Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:13:17

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 wants to optimize its investment in book clubs and movies to maximize its cultural impact while staying within budget constraints.",
  "optimization_problem_description": "The company needs to decide how much to invest in each book club and movie to maximize its cultural impact score, which is a weighted sum of the Group Equity Shareholding in each book club and movie. The company has a limited budget for these investments and must ensure that the total investment does not exceed this budget.",
  "optimization_formulation": {
    "objective": "maximize total_cultural_impact = sum(Group_Equity_Shareholding[book_club_id] * x[book_club_id] + Group_Equity_Shareholding[movie_id] * y[movie_id])",
    "decision_variables": "x[book_club_id] and y[movie_id] represent the investment decision in each book club and movie, respectively (continuous)",
    "constraints": [
      "sum(Budget_million[movie_id] * y[movie_id]) + sum(Investment_cost[book_club_id] * x[book_club_id]) <= Total_Budget",
      "x[book_club_id] >= 0 for all book_club_id",
      "y[movie_id] >= 0 for all movie_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Group_Equity_Shareholding[book_club_id]": {
        "currently_mapped_to": "culture_company.Group_Equity_Shareholding",
        "mapping_adequacy": "good",
        "description": "Represents the cultural impact score contribution from each book club"
      },
      "Group_Equity_Shareholding[movie_id]": {
        "currently_mapped_to": "culture_company.Group_Equity_Shareholding",
        "mapping_adequacy": "good",
        "description": "Represents the cultural impact score contribution from each movie"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Represents the total budget available for investment in book clubs and movies"
      }
    },
    "decision_variables": {
      "x[book_club_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Represents the investment decision in each book club",
        "variable_type": "continuous"
      },
      "y[movie_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Represents the investment decision in each movie",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Investment cost for each book club",
    "Total budget available for investment"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine the investment cost for each book club and the total budget available for investment"
  }
}
