Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 21:59:36

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_4

```sql
CREATE TABLE artist (
  Artist_ID NUMBER,
  Artist TEXT,
  Age NUMBER,
  Famous_Title TEXT,
  Famous_Release_date TEXT
);
```

```sql
CREATE TABLE volume (
  Volume_ID NUMBER,
  Volume_Issue TEXT,
  Issue_Date TEXT,
  Weeks_on_Top NUMBER,
  Song TEXT,
  Artist_ID NUMBER
);
```

```sql
CREATE TABLE music_festival (
  ID NUMBER,
  Music_Festival TEXT,
  Date_of_ceremony TEXT,
  Category TEXT,
  Volume NUMBER,
  Result TEXT
);
```



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_4",
  "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_4",
  "iteration": 0,
  "business_context": "A music festival organizer wants to maximize the exposure of artists by selecting the optimal set of artists to perform at a festival, considering their popularity and availability.",
  "optimization_problem_description": "The goal is to maximize the total weeks on top of the charts for the selected artists while ensuring that the total number of artists selected does not exceed the festival's capacity and that each artist is available on the festival date.",
  "optimization_formulation": {
    "objective": "maximize total_weeks_on_top = \u2211(Weeks_on_Top[i] * x[i])",
    "decision_variables": "x[i] = 1 if artist i is selected to perform, 0 otherwise (binary)",
    "constraints": [
      "\u2211(x[i]) \u2264 festival_capacity",
      "x[i] = 0 if artist i is not available on the festival date"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Weeks_on_Top[i]": {
        "currently_mapped_to": "volume.Weeks_on_Top",
        "mapping_adequacy": "good",
        "description": "Represents the popularity of artist i based on weeks on top of the charts"
      }
    },
    "constraint_bounds": {
      "festival_capacity": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of artists that can be selected for the festival"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "artist.Artist_ID",
        "mapping_adequacy": "partial",
        "description": "Binary variable indicating if artist i is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Festival capacity data",
    "Artist availability on the festival date"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Incorporate artist availability and festival capacity into the model"
  }
}
