Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:25:25

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": "An airline company wants to optimize its flight scheduling to minimize operational costs while ensuring all flights are covered by available aircraft and certified employees.",
  "optimization_problem": "The goal is to minimize the total operational cost of flights, which includes the cost of using aircraft and employee salaries, while ensuring that each flight is assigned an aircraft that can cover the distance and has certified employees available.",
  "objective": "minimize total_cost = sum(flight_cost[flno] * x[flno, aid, eid])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for decision variables and updating business configuration logic for budget constraints. Adjustments ensure all optimization requirements are met and data is organized according to best practices."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine decision variable mapping and ensure all constraints are feasible with available data",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for decision variables and updating business configuration logic for budget constraints. Adjustments ensure all optimization requirements are met and data is organized according to best practices.

CREATE TABLE flight (
  flno INTEGER,
  price FLOAT,
  distance FLOAT
);

CREATE TABLE aircraft (
  aid INTEGER,
  distance FLOAT
);

CREATE TABLE employee (
  eid INTEGER,
  salary FLOAT
);

CREATE TABLE flight_assignment (
  flno INTEGER,
  aid INTEGER,
  eid INTEGER,
  binary_decision BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "flight": {
      "business_purpose": "Stores information about flights",
      "optimization_role": "objective_coefficients/constraint_bounds",
      "columns": {
        "flno": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each flight",
          "optimization_purpose": "Used to index flights in optimization",
          "sample_values": "101, 102, 103"
        },
        "price": {
          "data_type": "FLOAT",
          "business_meaning": "Cost associated with operating a specific flight",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "5000.0, 7500.0, 10000.0"
        },
        "distance": {
          "data_type": "FLOAT",
          "business_meaning": "Distance that needs to be covered by the assigned aircraft",
          "optimization_purpose": "Constraint bound for aircraft assignment",
          "sample_values": "300.0, 450.0, 600.0"
        }
      }
    },
    "aircraft": {
      "business_purpose": "Stores information about aircraft",
      "optimization_role": "constraint_bounds",
      "columns": {
        "aid": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each aircraft",
          "optimization_purpose": "Used to index aircraft in optimization",
          "sample_values": "1, 2, 3"
        },
        "distance": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum distance an aircraft can cover",
          "optimization_purpose": "Constraint bound for flight assignment",
          "sample_values": "500.0, 700.0, 1000.0"
        }
      }
    },
    "employee": {
      "business_purpose": "Stores information about employees",
      "optimization_role": "constraint_bounds",
      "columns": {
        "eid": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each employee",
          "optimization_purpose": "Used to index employees in optimization",
          "sample_values": "10, 20, 30"
        },
        "salary": {
          "data_type": "FLOAT",
          "business_meaning": "Salary cost of assigning an employee to a flight",
          "optimization_purpose": "Constraint bound for budget",
          "sample_values": "3000.0, 4000.0, 5000.0"
        }
      }
    },
    "flight_assignment": {
      "business_purpose": "Tracks flight assignments to aircraft and employees",
      "optimization_role": "decision_variables",
      "columns": {
        "flno": {
          "data_type": "INTEGER",
          "business_meaning": "Flight number assigned",
          "optimization_purpose": "Part of decision variable index",
          "sample_values": "101, 102, 103"
        },
        "aid": {
          "data_type": "INTEGER",
          "business_meaning": "Aircraft assigned to flight",
          "optimization_purpose": "Part of decision variable index",
          "sample_values": "1, 2, 3"
        },
        "eid": {
          "data_type": "INTEGER",
          "business_meaning": "Employee assigned to flight",
          "optimization_purpose": "Part of decision variable index",
          "sample_values": "10, 20, 30"
        },
        "binary_decision": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the flight is assigned to the aircraft and employee",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "budget_constraint": {
    "sample_value": "1000000",
    "data_type": "FLOAT",
    "business_meaning": "Maximum allowable budget for employee salaries",
    "optimization_role": "Used to ensure salary costs do not exceed budget",
    "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": 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": "flight_1",
  "iteration": 1,
  "business_context": "An airline company aims to optimize its flight scheduling to minimize operational costs while ensuring all flights are covered by available aircraft and certified employees. The optimization must adhere to budget constraints and operational feasibility.",
  "optimization_problem_description": "The objective is to minimize the total operational cost of flights, which includes the cost of using aircraft and employee salaries, while ensuring that each flight is assigned an aircraft that can cover the distance and has certified employees available. The problem is formulated as a linear programming model with constraints on aircraft distance capabilities and budget limits.",
  "optimization_formulation": {
    "objective": "minimize total_cost = sum(flight.price * flight_assignment.binary_decision) + sum(employee.salary * flight_assignment.binary_decision)",
    "decision_variables": "x[flno, aid, eid] where x is binary indicating if flight flno is assigned to aircraft aid and employee eid",
    "constraints": [
      "sum(x[flno, aid, eid] for aid, eid) = 1 for each flno",
      "sum(flight.distance * x[flno, aid, eid]) <= aircraft.distance for each aid",
      "sum(employee.salary * x[flno, aid, eid]) <= budget_constraint",
      "x[flno, aid, eid] is binary"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "flight.price[flno]": {
        "currently_mapped_to": "flight.price",
        "mapping_adequacy": "good",
        "description": "Cost associated with operating a specific flight"
      },
      "employee.salary[eid]": {
        "currently_mapped_to": "employee.salary",
        "mapping_adequacy": "good",
        "description": "Salary cost of assigning an employee to a flight"
      }
    },
    "constraint_bounds": {
      "aircraft.distance[aid]": {
        "currently_mapped_to": "aircraft.distance",
        "mapping_adequacy": "good",
        "description": "Maximum distance an aircraft can cover"
      },
      "budget_constraint": {
        "currently_mapped_to": "business_configuration_logic.budget_constraint",
        "mapping_adequacy": "good",
        "description": "Maximum allowable budget for employee salaries"
      }
    },
    "decision_variables": {
      "x[flno, aid, eid]": {
        "currently_mapped_to": "flight_assignment.binary_decision",
        "mapping_adequacy": "good",
        "description": "Indicates if the flight is assigned to the aircraft and employee",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
