Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:31:07

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 dormitory assignments to minimize the total distance students travel from their home cities to their assigned dorms, while respecting dorm capacity and gender constraints.",
  "optimization_problem": "The goal is to assign students to dorms in a way that minimizes the total distance traveled from their home cities to their assigned dorms. The assignment must respect the capacity of each dorm and ensure that students are assigned to dorms that match their gender.",
  "objective": "minimize \u2211(distance[stuid, dormid] * assign[stuid, dormid])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for distance matrix and gender information, updating Dorm table for capacity, and adding business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Obtain distance data and ensure gender information is available for both students and dorms.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for distance matrix and gender information, updating Dorm table for capacity, and adding business configuration logic for scalar parameters and formulas.

CREATE TABLE DistanceMatrix (
  student_id INTEGER,
  dorm_id INTEGER,
  distance FLOAT
);

CREATE TABLE GenderInfo (
  student_id INTEGER,
  dorm_id INTEGER,
  gender STRING
);

CREATE TABLE Dorm (
  dorm_id INTEGER,
  student_capacity INTEGER,
  gender STRING
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "DistanceMatrix": {
      "business_purpose": "Stores distances between student home cities and dorms",
      "optimization_role": "objective_coefficients",
      "columns": {
        "student_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for student",
          "optimization_purpose": "Links student to their home city",
          "sample_values": "1, 2, 3"
        },
        "dorm_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for dorm",
          "optimization_purpose": "Links dorm to its location",
          "sample_values": "1, 2, 3"
        },
        "distance": {
          "data_type": "FLOAT",
          "business_meaning": "Distance from student's home city to dorm",
          "optimization_purpose": "Used in objective function to minimize total distance",
          "sample_values": "10.5, 15.3, 20.1"
        }
      }
    },
    "GenderInfo": {
      "business_purpose": "Stores gender information for students and dorms",
      "optimization_role": "constraint_bounds",
      "columns": {
        "student_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for student",
          "optimization_purpose": "Links student to their gender",
          "sample_values": "1, 2, 3"
        },
        "dorm_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for dorm",
          "optimization_purpose": "Links dorm to its gender constraint",
          "sample_values": "1, 2, 3"
        },
        "gender": {
          "data_type": "STRING",
          "business_meaning": "Gender of student or dorm",
          "optimization_purpose": "Ensures gender constraints are respected",
          "sample_values": "Male, Female"
        }
      }
    },
    "Dorm": {
      "business_purpose": "Stores information about dorms",
      "optimization_role": "constraint_bounds",
      "columns": {
        "dorm_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for dorm",
          "optimization_purpose": "Links dorm to its capacity and gender",
          "sample_values": "1, 2, 3"
        },
        "student_capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of students a dorm can accommodate",
          "optimization_purpose": "Used in capacity constraints",
          "sample_values": "100, 150, 200"
        },
        "gender": {
          "data_type": "STRING",
          "business_meaning": "Gender constraint for dorm",
          "optimization_purpose": "Ensures gender constraints are respected",
          "sample_values": "Male, Female"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "dorm_capacity_threshold": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of students a dorm can accommodate",
    "optimization_role": "Used in capacity constraints",
    "configuration_type": "scalar_parameter"
  },
  "distance_calculation_formula": {
    "formula_expression": "sqrt((x2 - x1)^2 + (y2 - y1)^2)",
    "data_type": "STRING",
    "business_meaning": "Calculates Euclidean distance between two points",
    "optimization_role": "Used in objective function to minimize total distance",
    "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": "dorm_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": "dorm_1",
  "iteration": 1,
  "business_context": "Optimize dormitory assignments to minimize the total distance students travel from their home cities to their assigned dorms, while respecting dorm capacity and gender constraints.",
  "optimization_problem_description": "Minimize the total distance traveled by students from their home cities to their assigned dorms, subject to dorm capacity limits and gender matching constraints.",
  "optimization_formulation": {
    "objective": "minimize \u2211(distance[student_id, dorm_id] * assign[student_id, dorm_id])",
    "decision_variables": "assign[student_id, dorm_id] \u2208 {0, 1} (binary variable indicating whether student is assigned to dorm)",
    "constraints": [
      "\u2211(assign[student_id, dorm_id]) = 1 for all student_id (each student is assigned to exactly one dorm)",
      "\u2211(assign[student_id, dorm_id]) \u2264 student_capacity[dorm_id] for all dorm_id (dorm capacity constraint)",
      "assign[student_id, dorm_id] = 0 if gender[student_id] \u2260 gender[dorm_id] (gender matching constraint)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "distance[student_id, dorm_id]": {
        "currently_mapped_to": "DistanceMatrix.distance",
        "mapping_adequacy": "good",
        "description": "Distance from student's home city to dorm"
      }
    },
    "constraint_bounds": {
      "student_capacity[dorm_id]": {
        "currently_mapped_to": "Dorm.student_capacity",
        "mapping_adequacy": "good",
        "description": "Maximum number of students a dorm can accommodate"
      },
      "gender[student_id]": {
        "currently_mapped_to": "GenderInfo.gender",
        "mapping_adequacy": "good",
        "description": "Gender of student"
      },
      "gender[dorm_id]": {
        "currently_mapped_to": "Dorm.gender",
        "mapping_adequacy": "good",
        "description": "Gender constraint for dorm"
      }
    },
    "decision_variables": {
      "assign[student_id, dorm_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating whether student is assigned to dorm",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Decision variable assign[student_id, dorm_id] needs to be defined in the schema"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define the decision variable assign[student_id, dorm_id] in the schema"
  }
}
