Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:04:33

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: entertainment_awards

```sql
CREATE TABLE festival_detail (
  Festival_ID NUMBER,
  Festival_Name TEXT,
  Chair_Name TEXT,
  Location TEXT,
  Year NUMBER,
  Num_of_Audience NUMBER
);
```

```sql
CREATE TABLE artwork (
  Artwork_ID NUMBER,
  Type TEXT,
  Name TEXT
);
```

```sql
CREATE TABLE nomination (
  Artwork_ID NUMBER,
  Festival_ID 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": "entertainment_awards",
  "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": "entertainment_awards",
  "iteration": 0,
  "business_context": "An entertainment festival wants to maximize the number of successful nominations (wins) for artworks across different festivals while considering the audience size as a factor for prioritization.",
  "optimization_problem_description": "The goal is to maximize the number of successful nominations for artworks at various festivals, taking into account the audience size as a weight for each festival. The decision variables will determine whether an artwork is nominated at a particular festival, subject to constraints on the number of nominations per artwork and the capacity of each festival.",
  "optimization_formulation": {
    "objective": "maximize sum(audience_size[festival_id] * nomination_success[artwork_id, festival_id])",
    "decision_variables": "nomination_success[artwork_id, festival_id] (binary: 1 if artwork wins at festival, 0 otherwise)",
    "constraints": [
      "sum(nomination_success[artwork_id, festival_id] for all festival_id) <= max_nominations_per_artwork for each artwork_id",
      "sum(nomination_success[artwork_id, festival_id] for all artwork_id) <= max_capacity_per_festival for each festival_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "audience_size[festival_id]": {
        "currently_mapped_to": "festival_detail.Num_of_Audience",
        "mapping_adequacy": "good",
        "description": "Represents the audience size at each festival, used as a weight in the objective function"
      }
    },
    "constraint_bounds": {
      "max_nominations_per_artwork": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of nominations allowed per artwork"
      },
      "max_capacity_per_festival": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of artworks that can be nominated at each festival"
      }
    },
    "decision_variables": {
      "nomination_success[artwork_id, festival_id]": {
        "currently_mapped_to": "nomination.Result",
        "mapping_adequacy": "partial",
        "description": "Binary variable indicating if an artwork wins at a festival",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on max_nominations_per_artwork",
    "Data on max_capacity_per_festival"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints and ensure all necessary data is available for optimization"
  }
}
