Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:31:07

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "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": "Minimize the total distance traveled by students from their home cities to their assigned dorms, subject to dorm capacity limits and gender matching constraints.",
  "objective": "minimize \u2211(distance[student_id, dorm_id] * assign[student_id, dorm_id])",
  "table_count": 1,
  "key_changes": [
    "Added Assignment table for decision variables, updated data dictionary, and ensured all optimization mappings are complete."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define the decision variable assign[student_id, dorm_id] in the schema",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added Assignment table for decision variables, updated data dictionary, and ensured all optimization mappings are complete.

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
);

CREATE TABLE Assignment (
  student_id INTEGER,
  dorm_id INTEGER,
  assign BOOLEAN
);


```

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"
        }
      }
    },
    "Assignment": {
      "business_purpose": "Stores binary assignment of students to dorms",
      "optimization_role": "decision_variables",
      "columns": {
        "student_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for student",
          "optimization_purpose": "Links student to their assignment",
          "sample_values": "1, 2, 3"
        },
        "dorm_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for dorm",
          "optimization_purpose": "Links dorm to its assignment",
          "sample_values": "1, 2, 3"
        },
        "assign": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary variable indicating whether student is assigned to dorm",
          "optimization_purpose": "Used in decision variables for optimization",
          "sample_values": "true, false"
        }
      }
    }
  }
}



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": 2,
  "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": 2,
  "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 decision 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 is not exceeded)",
      "assign[student_id, dorm_id] = 0 if gender[student_id] \u2260 gender[dorm_id] (gender constraints are respected)"
    ]
  },
  "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": "Assignment.assign",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating whether student is assigned to dorm",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
