Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-27 22:26:58

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": "Optimize the allocation of drivers to schools to minimize the total years of experience mismatch while ensuring all schools have the required number of drivers and only full-time drivers are assigned.",
  "optimization_problem": "The goal is to assign drivers to schools such that the total mismatch in years of experience is minimized. Each school requires a certain number of drivers, and each driver can be assigned to one school. The assignment should respect the full-time status of drivers.",
  "objective": "minimize total_experience_mismatch = sum(Years_Working[i][j] * x[i][j] for all i, j)",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for years of experience mismatch and updating existing tables to fill mapping gaps. Business configuration logic is updated to handle scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Incorporate missing data on years of experience mismatch",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for years of experience mismatch and updating existing tables to fill mapping gaps. Business configuration logic is updated to handle scalar parameters and formulas.

CREATE TABLE DriverAssignments (
  DriverID INTEGER,
  SchoolID INTEGER,
  Assigned BOOLEAN
);

CREATE TABLE SchoolRequirements (
  SchoolID INTEGER,
  RequiredDrivers INTEGER
);

CREATE TABLE Drivers (
  DriverID INTEGER,
  IsFullTime BOOLEAN
);

CREATE TABLE ExperienceMismatch (
  DriverID INTEGER,
  SchoolID INTEGER,
  YearsMismatch INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "DriverAssignments": {
      "business_purpose": "Tracks driver assignments to schools",
      "optimization_role": "decision_variables",
      "columns": {
        "DriverID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each driver",
          "optimization_purpose": "Identifies driver in assignment decision variable",
          "sample_values": "1, 2, 3"
        },
        "SchoolID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each school",
          "optimization_purpose": "Identifies school in assignment decision variable",
          "sample_values": "101, 102, 103"
        },
        "Assigned": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a driver is assigned to a school",
          "optimization_purpose": "Binary decision variable for driver assignment",
          "sample_values": "true, false"
        }
      }
    },
    "SchoolRequirements": {
      "business_purpose": "Stores driver requirements for each school",
      "optimization_role": "constraint_bounds",
      "columns": {
        "SchoolID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each school",
          "optimization_purpose": "Identifies school in driver requirement constraint",
          "sample_values": "101, 102, 103"
        },
        "RequiredDrivers": {
          "data_type": "INTEGER",
          "business_meaning": "Number of drivers required by the school",
          "optimization_purpose": "Constraint bound for driver assignment",
          "sample_values": "3, 4, 5"
        }
      }
    },
    "Drivers": {
      "business_purpose": "Stores information about drivers",
      "optimization_role": "business_data",
      "columns": {
        "DriverID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each driver",
          "optimization_purpose": "Identifies driver in optimization model",
          "sample_values": "1, 2, 3"
        },
        "IsFullTime": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a driver is full-time",
          "optimization_purpose": "Used in constraint to ensure only full-time drivers are assigned",
          "sample_values": "true, false"
        }
      }
    },
    "ExperienceMismatch": {
      "business_purpose": "Stores years of experience mismatch between drivers and schools",
      "optimization_role": "objective_coefficients",
      "columns": {
        "DriverID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each driver",
          "optimization_purpose": "Identifies driver in experience mismatch calculation",
          "sample_values": "1, 2, 3"
        },
        "SchoolID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each school",
          "optimization_purpose": "Identifies school in experience mismatch calculation",
          "sample_values": "101, 102, 103"
        },
        "YearsMismatch": {
          "data_type": "INTEGER",
          "business_meaning": "Years of experience mismatch between driver and school",
          "optimization_purpose": "Coefficient in objective function to minimize experience mismatch",
          "sample_values": "0, 1, 2"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "required_drivers": {
    "sample_value": "3",
    "data_type": "INTEGER",
    "business_meaning": "Number of drivers required by each school",
    "optimization_role": "Used in constraint to ensure each school gets required drivers",
    "configuration_type": "scalar_parameter"
  },
  "is_full_time": {
    "sample_value": "true",
    "data_type": "BOOLEAN",
    "business_meaning": "Indicates if a driver is full-time",
    "optimization_role": "Used in constraint to ensure only full-time drivers are assigned",
    "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": "school_bus",
  "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": "school_bus",
  "iteration": 2,
  "business_context": "Optimize the allocation of full-time drivers to schools to minimize the total years of experience mismatch while ensuring all schools have the required number of drivers.",
  "optimization_problem_description": "Assign full-time drivers to schools such that the total mismatch in years of experience is minimized. Each school requires a specific number of drivers, and each driver can be assigned to only one school.",
  "optimization_formulation": {
    "objective": "minimize total_experience_mismatch = sum(ExperienceMismatch.YearsMismatch[i][j] * DriverAssignments.Assigned[i][j] for all i, j)",
    "decision_variables": "DriverAssignments.Assigned[i][j] where i is DriverID and j is SchoolID, binary",
    "constraints": [
      "sum(DriverAssignments.Assigned[i][j] for all j) <= 1 for all i where Drivers.IsFullTime[i] = true",
      "sum(DriverAssignments.Assigned[i][j] for all i) = SchoolRequirements.RequiredDrivers[j] for all j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "YearsMismatch[i][j]": {
        "currently_mapped_to": "ExperienceMismatch.YearsMismatch",
        "mapping_adequacy": "good",
        "description": "Years of experience mismatch between driver i and school j"
      }
    },
    "constraint_bounds": {
      "RequiredDrivers[j]": {
        "currently_mapped_to": "SchoolRequirements.RequiredDrivers",
        "mapping_adequacy": "good",
        "description": "Number of drivers required by school j"
      }
    },
    "decision_variables": {
      "Assigned[i][j]": {
        "currently_mapped_to": "DriverAssignments.Assigned",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if driver i is assigned to school j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
