Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:26:58

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 drivers to schools to minimize the total years of experience mismatch while ensuring all schools have the required number of drivers.",
  "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": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing data requirements 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 school driver requirements and full-time status of drivers",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing data requirements 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
);


```

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"
        }
      }
    }
  }
}


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": 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": "school_bus",
  "iteration": 1,
  "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_description": "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.",
  "optimization_formulation": {
    "objective": "minimize total_experience_mismatch = sum(Years_Working[i][j] * x[i][j] for all i, j)",
    "decision_variables": "x[i][j] is a binary variable indicating if driver i is assigned to school j",
    "constraints": [
      "sum(x[i][j] for all j) <= 1 for all i (each driver can be assigned to at most one school)",
      "sum(x[i][j] for all i) = RequiredDrivers[j] for all j (each school must have the required number of drivers)",
      "x[i][j] <= IsFullTime[i] for all i, j (only full-time drivers can be assigned)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Years_Working[i][j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "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": {
      "x[i][j]": {
        "currently_mapped_to": "DriverAssignments.Assigned",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if driver i is assigned to school j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Years_Working[i][j]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Incorporate missing data on years of experience mismatch"
  }
}
