Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:46:46

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "A film festival aims to maximize the total audience engagement by selecting a subset of artworks to nominate, considering constraints such as the number of nominations per festival and the diversity of artwork types.",
  "optimization_problem": "Maximize the total audience engagement by selecting a subset of artworks to nominate, subject to constraints on the maximum number of nominations per festival and ensuring a minimum diversity of artwork types.",
  "objective": "maximize \u2211(Engagement_Score[Artwork_ID, Festival_ID] \u00d7 Nomination_Decision[Artwork_ID, Festival_ID])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a table for nomination decisions and updating the data dictionary. Configuration logic remains unchanged as it already meets the requirements."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map the missing decision variable for nomination decisions.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a table for nomination decisions and updating the data dictionary. Configuration logic remains unchanged as it already meets the requirements.

CREATE TABLE engagement_scores (
  Artwork_ID INTEGER,
  Festival_ID INTEGER,
  score FLOAT
);

CREATE TABLE festival_nominations (
  Festival_ID INTEGER,
  max_nominations INTEGER
);

CREATE TABLE artwork_types (
  Type STRING,
  diversity_score FLOAT
);

CREATE TABLE nomination_decisions (
  Artwork_ID INTEGER,
  Festival_ID INTEGER,
  decision BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "engagement_scores": {
      "business_purpose": "Engagement scores for artworks at festivals",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Artwork_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the artwork",
          "optimization_purpose": "Index for engagement score",
          "sample_values": "1, 2, 3"
        },
        "Festival_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the festival",
          "optimization_purpose": "Index for engagement score",
          "sample_values": "1, 2, 3"
        },
        "score": {
          "data_type": "FLOAT",
          "business_meaning": "Engagement score for the artwork at the festival",
          "optimization_purpose": "Objective coefficient in optimization model",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    },
    "festival_nominations": {
      "business_purpose": "Maximum number of nominations allowed per festival",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Festival_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the festival",
          "optimization_purpose": "Index for max nominations",
          "sample_values": "1, 2, 3"
        },
        "max_nominations": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of nominations allowed per festival",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": "5, 6, 7"
        }
      }
    },
    "artwork_types": {
      "business_purpose": "Types of artworks and their diversity scores",
      "optimization_role": "business_data",
      "columns": {
        "Type": {
          "data_type": "STRING",
          "business_meaning": "Type of artwork",
          "optimization_purpose": "Index for type diversity",
          "sample_values": "Film, Short, Documentary"
        },
        "diversity_score": {
          "data_type": "FLOAT",
          "business_meaning": "Diversity score for the artwork type",
          "optimization_purpose": "Used in diversity constraint",
          "sample_values": "0.8, 0.9, 1.0"
        }
      }
    },
    "nomination_decisions": {
      "business_purpose": "Binary decision variable indicating whether an artwork is nominated at a festival",
      "optimization_role": "decision_variables",
      "columns": {
        "Artwork_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the artwork",
          "optimization_purpose": "Index for nomination decision",
          "sample_values": "1, 2, 3"
        },
        "Festival_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the festival",
          "optimization_purpose": "Index for nomination decision",
          "sample_values": "1, 2, 3"
        },
        "decision": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary decision indicating nomination",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    }
  }
}



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

JSON STRUCTURE REQUIRED:

{
  "database_id": "entertainment_awards",
  "iteration": 2,
  "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": "entertainment_awards",
  "iteration": 2,
  "business_context": "A film festival aims to maximize the total audience engagement by selecting a subset of artworks to nominate, considering constraints such as the number of nominations per festival and the diversity of artwork types.",
  "optimization_problem_description": "Maximize the total audience engagement by selecting a subset of artworks to nominate, subject to constraints on the maximum number of nominations per festival and ensuring a minimum diversity of artwork types.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Engagement_Score[Artwork_ID, Festival_ID] \u00d7 Nomination_Decision[Artwork_ID, Festival_ID])",
    "decision_variables": "Nomination_Decision[Artwork_ID, Festival_ID] \u2208 {0, 1}",
    "constraints": [
      "\u2211(Nomination_Decision[Artwork_ID, Festival_ID]) \u2264 max_nominations[Festival_ID] for each Festival_ID",
      "\u2211(diversity_score[Type] \u00d7 Nomination_Decision[Artwork_ID, Festival_ID]) \u2265 minimum_diversity_score"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Engagement_Score[Artwork_ID, Festival_ID]": {
        "currently_mapped_to": "engagement_scores.score",
        "mapping_adequacy": "good",
        "description": "Engagement score for the artwork at the festival"
      }
    },
    "constraint_bounds": {
      "max_nominations[Festival_ID]": {
        "currently_mapped_to": "festival_nominations.max_nominations",
        "mapping_adequacy": "good",
        "description": "Maximum number of nominations allowed per festival"
      },
      "minimum_diversity_score": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum required diversity score for nominated artworks"
      }
    },
    "decision_variables": {
      "Nomination_Decision[Artwork_ID, Festival_ID]": {
        "currently_mapped_to": "nomination_decisions.decision",
        "mapping_adequacy": "good",
        "description": "Binary decision indicating whether an artwork is nominated at a festival",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "minimum_diversity_score"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map the missing constraint bound for minimum diversity score."
  }
}
