Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:28:57

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 district aims to optimize the assignment of students to classrooms to balance the workload among teachers while ensuring that each classroom does not exceed its capacity.",
  "optimization_problem": "The goal is to minimize the maximum number of students assigned to any classroom, ensuring that each student is assigned to exactly one classroom and that the total number of students in each classroom does not exceed a predefined capacity.",
  "objective": "minimize the maximum number of students in any classroom",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for classroom capacities and student assignments, and updating business configuration logic for maximum allowed students per classroom."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather classroom capacities and define the maximum allowed students per classroom to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for classroom capacities and student assignments, and updating business configuration logic for maximum allowed students per classroom.

CREATE TABLE classroom_capacities (
  classroom_id INTEGER,
  capacity INTEGER
);

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


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "classroom_capacities": {
      "business_purpose": "The capacity of each classroom in the school district",
      "optimization_role": "constraint_bounds",
      "columns": {
        "classroom_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each classroom",
          "optimization_purpose": "Used to identify the classroom in constraints",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "The maximum number of students allowed in the classroom",
          "optimization_purpose": "Used to constrain the number of students assigned to the classroom",
          "sample_values": "25, 30, 35"
        }
      }
    },
    "student_assignments": {
      "business_purpose": "Assignment of students to classrooms",
      "optimization_role": "decision_variables",
      "columns": {
        "student_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each student",
          "optimization_purpose": "Used to identify the student in assignments",
          "sample_values": "101, 102, 103"
        },
        "classroom_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each classroom",
          "optimization_purpose": "Used to identify the classroom in assignments",
          "sample_values": "1, 2, 3"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates whether the student is assigned to the classroom",
          "optimization_purpose": "Used as a binary decision variable in the optimization model",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_students_per_classroom": {
    "sample_value": 30,
    "data_type": "INTEGER",
    "business_meaning": "The maximum number of students allowed in any classroom",
    "optimization_role": "Used to minimize the maximum number of students in any classroom",
    "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 district aims to optimize the assignment of students to classrooms to balance the workload among teachers while ensuring that each classroom does not exceed its capacity.",
  "optimization_problem_description": "Minimize the maximum number of students assigned to any classroom, ensuring that each student is assigned to exactly one classroom and that the total number of students in each classroom does not exceed its predefined capacity.",
  "optimization_formulation": {
    "objective": "minimize z, where z is the maximum number of students in any classroom",
    "decision_variables": "x_ij (binary): 1 if student i is assigned to classroom j, 0 otherwise",
    "constraints": [
      "sum(x_ij for all j) = 1 for each student i (each student is assigned to exactly one classroom)",
      "sum(x_ij for all i) <= capacity_j for each classroom j (classroom capacity constraint)",
      "sum(x_ij for all i) <= z for each classroom j (z represents the maximum number of students in any classroom)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "z": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum number of students in any classroom"
      }
    },
    "constraint_bounds": {
      "capacity_j": {
        "currently_mapped_to": "classroom_capacities.capacity",
        "mapping_adequacy": "good",
        "description": "The maximum number of students allowed in classroom j"
      },
      "student_assignment": {
        "currently_mapped_to": "student_assignments.assignment",
        "mapping_adequacy": "good",
        "description": "Ensures each student is assigned to exactly one classroom"
      }
    },
    "decision_variables": {
      "x_ij": {
        "currently_mapped_to": "student_assignments.assignment",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if student i is assigned to classroom j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "A variable or parameter to represent the maximum number of students in any classroom (z)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define a variable or parameter to represent the maximum number of students in any classroom (z) to complete the linear formulation."
  }
}
