Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-28 00:17:15

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": "A university wants to optimize the allocation of student representatives to various positions based on voting records to maximize student satisfaction.",
  "optimization_problem": "Maximize the total number of votes received by elected student representatives across different positions while ensuring that each position is filled and each student can hold only one position.",
  "objective": "maximize total_votes = sum(President_Vote[i] * x[i] + Vice_President_Vote[i] * y[i] + Secretary_Vote[i] * z[i] + Treasurer_Vote[i] * w[i] + Class_President_Vote[i] * u[i] + Class_Senator_Vote[i] * v[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for decision variables and constraint bounds, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine mapping of decision variables and constraints to existing schema or business logic",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Voting_record (
  President_Vote INTEGER,
  Vice_President_Vote INTEGER,
  Secretary_Vote INTEGER,
  Treasurer_Vote INTEGER,
  Class_President_Vote INTEGER,
  Class_Senator_Vote INTEGER
);

CREATE TABLE Decision_Variables (
  President BOOLEAN,
  Vice_President BOOLEAN,
  Secretary BOOLEAN,
  Treasurer BOOLEAN,
  Class_President BOOLEAN,
  Class_Senator BOOLEAN
);

CREATE TABLE Constraint_Bounds (
  Position_Filled STRING,
  Student_Position_Limit STRING
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Voting_record": {
      "business_purpose": "Stores the number of votes each student received for each position",
      "optimization_role": "objective_coefficients",
      "columns": {
        "President_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for President position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "10, 20, 30"
        },
        "Vice_President_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Vice President position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "5, 15, 25"
        },
        "Secretary_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Secretary position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "8, 18, 28"
        },
        "Treasurer_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Treasurer position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "12, 22, 32"
        },
        "Class_President_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Class President position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "7, 17, 27"
        },
        "Class_Senator_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Class Senator position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "9, 19, 29"
        }
      }
    },
    "Decision_Variables": {
      "business_purpose": "Stores binary decision variables indicating if a student is elected to a specific position",
      "optimization_role": "decision_variables",
      "columns": {
        "President": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as President",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Vice_President": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Vice President",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Secretary": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Secretary",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Treasurer": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Treasurer",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Class_President": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Class President",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Class_Senator": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Class Senator",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    },
    "Constraint_Bounds": {
      "business_purpose": "Stores constraints ensuring each position is filled by exactly one student and each student holds at most one position",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Position_Filled": {
          "data_type": "STRING",
          "business_meaning": "Constraint ensuring each position is filled by exactly one student",
          "optimization_purpose": "Constraint in optimization model",
          "sample_values": "sum(x[i] for all i) = 1"
        },
        "Student_Position_Limit": {
          "data_type": "STRING",
          "business_meaning": "Constraint ensuring each student holds at most one position",
          "optimization_purpose": "Constraint in optimization model",
          "sample_values": "x[i] + y[i] + z[i] + w[i] + u[i] + v[i] <= 1"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "position_filled_constraint": {
    "formula_expression": "sum(x[i] for all i) = 1",
    "data_type": "STRING",
    "business_meaning": "Ensures exactly one student is elected to each position",
    "optimization_role": "Constraint in optimization model",
    "configuration_type": "business_logic_formula"
  },
  "student_position_limit_constraint": {
    "formula_expression": "x[i] + y[i] + z[i] + w[i] + u[i] + v[i] <= 1 for all i",
    "data_type": "STRING",
    "business_meaning": "Ensures each student can hold only one position",
    "optimization_role": "Constraint in optimization model",
    "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": "voter_2",
  "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": "voter_2",
  "iteration": 1,
  "business_context": "A university is optimizing the allocation of student representatives to various positions based on voting records to maximize student satisfaction, ensuring each position is filled and each student holds only one position.",
  "optimization_problem_description": "Maximize the total number of votes received by elected student representatives across different positions while ensuring that each position is filled by exactly one student and each student can hold at most one position.",
  "optimization_formulation": {
    "objective": "maximize total_votes = sum(President_Vote[i] * President[i] + Vice_President_Vote[i] * Vice_President[i] + Secretary_Vote[i] * Secretary[i] + Treasurer_Vote[i] * Treasurer[i] + Class_President_Vote[i] * Class_President[i] + Class_Senator_Vote[i] * Class_Senator[i])",
    "decision_variables": "President[i], Vice_President[i], Secretary[i], Treasurer[i], Class_President[i], Class_Senator[i] are binary variables indicating if student i is elected to the respective position",
    "constraints": "sum(President[i] for all i) = 1, sum(Vice_President[i] for all i) = 1, sum(Secretary[i] for all i) = 1, sum(Treasurer[i] for all i) = 1, sum(Class_President[i] for all i) = 1, sum(Class_Senator[i] for all i) = 1, President[i] + Vice_President[i] + Secretary[i] + Treasurer[i] + Class_President[i] + Class_Senator[i] <= 1 for all i"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "President_Vote[i]": {
        "currently_mapped_to": "Voting_record.President_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for President position"
      },
      "Vice_President_Vote[i]": {
        "currently_mapped_to": "Voting_record.Vice_President_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Vice President position"
      },
      "Secretary_Vote[i]": {
        "currently_mapped_to": "Voting_record.Secretary_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Secretary position"
      },
      "Treasurer_Vote[i]": {
        "currently_mapped_to": "Voting_record.Treasurer_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Treasurer position"
      },
      "Class_President_Vote[i]": {
        "currently_mapped_to": "Voting_record.Class_President_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Class President position"
      },
      "Class_Senator_Vote[i]": {
        "currently_mapped_to": "Voting_record.Class_Senator_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Class Senator position"
      }
    },
    "constraint_bounds": {
      "Position_Filled": {
        "currently_mapped_to": "business_configuration_logic.position_filled_constraint",
        "mapping_adequacy": "good",
        "description": "Ensures exactly one student is elected to each position"
      },
      "Student_Position_Limit": {
        "currently_mapped_to": "business_configuration_logic.student_position_limit_constraint",
        "mapping_adequacy": "good",
        "description": "Ensures each student can hold only one position"
      }
    },
    "decision_variables": {
      "President[i]": {
        "currently_mapped_to": "Decision_Variables.President",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as President",
        "variable_type": "binary"
      },
      "Vice_President[i]": {
        "currently_mapped_to": "Decision_Variables.Vice_President",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Vice President",
        "variable_type": "binary"
      },
      "Secretary[i]": {
        "currently_mapped_to": "Decision_Variables.Secretary",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Secretary",
        "variable_type": "binary"
      },
      "Treasurer[i]": {
        "currently_mapped_to": "Decision_Variables.Treasurer",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Treasurer",
        "variable_type": "binary"
      },
      "Class_President[i]": {
        "currently_mapped_to": "Decision_Variables.Class_President",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Class President",
        "variable_type": "binary"
      },
      "Class_Senator[i]": {
        "currently_mapped_to": "Decision_Variables.Class_Senator",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Class Senator",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
