Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:27:49

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_2

```sql
CREATE TABLE airlines (
  uid NUMBER,
  Airline TEXT,
  Abbreviation TEXT,
  Country TEXT
);
```

```sql
CREATE TABLE airports (
  City TEXT,
  AirportCode TEXT,
  AirportName TEXT,
  Country TEXT,
  CountryAbbrev TEXT
);
```

```sql
CREATE TABLE flights (
  Airline NUMBER,
  FlightNo NUMBER,
  SourceAirport TEXT,
  DestAirport TEXT
);
```



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_2",
  "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_2",
  "iteration": 0,
  "business_context": "An airline company aims to minimize the total cost of operating flights while ensuring that each flight route is covered and that the number of flights does not exceed the capacity of each airport.",
  "optimization_problem_description": "The objective is to minimize the total operating cost of flights, which is a linear function of the number of flights on each route. Constraints include ensuring that each route is covered by at least one flight and that the number of flights departing from and arriving at each airport does not exceed the airport's capacity.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_flight[route] \u00d7 flights[route])",
    "decision_variables": "flights[route]: number of flights on each route (integer)",
    "constraints": [
      "\u2211(flights[route]) \u2265 1 for each route",
      "\u2211(flights[route] where route departs from airport) \u2264 airport_capacity[airport] for each airport",
      "\u2211(flights[route] where route arrives at airport) \u2264 airport_capacity[airport] for each airport"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_flight[route]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "cost of operating a flight on a specific route"
      }
    },
    "constraint_bounds": {
      "airport_capacity[airport]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of flights an airport can handle"
      }
    },
    "decision_variables": {
      "flights[route]": {
        "currently_mapped_to": "flights.FlightNo",
        "mapping_adequacy": "partial",
        "description": "number of flights on a specific route",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "cost_per_flight[route]",
    "airport_capacity[airport]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map missing data for cost_per_flight and airport_capacity"
  }
}
