Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:28:42

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: music_1

```sql
CREATE TABLE genre (
  g_name TEXT,
  rating TEXT,
  most_popular_in TEXT
);
```

```sql
CREATE TABLE artist (
  artist_name TEXT,
  country TEXT,
  gender TEXT,
  preferred_genre TEXT
);
```

```sql
CREATE TABLE files (
  f_id NUMBER,
  artist_name TEXT,
  file_size TEXT,
  duration TEXT,
  formats TEXT
);
```

```sql
CREATE TABLE song (
  song_name TEXT,
  artist_name TEXT,
  country TEXT,
  f_id NUMBER,
  genre_is TEXT,
  rating NUMBER,
  languages TEXT,
  releasedate TIME,
  resolution 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": "music_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": "music_1",
  "iteration": 0,
  "business_context": "A music streaming platform aims to optimize its storage and bandwidth usage by selecting a subset of songs to store locally on servers, minimizing the total file size while ensuring a diverse and high-quality music library.",
  "optimization_problem_description": "The platform wants to minimize the total file size of songs stored locally, subject to constraints on the minimum number of songs per genre, the minimum average rating of songs, and the maximum number of songs per artist.",
  "optimization_formulation": {
    "objective": "minimize \u2211(file_size_i \u00d7 x_i), where x_i is a binary decision variable indicating whether song i is stored locally.",
    "decision_variables": "x_i: binary variable indicating whether song i is stored locally.",
    "constraints": [
      "\u2211(x_i) \u2265 min_songs: Ensure a minimum number of songs are stored locally.",
      "\u2211(rating_i \u00d7 x_i) / \u2211(x_i) \u2265 min_avg_rating: Ensure the average rating of stored songs meets a minimum threshold.",
      "\u2211(x_i) \u2264 max_songs_per_artist for each artist: Limit the number of songs stored per artist.",
      "\u2211(x_i) \u2265 min_songs_per_genre for each genre: Ensure a minimum number of songs per genre are stored."
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "file_size_i": {
        "currently_mapped_to": "files.file_size",
        "mapping_adequacy": "good",
        "description": "File size of song i."
      }
    },
    "constraint_bounds": {
      "min_songs": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of songs to store locally."
      },
      "min_avg_rating": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum average rating of stored songs."
      },
      "max_songs_per_artist": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of songs per artist to store locally."
      },
      "min_songs_per_genre": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of songs per genre to store locally."
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether song i is stored locally.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Minimum number of songs to store locally (min_songs).",
    "Minimum average rating of stored songs (min_avg_rating).",
    "Maximum number of songs per artist to store locally (max_songs_per_artist).",
    "Minimum number of songs per genre to store locally (min_songs_per_genre)."
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints and ensure all necessary parameters are available for the optimization model."
  }
}
