Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:31:07

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": "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": "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.",
  "optimization_formulation": {
    "objective": "minimize \u2211(distance[stuid, dormid] * assign[stuid, dormid])",
    "decision_variables": "assign[stuid, dormid] (binary: 1 if student stuid is assigned to dorm dormid, 0 otherwise)",
    "constraints": [
      "\u2211(assign[stuid, dormid] for all stuid) \u2264 student_capacity[dormid] for all dormid",
      "\u2211(assign[stuid, dormid] for all dormid) = 1 for all stuid",
      "assign[stuid, dormid] = 0 if gender[stuid] \u2260 gender[dormid] for all stuid, dormid"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "distance[stuid, dormid]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Distance from student's home city to dorm"
      }
    },
    "constraint_bounds": {
      "student_capacity[dormid]": {
        "currently_mapped_to": "Dorm.student_capacity",
        "mapping_adequacy": "good",
        "description": "Maximum number of students a dorm can accommodate"
      }
    },
    "decision_variables": {
      "assign[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": [
    "Distance matrix between student home cities and dorms",
    "Gender information for students and dorms"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Obtain distance data and ensure gender information is available for both students and dorms."
  }
}
