Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:46:28

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 pilot assignments to aircraft to minimize operational costs while ensuring pilots are assigned to aircraft they are qualified to fly and respecting pilot availability constraints.",
  "optimization_problem": "The goal is to minimize the total operational cost of assigning pilots to aircraft. The cost is influenced by the pilot's rank and the aircraft's fuel efficiency. Constraints include ensuring each pilot is assigned to at most one aircraft per day, each aircraft is assigned exactly one pilot, and pilots are only assigned to aircraft they are qualified to fly based on their rank.",
  "objective": "minimize \u2211(cost_coefficient[pilot_id, aircraft_id] * assignment[pilot_id, aircraft_id])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for cost coefficients and pilot qualifications, and updating business configuration logic with scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define cost coefficients and pilot qualification data to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for cost coefficients and pilot qualifications, and updating business configuration logic with scalar parameters and formulas.

CREATE TABLE cost_coefficients (
  pilot_id INTEGER,
  aircraft_id INTEGER,
  cost_value FLOAT
);

CREATE TABLE pilot_qualifications (
  pilot_id INTEGER,
  aircraft_id INTEGER,
  is_qualified BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "cost_coefficients": {
      "business_purpose": "cost of assigning a pilot to an aircraft based on pilot rank and aircraft fuel efficiency",
      "optimization_role": "objective_coefficients",
      "columns": {
        "pilot_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the pilot",
          "optimization_purpose": "used to identify the pilot in the cost coefficient",
          "sample_values": "1, 2, 3"
        },
        "aircraft_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the aircraft",
          "optimization_purpose": "used to identify the aircraft in the cost coefficient",
          "sample_values": "101, 102, 103"
        },
        "cost_value": {
          "data_type": "FLOAT",
          "business_meaning": "calculated cost of assigning the pilot to the aircraft",
          "optimization_purpose": "used in the objective function to minimize costs",
          "sample_values": "2.55, 3.40, 4.25"
        }
      }
    },
    "pilot_qualifications": {
      "business_purpose": "binary indicator of whether a pilot is qualified to fly a specific aircraft",
      "optimization_role": "constraint_bounds",
      "columns": {
        "pilot_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the pilot",
          "optimization_purpose": "used to identify the pilot in the qualification constraint",
          "sample_values": "1, 2, 3"
        },
        "aircraft_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the aircraft",
          "optimization_purpose": "used to identify the aircraft in the qualification constraint",
          "sample_values": "101, 102, 103"
        },
        "is_qualified": {
          "data_type": "BOOLEAN",
          "business_meaning": "indicates if the pilot is qualified to fly the aircraft",
          "optimization_purpose": "used in the qualification constraint",
          "sample_values": "true, false, true"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "pilot_rank": {
    "sample_value": "3",
    "data_type": "INTEGER",
    "business_meaning": "rank of the pilot influencing the cost",
    "optimization_role": "used in cost coefficient calculation",
    "configuration_type": "scalar_parameter"
  },
  "aircraft_fuel_efficiency": {
    "sample_value": "0.85",
    "data_type": "FLOAT",
    "business_meaning": "fuel efficiency of the aircraft influencing the cost",
    "optimization_role": "used in cost coefficient calculation",
    "configuration_type": "scalar_parameter"
  },
  "cost_coefficient_formula": {
    "formula_expression": "pilot_rank * aircraft_fuel_efficiency",
    "data_type": "STRING",
    "business_meaning": "formula to calculate the cost of assigning a pilot to an aircraft",
    "optimization_role": "used to determine the cost coefficient",
    "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": "pilot_record",
  "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": "pilot_record",
  "iteration": 1,
  "business_context": "Optimize pilot assignments to aircraft to minimize operational costs while ensuring pilots are assigned to aircraft they are qualified to fly and respecting pilot availability constraints.",
  "optimization_problem_description": "Minimize the total operational cost of assigning pilots to aircraft, ensuring each pilot is assigned to at most one aircraft per day, each aircraft is assigned exactly one pilot, and pilots are only assigned to aircraft they are qualified to fly based on their rank.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_coefficients.cost_value * assignment[pilot_id, aircraft_id])",
    "decision_variables": "assignment[pilot_id, aircraft_id]: binary variable indicating if pilot is assigned to aircraft",
    "constraints": "\u2211(assignment[pilot_id, aircraft_id]) \u2264 1 for each pilot_id, \u2211(assignment[pilot_id, aircraft_id]) = 1 for each aircraft_id, assignment[pilot_id, aircraft_id] \u2264 pilot_qualifications.is_qualified for each pilot_id and aircraft_id"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_coefficient[pilot_id, aircraft_id]": {
        "currently_mapped_to": "cost_coefficients.cost_value",
        "mapping_adequacy": "good",
        "description": "cost of assigning a pilot to an aircraft"
      }
    },
    "constraint_bounds": {
      "pilot_assignment_limit[pilot_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of aircraft a pilot can be assigned to per day"
      },
      "aircraft_assignment_requirement[aircraft_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "requirement that each aircraft must be assigned exactly one pilot"
      },
      "pilot_qualification[pilot_id, aircraft_id]": {
        "currently_mapped_to": "pilot_qualifications.is_qualified",
        "mapping_adequacy": "good",
        "description": "indicates if a pilot is qualified to fly a specific aircraft"
      }
    },
    "decision_variables": {
      "assignment[pilot_id, aircraft_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if a pilot is assigned to an aircraft",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "pilot_assignment_limit[pilot_id]",
    "aircraft_assignment_requirement[aircraft_id]",
    "assignment[pilot_id, aircraft_id]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define pilot assignment limits and aircraft assignment requirements, and create decision variables for pilot assignments."
  }
}
