Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:38:04

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "An airline aims to minimize the total cost of operating flights while ensuring that all flights are staffed with certified employees and that aircraft are not overutilized. The optimization problem is formulated as a linear programming model to ensure computational efficiency and scalability.",
  "optimization_problem": "The airline needs to decide the number of flights to operate between different origins and destinations, considering aircraft availability, employee certifications, and cost constraints. The objective is to minimize the total operational cost, which includes flight costs and employee salaries. The problem is formulated as a linear programming model with linear objective and constraints.",
  "objective": "minimize \u2211(price[flno] \u00d7 x_flight[flno]) + \u2211(salary[eid] \u00d7 y_employee[eid])",
  "table_count": 0,
  "key_changes": [
    "Schema changes include creating tables for flight costs and employee salaries to address missing optimization requirements. Business configuration logic updated to include scalar parameters for flight costs and employee salaries."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Map the missing objective coefficients (price[flno] and salary[eid]) to the schema or business configuration logic.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating tables for flight costs and employee salaries to address missing optimization requirements. Business configuration logic updated to include scalar parameters for flight costs and employee salaries.

CREATE TABLE aircraft_capacity (
  origin STRING,
  destination STRING,
  max_flights INTEGER
);

CREATE TABLE employee_assignment (
  eid INTEGER,
  flno INTEGER
);

CREATE TABLE flight_operation (
  flno INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "aircraft_capacity": {
      "business_purpose": "Maximum number of flights between origin and destination",
      "optimization_role": "constraint_bounds",
      "columns": {
        "origin": {
          "data_type": "STRING",
          "business_meaning": "Origin airport code",
          "optimization_purpose": "Constraint bound for origin",
          "sample_values": "JFK, LAX"
        },
        "destination": {
          "data_type": "STRING",
          "business_meaning": "Destination airport code",
          "optimization_purpose": "Constraint bound for destination",
          "sample_values": "LAX, JFK"
        },
        "max_flights": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of flights between origin and destination",
          "optimization_purpose": "Constraint bound for aircraft capacity",
          "sample_values": "5, 10"
        }
      }
    },
    "employee_assignment": {
      "business_purpose": "Whether employee is assigned to a flight",
      "optimization_role": "decision_variables",
      "columns": {
        "eid": {
          "data_type": "INTEGER",
          "business_meaning": "Employee ID",
          "optimization_purpose": "Decision variable for employee assignment",
          "sample_values": "1, 2, 3"
        },
        "flno": {
          "data_type": "INTEGER",
          "business_meaning": "Flight number",
          "optimization_purpose": "Decision variable for flight operation",
          "sample_values": "101, 102, 103"
        }
      }
    },
    "flight_operation": {
      "business_purpose": "Whether flight is operated",
      "optimization_role": "decision_variables",
      "columns": {
        "flno": {
          "data_type": "INTEGER",
          "business_meaning": "Flight number",
          "optimization_purpose": "Decision variable for flight operation",
          "sample_values": "101, 102, 103"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "price[flno]": {
    "sample_value": 5000,
    "data_type": "INTEGER",
    "business_meaning": "Cost of operating flight flno",
    "optimization_role": "Objective coefficient for flight cost",
    "configuration_type": "scalar_parameter"
  },
  "salary[eid]": {
    "sample_value": 3000,
    "data_type": "INTEGER",
    "business_meaning": "Salary of employee eid",
    "optimization_role": "Objective coefficient for employee salary",
    "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": "flight_1",
  "iteration": 2,
  "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": "flight_1",
  "iteration": 2,
  "business_context": "An airline aims to minimize the total cost of operating flights while ensuring that all flights are staffed with certified employees and that aircraft are not overutilized. The optimization problem is formulated as a linear programming model to ensure computational efficiency and scalability.",
  "optimization_problem_description": "The airline needs to decide the number of flights to operate between different origins and destinations, considering aircraft availability, employee certifications, and cost constraints. The objective is to minimize the total operational cost, which includes flight costs and employee salaries. The problem is formulated as a linear programming model with linear objective and constraints.",
  "optimization_formulation": {
    "objective": "minimize \u2211(price[flno] \u00d7 x_flight[flno]) + \u2211(salary[eid] \u00d7 y_employee[eid])",
    "decision_variables": {
      "x_flight[flno]": "Binary decision variable indicating whether flight flno is operated",
      "y_employee[eid]": "Binary decision variable indicating whether employee eid is assigned to a flight"
    },
    "constraints": [
      "\u2211(x_flight[flno]) \u2264 max_flights[origin, destination] for all origin, destination pairs",
      "\u2211(y_employee[eid]) \u2265 x_flight[flno] for all flno"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "price[flno]": {
        "currently_mapped_to": "business_configuration_logic.price[flno]",
        "mapping_adequacy": "good",
        "description": "Cost of operating flight flno"
      },
      "salary[eid]": {
        "currently_mapped_to": "business_configuration_logic.salary[eid]",
        "mapping_adequacy": "good",
        "description": "Salary of employee eid"
      }
    },
    "constraint_bounds": {
      "max_flights[origin, destination]": {
        "currently_mapped_to": "aircraft_capacity.max_flights",
        "mapping_adequacy": "good",
        "description": "Maximum number of flights between origin and destination"
      }
    },
    "decision_variables": {
      "x_flight[flno]": {
        "currently_mapped_to": "flight_operation.flno",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether flight flno is operated",
        "variable_type": "binary"
      },
      "y_employee[eid]": {
        "currently_mapped_to": "employee_assignment.eid",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether employee eid is assigned to a flight",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
