Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:47:08

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "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": "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.",
  "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",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for operational costs and aircraft capacities, modifying the airport table to better align with constraints, and adding configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data on operational costs and aircraft capacities to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for operational costs and aircraft capacities, modifying the airport table to better align with constraints, and adding configuration logic for scalar parameters and formulas.

CREATE TABLE aircraft_capacity (
  aircraft_type STRING,
  passenger_capacity INTEGER
);

CREATE TABLE operational_costs (
  aircraft_type STRING,
  airport_code STRING,
  cost FLOAT,
  aircraft_count INTEGER
);

CREATE TABLE airport (
  airport_code STRING,
  passenger_demand INTEGER,
  aircraft_movements INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "aircraft_capacity": {
      "business_purpose": "Stores passenger capacity of each aircraft type",
      "optimization_role": "business_data",
      "columns": {
        "aircraft_type": {
          "data_type": "STRING",
          "business_meaning": "Type of aircraft",
          "optimization_purpose": "Identifies aircraft type",
          "sample_values": "Boeing 737, Airbus A320"
        },
        "passenger_capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of passengers the aircraft can carry",
          "optimization_purpose": "Used in demand_j[j] constraint",
          "sample_values": "150, 200"
        }
      }
    },
    "operational_costs": {
      "business_purpose": "Stores operational costs of assigning aircraft to airports",
      "optimization_role": "objective_coefficients",
      "columns": {
        "aircraft_type": {
          "data_type": "STRING",
          "business_meaning": "Type of aircraft",
          "optimization_purpose": "Identifies aircraft type",
          "sample_values": "Boeing 737, Airbus A320"
        },
        "airport_code": {
          "data_type": "STRING",
          "business_meaning": "Code of the airport",
          "optimization_purpose": "Identifies airport",
          "sample_values": "JFK, LAX"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "Operational cost of assigning the aircraft to the airport",
          "optimization_purpose": "Used in objective function",
          "sample_values": "5000.0, 7500.0"
        },
        "aircraft_count": {
          "data_type": "INTEGER",
          "business_meaning": "Number of aircraft assigned",
          "optimization_purpose": "Decision variable x_ij[i,j]",
          "sample_values": "2, 3"
        }
      }
    },
    "airport": {
      "business_purpose": "Stores airport-specific data",
      "optimization_role": "constraint_bounds",
      "columns": {
        "airport_code": {
          "data_type": "STRING",
          "business_meaning": "Code of the airport",
          "optimization_purpose": "Identifies airport",
          "sample_values": "JFK, LAX"
        },
        "passenger_demand": {
          "data_type": "INTEGER",
          "business_meaning": "Total passenger demand at the airport",
          "optimization_purpose": "Used in demand_j[j] constraint",
          "sample_values": "10000, 15000"
        },
        "aircraft_movements": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of aircraft movements at the airport",
          "optimization_purpose": "Used in movement_capacity_j[j] constraint",
          "sample_values": "50, 75"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_aircraft_movements": {
    "sample_value": 50,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of aircraft movements allowed at an airport",
    "optimization_role": "Used in movement_capacity_j[j] constraint",
    "configuration_type": "scalar_parameter"
  },
  "total_operational_cost_formula": {
    "formula_expression": "sum(cost_ij * x_ij)",
    "data_type": "STRING",
    "business_meaning": "Total operational cost of aircraft assignments",
    "optimization_role": "Used in objective function",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "aircraft",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "aircraft",
  "iteration": 1,
  "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": "Minimize the total operational costs associated with assigning aircraft to airports, ensuring 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 sum(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[i,j]: number of aircraft i assigned to airport j (integer)",
    "constraints": [
      "sum(passenger_capacity_i * x_ij[i,j]) >= passenger_demand_j[j] for each airport j",
      "sum(x_ij[i,j]) <= aircraft_movements_j[j] for each airport j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_ij[i,j]": {
        "currently_mapped_to": "operational_costs.cost",
        "mapping_adequacy": "good",
        "description": "Operational cost of assigning aircraft i to airport j"
      }
    },
    "constraint_bounds": {
      "passenger_demand_j[j]": {
        "currently_mapped_to": "airport.passenger_demand",
        "mapping_adequacy": "good",
        "description": "Passenger demand at airport j"
      },
      "aircraft_movements_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": "operational_costs.aircraft_count",
        "mapping_adequacy": "good",
        "description": "Number of aircraft i assigned to airport j",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
