Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:43:37

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": "Optimize the allocation of aircraft to airports to maximize the total number of passengers transported, considering aircraft capacity and airport constraints.",
  "optimization_problem": "The goal is to allocate aircraft to different airports in a way that maximizes the total number of passengers transported. Each aircraft has a maximum capacity, and each airport has a limit on the number of aircraft movements it can handle. The optimization will determine the number of aircraft assigned to each airport while respecting these constraints.",
  "objective": "maximize total_passengers = \u2211(passenger_capacity[i] * x[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include adding tables for passenger capacity and aircraft assignments, modifying existing tables to include missing data, and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Incorporate passenger capacity data and refine aircraft-to-airport mapping",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding tables for passenger capacity and aircraft assignments, modifying existing tables to include missing data, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE passenger_capacity (
  aircraft_id INTEGER,
  capacity INTEGER
);

CREATE TABLE aircraft_assignment (
  airport_id INTEGER,
  number_of_aircraft INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "passenger_capacity": {
      "business_purpose": "Stores passenger capacity for each aircraft",
      "optimization_role": "objective_coefficients",
      "columns": {
        "aircraft_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each aircraft",
          "optimization_purpose": "Links passenger capacity to specific aircraft",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Passenger capacity of the aircraft",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "150, 180, 200"
        }
      }
    },
    "aircraft_assignment": {
      "business_purpose": "Tracks the number of aircraft assigned to each airport",
      "optimization_role": "decision_variables",
      "columns": {
        "airport_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each airport",
          "optimization_purpose": "Links aircraft assignments to specific airports",
          "sample_values": "1, 2, 3"
        },
        "number_of_aircraft": {
          "data_type": "INTEGER",
          "business_meaning": "Number of aircraft assigned to the airport",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "3, 5, 7"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Max_Gross_Weight": {
    "sample_value": "50000",
    "data_type": "INTEGER",
    "business_meaning": "Maximum weight capacity of aircraft",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "Aircraft_Movements": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of aircraft movements allowed at an airport",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  }
}


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": "Optimize the allocation of aircraft to airports to maximize the total number of passengers transported, considering aircraft capacity and airport constraints.",
  "optimization_problem_description": "Allocate aircraft to airports to maximize passenger transport, considering aircraft capacity and airport movement limits.",
  "optimization_formulation": {
    "objective": "maximize total_passengers = \u2211(capacity[i] * number_of_aircraft[i])",
    "decision_variables": {
      "number_of_aircraft[i]": {
        "description": "Number of aircraft assigned to airport i",
        "variable_type": "integer"
      }
    },
    "constraints": {
      "aircraft_capacity_constraint[i]": {
        "description": "Number of passengers transported by aircraft i cannot exceed its capacity",
        "expression": "number_of_aircraft[i] * capacity[i] <= Max_Gross_Weight"
      },
      "airport_movement_constraint[j]": {
        "description": "Total aircraft movements at airport j cannot exceed its limit",
        "expression": "\u2211(number_of_aircraft[j]) <= Aircraft_Movements"
      }
    }
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "capacity[i]": {
        "currently_mapped_to": "passenger_capacity.capacity",
        "mapping_adequacy": "good",
        "description": "Passenger capacity of aircraft i"
      }
    },
    "constraint_bounds": {
      "Max_Gross_Weight": {
        "currently_mapped_to": "business_configuration_logic.Max_Gross_Weight",
        "mapping_adequacy": "good",
        "description": "Maximum weight capacity of aircraft"
      },
      "Aircraft_Movements": {
        "currently_mapped_to": "business_configuration_logic.Aircraft_Movements",
        "mapping_adequacy": "good",
        "description": "Maximum number of aircraft movements allowed at an airport"
      }
    },
    "decision_variables": {
      "number_of_aircraft[i]": {
        "currently_mapped_to": "aircraft_assignment.number_of_aircraft",
        "mapping_adequacy": "good",
        "description": "Number of aircraft assigned to airport i",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
