Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:13:17

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "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": "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.",
  "objective": "maximize total_cultural_impact = sum(Group_Equity_Shareholding[book_club_id] * x[book_club_id] + Group_Equity_Shareholding[movie_id] * y[movie_id])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to include missing data, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine the investment cost for each book club and the total budget available for investment",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to include missing data, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Group_Equity_Shareholding (
  book_club_id INTEGER,
  movie_id INTEGER,
  equity_shareholding FLOAT
);

CREATE TABLE Decision_Variables (
  x FLOAT,
  y FLOAT
);

CREATE TABLE Constraint_Bounds (
  budget_constraint FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Group_Equity_Shareholding": {
      "business_purpose": "Stores cultural impact scores for book clubs and movies",
      "optimization_role": "objective_coefficients",
      "columns": {
        "book_club_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each book club",
          "optimization_purpose": "Used to map equity shareholding to book clubs",
          "sample_values": "1, 2, 3"
        },
        "movie_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each movie",
          "optimization_purpose": "Used to map equity shareholding to movies",
          "sample_values": "1, 2, 3"
        },
        "equity_shareholding": {
          "data_type": "FLOAT",
          "business_meaning": "Cultural impact score contribution",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    },
    "Decision_Variables": {
      "business_purpose": "Stores investment decisions for optimization",
      "optimization_role": "decision_variables",
      "columns": {
        "x": {
          "data_type": "FLOAT",
          "business_meaning": "Investment decision in book clubs",
          "optimization_purpose": "Decision variable for book clubs",
          "sample_values": "10000, 20000, 30000"
        },
        "y": {
          "data_type": "FLOAT",
          "business_meaning": "Investment decision in movies",
          "optimization_purpose": "Decision variable for movies",
          "sample_values": "15000, 25000, 35000"
        }
      }
    },
    "Constraint_Bounds": {
      "business_purpose": "Stores budget constraints for optimization",
      "optimization_role": "constraint_bounds",
      "columns": {
        "budget_constraint": {
          "data_type": "FLOAT",
          "business_meaning": "Total budget constraint for investments",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": "1000000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Budget": {
    "sample_value": "1000000",
    "data_type": "FLOAT",
    "business_meaning": "Represents the total budget available for investment",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "Investment_Cost_Per_Book_Club": {
    "sample_value": "50000",
    "data_type": "FLOAT",
    "business_meaning": "Represents the investment cost for each book club",
    "optimization_role": "Used in constraint calculations",
    "configuration_type": "scalar_parameter"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "culture_company",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "culture_company",
  "iteration": 1,
  "business_context": "A culture company aims to optimize its investment in book clubs and movies to maximize its cultural impact while adhering to budget constraints.",
  "optimization_problem_description": "The company needs to decide on the investment amounts for 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 total investment must not exceed the available 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], y[movie_id] - continuous variables representing investment in book clubs and movies respectively",
    "constraints": "sum(Investment_Cost_Per_Book_Club * x[book_club_id] + y[movie_id]) <= Total_Budget"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Group_Equity_Shareholding[book_club_id]": {
        "currently_mapped_to": "Group_Equity_Shareholding.equity_shareholding",
        "mapping_adequacy": "good",
        "description": "Cultural impact score contribution for book clubs"
      },
      "Group_Equity_Shareholding[movie_id]": {
        "currently_mapped_to": "Group_Equity_Shareholding.equity_shareholding",
        "mapping_adequacy": "good",
        "description": "Cultural impact score contribution for movies"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for investment"
      }
    },
    "decision_variables": {
      "x[book_club_id]": {
        "currently_mapped_to": "Decision_Variables.x",
        "mapping_adequacy": "good",
        "description": "Investment decision in book clubs",
        "variable_type": "continuous"
      },
      "y[movie_id]": {
        "currently_mapped_to": "Decision_Variables.y",
        "mapping_adequacy": "good",
        "description": "Investment decision in movies",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
