Iteration 3 - OR_EXPERT_REFINEMENT
Sequence: 7
Timestamp: 2025-07-25 22:46:46

Prompt:
You are an Operations Research (OR) expert in iteration 3 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.


CONVERGENCE PRESSURE (Iteration 3/5):
- Focus on finalizing the linear optimization model
- Set complete=true if formulation is mathematically sound and linear
- Minimize further schema change requests


CURRENT STATE (iteration 2):
{
  "iteration": 3,
  "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": 0,
  "key_changes": [
    "Schema changes include adding a minimum diversity score constraint to the business configuration logic and updating the data dictionary to reflect this addition. No new tables were created or deleted as the existing schema adequately supports the optimization requirements."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map the missing constraint bound for minimum diversity score.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 3 Database Schema
-- Objective: Schema changes include adding a minimum diversity score constraint to the business configuration logic and updating the data dictionary to reflect this addition. No new tables were created or deleted as the existing schema adequately supports the optimization 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"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "minimum_diversity_score": {
    "sample_value": 0.7,
    "data_type": "FLOAT",
    "business_meaning": "Minimum required diversity score for nominated artworks",
    "optimization_role": "Constraint bound in optimization model",
    "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": "entertainment_awards",
  "iteration": 3,
  "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": 3,
  "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 for each Festival_ID"
    ]
  },
  "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": "business_configuration_logic.minimum_diversity_score",
        "mapping_adequacy": "good",
        "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 nomination",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
