Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:19:49

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either 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
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: dorm_1

```sql
CREATE TABLE Student (
  StuID NUMBER,
  LName TEXT,
  Fname TEXT,
  Age NUMBER,
  Sex TEXT,
  Major NUMBER,
  Advisor NUMBER,
  city_code TEXT
);
```

```sql
CREATE TABLE Dorm (
  dormid NUMBER,
  dorm_name TEXT,
  student_capacity NUMBER,
  gender TEXT
);
```

```sql
CREATE TABLE Dorm_amenity (
  amenid NUMBER,
  amenity_name TEXT
);
```

```sql
CREATE TABLE Has_amenity (
  dormid NUMBER,
  amenid NUMBER
);
```

```sql
CREATE TABLE Lives_in (
  stuid NUMBER,
  dormid NUMBER,
  room_number NUMBER
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "dorm_1",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 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 needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "dorm_1",
  "iteration": 0,
  "business_context": "Assign students to dorms in a way that maximizes the utilization of dorm capacity while respecting gender constraints.",
  "optimization_problem_description": "Optimize the allocation of students to dorms to maximize the utilization of available dorm capacity, ensuring that students are assigned to dorms that match their gender.",
  "optimization_formulation": {
    "objective": "maximize \u2211(1 \u00d7 x[StuID, DormID])",
    "decision_variables": "x[StuID, DormID] - binary variable indicating if student StuID is assigned to dorm DormID",
    "constraints": [
      "\u2211(x[StuID, DormID]) \u2264 Dorm.student_capacity for each DormID",
      "x[StuID, DormID] = 0 if Student.Sex does not match Dorm.gender",
      "\u2211(x[StuID, DormID]) = 1 for each StuID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "1[StuID, DormID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "coefficient representing the assignment of a student to a dorm"
      }
    },
    "constraint_bounds": {
      "Dorm.student_capacity[DormID]": {
        "currently_mapped_to": "Dorm.student_capacity",
        "mapping_adequacy": "good",
        "description": "maximum number of students that can be assigned to a dorm"
      },
      "Student.Sex[StuID]": {
        "currently_mapped_to": "Student.Sex",
        "mapping_adequacy": "good",
        "description": "gender of the student for matching with dorm gender"
      },
      "Dorm.gender[DormID]": {
        "currently_mapped_to": "Dorm.gender",
        "mapping_adequacy": "good",
        "description": "gender restriction of the dorm"
      }
    },
    "decision_variables": {
      "x[StuID, DormID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if a student is assigned to a dorm",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on which students are eligible for which dorms based on gender",
    "Binary decision variable setup for student-dorm assignments"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine decision variable mapping and ensure all necessary data is available for constraints"
  }
}
