Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:39:30

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: culture_company

```sql
CREATE TABLE book_club (
  book_club_id NUMBER,
  Year NUMBER,
  Author_or_Editor TEXT,
  Book_Title TEXT,
  Publisher TEXT,
  Category TEXT,
  Result TEXT
);
```

```sql
CREATE TABLE movie (
  movie_id NUMBER,
  Title TEXT,
  Year NUMBER,
  Director TEXT,
  Budget_million NUMBER,
  Gross_worldwide NUMBER
);
```

```sql
CREATE TABLE culture_company (
  Company_name TEXT,
  Type TEXT,
  Incorporated_in TEXT,
  Group_Equity_Shareholding NUMBER,
  book_club_id TEXT,
  movie_id 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": "culture_company",
  "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": "culture_company",
  "iteration": 0,
  "business_context": "A culture company aims to maximize its annual profit by optimizing the allocation of its resources between book clubs and movie productions, considering budget constraints and expected returns.",
  "optimization_problem_description": "The company wants to maximize its total profit from book clubs and movies by deciding how much to invest in each category, given budget limitations and expected returns.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Profit_book_club \u00d7 x_book_club) + \u2211(Profit_movie \u00d7 x_movie)",
    "decision_variables": "x_book_club (continuous): investment in book clubs, x_movie (continuous): investment in movies",
    "constraints": [
      "x_book_club + x_movie \u2264 Total_Budget",
      "x_book_club \u2265 Minimum_Investment_Book_Club",
      "x_movie \u2265 Minimum_Investment_Movie",
      "x_book_club \u2264 Maximum_Investment_Book_Club",
      "x_movie \u2264 Maximum_Investment_Movie",
      "Profit_book_club \u00d7 x_book_club + Profit_movie \u00d7 x_movie \u2265 Minimum_Profit"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Profit_book_club": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Expected profit per unit investment in book clubs"
      },
      "Profit_movie": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Expected profit per unit investment in movies"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total available budget for investments"
      },
      "Minimum_Investment_Book_Club": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum required investment in book clubs"
      },
      "Minimum_Investment_Movie": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum required investment in movies"
      },
      "Maximum_Investment_Book_Club": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum allowed investment in book clubs"
      },
      "Maximum_Investment_Movie": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum allowed investment in movies"
      },
      "Minimum_Profit": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum required total profit"
      }
    },
    "decision_variables": {
      "x_book_club": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Investment in book clubs",
        "variable_type": "continuous"
      },
      "x_movie": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Investment in movies",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Expected profit per unit investment in book clubs",
    "Expected profit per unit investment in movies",
    "Total available budget for investments",
    "Minimum required investment in book clubs",
    "Minimum required investment in movies",
    "Maximum allowed investment in book clubs",
    "Maximum allowed investment in movies",
    "Minimum required total profit"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "low",
    "next_focus": "Gather data on expected profits, budget constraints, and investment limits to refine the optimization model."
  }
}
