Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:47:08

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: aircraft

```sql
CREATE TABLE pilot (
  Pilot_Id NUMBER,
  Name TEXT,
  Age NUMBER
);
```

```sql
CREATE TABLE aircraft (
  Aircraft_ID NUMBER,
  Aircraft TEXT,
  Description TEXT,
  Max_Gross_Weight TEXT,
  Total_disk_area TEXT,
  Max_disk_Loading TEXT
);
```

```sql
CREATE TABLE match (
  Round NUMBER,
  Location TEXT,
  Country TEXT,
  Date TEXT,
  Fastest_Qualifying TEXT,
  Winning_Pilot TEXT,
  Winning_Aircraft TEXT
);
```

```sql
CREATE TABLE airport (
  Airport_ID NUMBER,
  Airport_Name TEXT,
  Total_Passengers NUMBER,
  %_Change_2007 TEXT,
  International_Passengers NUMBER,
  Domestic_Passengers NUMBER,
  Transit_Passengers NUMBER,
  Aircraft_Movements NUMBER,
  Freight_Metric_Tonnes NUMBER
);
```

```sql
CREATE TABLE airport_aircraft (
  ID NUMBER,
  Airport_ID NUMBER,
  Aircraft_ID NUMBER
);
```



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": "aircraft",
  "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": "aircraft",
  "iteration": 0,
  "business_context": "Optimizing the assignment of aircraft to airports to minimize total operational costs while ensuring that each airport's passenger demand is met and aircraft capacity constraints are respected.",
  "optimization_problem_description": "The goal is to minimize the total operational costs associated with assigning aircraft to airports. The decision variables represent the number of each aircraft type assigned to each airport. Constraints ensure that the total passenger capacity of assigned aircraft meets or exceeds the airport's passenger demand, and that the number of aircraft assigned does not exceed the airport's aircraft movement capacity.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_ij * x_ij) where cost_ij is the operational cost of assigning aircraft i to airport j, and x_ij is the number of aircraft i assigned to airport j",
    "decision_variables": "x_ij: number of aircraft i assigned to airport j (integer)",
    "constraints": [
      "\u2211(capacity_i * x_ij) \u2265 demand_j for all j (airport passenger demand)",
      "\u2211(x_ij) \u2264 movement_capacity_j for all j (airport aircraft movement capacity)",
      "x_ij \u2265 0 for all i, j (non-negativity)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_ij[i,j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "operational cost of assigning aircraft i to airport j"
      }
    },
    "constraint_bounds": {
      "demand_j[j]": {
        "currently_mapped_to": "airport.Total_Passengers",
        "mapping_adequacy": "partial",
        "description": "total passenger demand at airport j"
      },
      "movement_capacity_j[j]": {
        "currently_mapped_to": "airport.Aircraft_Movements",
        "mapping_adequacy": "good",
        "description": "maximum number of aircraft movements at airport j"
      }
    },
    "decision_variables": {
      "x_ij[i,j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "number of aircraft i assigned to airport j",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Operational cost data for assigning each aircraft type to each airport",
    "Passenger capacity data for each aircraft type",
    "Mapping of aircraft types to their capacities"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data on operational costs and aircraft capacities to complete the optimization model."
  }
}
