Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:49:17

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 school wants to optimize the assignment of students to classrooms to minimize the total number of students per classroom, ensuring that each classroom has at least one teacher assigned.",
  "optimization_problem": "The goal is to distribute students across available classrooms such that the maximum number of students in any classroom is minimized, while ensuring each classroom has a teacher assigned.",
  "objective": "minimize max_students_per_classroom",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to fill mapping gaps, and moving scalar parameters to configuration logic."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the mapping of decision variables and ensure all necessary data for constraints are available",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to fill mapping gaps, and moving scalar parameters to configuration logic.

CREATE TABLE DecisionVariables (
  student_id INTEGER,
  classroom_id INTEGER,
  assignment BOOLEAN
);

CREATE TABLE ClassroomCapacity (
  classroom_id INTEGER,
  max_students INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "DecisionVariables": {
      "business_purpose": "Represents student assignments to classrooms",
      "optimization_role": "decision_variables",
      "columns": {
        "student_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each student",
          "optimization_purpose": "Identifies the student in the assignment matrix",
          "sample_values": "1, 2, 3"
        },
        "classroom_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each classroom",
          "optimization_purpose": "Identifies the classroom in the assignment matrix",
          "sample_values": "101, 102, 103"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a student is assigned to a classroom",
          "optimization_purpose": "Binary decision variable for student-classroom assignment",
          "sample_values": "0, 1"
        }
      }
    },
    "ClassroomCapacity": {
      "business_purpose": "Defines the capacity constraints for each classroom",
      "optimization_role": "constraint_bounds",
      "columns": {
        "classroom_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each classroom",
          "optimization_purpose": "Links capacity constraints to specific classrooms",
          "sample_values": "101, 102, 103"
        },
        "max_students": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of students allowed in the classroom",
          "optimization_purpose": "Sets the upper bound for students in each classroom",
          "sample_values": "25, 30, 35"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_students_per_classroom": {
    "sample_value": "30",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of students allowed in any classroom",
    "optimization_role": "Used to set the upper limit of students per classroom in the optimization model",
    "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": "student_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": "student_1",
  "iteration": 1,
  "business_context": "A school is optimizing the assignment of students to classrooms to minimize the maximum number of students in any classroom, ensuring each classroom has at least one teacher assigned.",
  "optimization_problem_description": "The goal is to distribute students across available classrooms such that the maximum number of students in any classroom is minimized, while ensuring each classroom has a teacher assigned.",
  "optimization_formulation": {
    "objective": "minimize max_students_per_classroom",
    "decision_variables": "assignment[student_id, classroom_id] - binary variable indicating if a student is assigned to a classroom",
    "constraints": [
      "sum(assignment[student_id, classroom_id] for all student_id) <= max_students for each classroom_id",
      "sum(assignment[student_id, classroom_id] for all classroom_id) = 1 for each student_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "max_students_per_classroom": {
        "currently_mapped_to": "business_configuration_logic.max_students_per_classroom",
        "mapping_adequacy": "good",
        "description": "Represents the upper limit of students per classroom in the optimization model"
      }
    },
    "constraint_bounds": {
      "classroom_capacity[classroom_id]": {
        "currently_mapped_to": "ClassroomCapacity.max_students",
        "mapping_adequacy": "good",
        "description": "Maximum number of students allowed in each classroom"
      }
    },
    "decision_variables": {
      "assignment[student_id, classroom_id]": {
        "currently_mapped_to": "DecisionVariables.assignment",
        "mapping_adequacy": "good",
        "description": "Binary decision variable for student-classroom assignment",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
