INTO capacity_airline (alid, capacity) VALUES (1, 8);
INSERT INTO capacity_airline (alid, capacity) VALUES (2, 12);
INSERT INTO capacity_airline (alid, capacity) VALUES (3, 6);

-- Realistic data for assign_airline_route
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 1, False);
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 2, False);
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 3, False);


```

DATA DICTIONARY:
{
  "tables": {
    "cost_airline_route": {
      "business_purpose": "cost of assigning a specific airline to a specific route",
      "optimization_role": "objective_coefficients",
      "columns": {
        "alid": {
          "data_type": "INTEGER",
          "business_meaning": "airline ID",
          "optimization_purpose": "identifier for airline",
          "sample_values": "1, 2, 3"
        },
        "rid": {
          "data_type": "INTEGER",
          "business_meaning": "route ID",
          "optimization_purpose": "identifier for route",
          "sample_values": "1, 2, 3"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "cost of assigning airline to route",
          "optimization_purpose": "coefficient in objective function",
          "sample_values": "1000.0, 1500.0, 2000.0"
        }
      }
    },
    "capacity_airline": {
      "business_purpose": "maximum number of routes an airline can handle",
      "optimization_role": "constraint_bounds",
      "columns": {
        "alid": {
          "data_type": "INTEGER",
          "business_meaning": "airline ID",
          "optimization_purpose": "identifier for airline",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "maximum number of routes",
          "optimization_purpose": "upper bound in capacity constraint",
          "sample_values": "5, 10, 15"
        }
      }
    },
    "assign_airline_route": {
      "business_purpose": "binary decision variable indicating if airline alid is assigned to route rid",
      "optimization_role": "decision_variables",
      "columns": {
        "alid": {
          "data_type": "INTEGER",
          "business_meaning": "airline ID",
          "optimization_purpose": "identifier for airline",
          "sample_values": "1, 2, 3"
        },
        "rid": {
          "data_type": "INTEGER",
          "business_meaning": "route ID",
          "optimization_purpose": "identifier for route",
          "sample_values": "1, 2, 3"
        },
        "assign": {
          "data_type": "BOOLEAN",
          "business_meaning": "binary decision variable",
          "optimization_purpose": "indicates if airline is assigned to route",
          "sample_values": "true, false"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "operational_threshold": {
    "data_type": "FLOAT",
    "business_meaning": "threshold for operational efficiency",
    "optimization_role": "used in evaluating airline performance",
    "configuration_type": "scalar_parameter",
    "value": 0.85,
    "business_justification": "A slightly higher threshold ensures that airlines maintain high operational efficiency."
  },
  "cost_calculation_formula": {
    "data_type": "STRING",
    "business_meaning": "formula to calculate total operational cost for a flight",
    "optimization_role": "used in the objective function",
    "configuration_type": "business_logic_formula",
    "formula_expression": "base_operational_cost + (distance * cost_per_mile) + (fuel_cost * fuel_efficiency)"
  }
}

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: assign_airline_route[alid, rid]: binary variable indicating if airline alid is assigned to route rid
- Operational parameters align with expected linear objective: minimize ∑(cost_airline_route[alid, rid] × assign_airline_route[alid, rid])
- Business configuration includes: threshold for operational efficiency (used for used in evaluating airline performance)
- Business logic formulas to express in natural language: formula to calculate total operational cost for a flight (calculation method for used in the 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 ∑(cost_airline_route[alid, rid] × assign_airline_route[alid, 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: ['∑(assign_airline_route[alid, rid] for all alid) = 1 for all rid (each route must be covered by exactly one airline)', '∑(assign_airline_route[alid, rid] for all rid) ≤ capacity_airline[alid] for all alid (no airline exceeds its capacity)'] (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: Added decision variable table assign_airline_route to address missing optimization requirement. Updated business configuration logic with additional scalar parameters and formulas.

CREATE TABLE cost_airline_route (
  alid INTEGER,
  rid INTEGER,
  cost FLOAT
);

CREATE TABLE capacity_airline (
  alid INTEGER,
  capacity INTEGER
);

CREATE TABLE assign_airline_route (
  alid INTEGER,
  rid INTEGER,
  assign 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, realistic operational costs, and airline capacities. The data ensures that the optimization problem is meaningful and solvable by maintaining logical relationships between tables and respecting business configuration logic.

-- Realistic data for cost_airline_route
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 1, 1200.0);
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 2, 1800.0);
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 3, 2500.0);

-- Realistic data for capacity_airline
INSERT INTO capacity_airline (alid, capacity) VALUES (1, 8);
INSERT INTO capacity_airline (alid, capacity) VALUES (2, 12);
INSERT INTO capacity_airline (alid, capacity) VALUES (3, 6);

-- Realistic data for assign_airline_route
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 1, False);
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 2, False);
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 3, False);


```

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 business problem revolves around optimizing the assignment of airlines to specific routes to minimize total operational costs while ensuring all required destinations are covered and no airline exceeds its capacity. The decision to assign an airline to a route is represented as a binary choice, where each route must be assigned to exactly one airline. The operational cost of assigning an airline to a route is a key factor in this decision, and it is calculated using a formula that includes base operational costs, distance-based costs, fuel costs, and fuel efficiency. Additionally, a threshold for operational efficiency is set to ensure that airlines maintain high performance standards. This threshold is used to evaluate airline performance but does not directly influence the optimization constraints. The problem is designed to avoid nonlinear relationships, ensuring that all calculations and constraints remain linear and straightforward.

### Goals  
The primary goal of this optimization is to minimize the total operational cost associated with assigning airlines to routes. This is achieved by summing the costs of all assignments, where each assignment is weighted by its corresponding operational cost. Success is measured by achieving the lowest possible total cost while ensuring that all routes are covered and no airline is assigned more routes than it can handle. The optimization process relies on precise operational data, including the costs of assignments and the capacities of airlines, to make informed decisions that align with business objectives.

## 2. Constraints    

The optimization problem is subject to two key constraints:  
1. **Route Coverage**: Each route must be assigned to exactly one airline. This ensures that all required destinations are covered without redundancy.  
2. **Airline Capacity**: No airline can be assigned more routes than its specified capacity. This ensures that airlines operate within their operational limits and maintain efficiency.  

These constraints are designed to be linear and straightforward, avoiding any complex relationships or nonlinear calculations. They directly align with the business requirements and ensure that the optimization problem remains solvable and meaningful.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Added decision variable table assign_airline_route to address missing optimization requirement. Updated business configuration logic with additional scalar parameters and formulas.

CREATE TABLE cost_airline_route (
  alid INTEGER,
  rid INTEGER,
  cost FLOAT
);

CREATE TABLE capacity_airline (
  alid INTEGER,
  capacity INTEGER
);

CREATE TABLE assign_airline_route (
  alid INTEGER,
  rid INTEGER,
  assign BOOLEAN
);
```

### Data Dictionary  
- **cost_airline_route**: This table contains the operational costs associated with assigning specific airlines to specific routes. Each record includes the airline ID, route ID, and the cost of the assignment. The cost is used as a coefficient in the optimization objective function.  
- **capacity_airline**: This table defines the maximum number of routes each airline can handle. It includes the airline ID and its corresponding capacity, which serves as an upper bound in the capacity constraint.  
- **assign_airline_route**: This table represents the decision variables in the optimization problem. Each record indicates whether a specific airline is assigned to a specific route, using a binary value (true or false).  

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards, realistic operational costs, and airline capacities. The data ensures that the optimization problem is meaningful and solvable by maintaining logical relationships between tables and respecting business configuration logic.

-- Realistic data for cost_airline_route
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 1, 1200.0);
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 2, 1800.0);
INSERT INTO cost_airline_route (alid, rid, cost) VALUES (1, 3, 2500.0);

-- Realistic data for capacity_airline
INSERT INTO capacity_airline (alid, capacity) VALUES (1, 8);
INSERT INTO capacity_airline (alid, capacity) VALUES (2, 12);
INSERT INTO capacity_airline (alid, capacity) VALUES (3, 6);

-- Realistic data for assign_airline_route
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 1, False);
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 2, False);
INSERT INTO assign_airline_route (alid, rid, assign) VALUES (1, 3, False);
```
