Iteration final - PROBLEM_DESCRIPTION
Sequence: 9
Timestamp: 2025-07-25 22:46:46

Prompt:
You are a business analyst creating structured optimization problem documentation.

DATA SOURCES EXPLANATION:
- FINAL OR ANALYSIS: Final converged optimization problem from alternating process (iteration 3), contains business context and schema mapping evaluation
- DATABASE SCHEMA: Current database structure after iterative adjustments  
- DATA DICTIONARY: Business meanings and optimization roles of tables and columns
- CURRENT STORED VALUES: Realistic business data generated by triple expert (business + data + optimization)
- BUSINESS CONFIGURATION: Scalar parameters and business logic formulas separated from table data

CRITICAL REQUIREMENTS: 
- Ensure problem description naturally leads to LINEAR or MIXED-INTEGER optimization formulation
- Make business context consistent with the intended decision variables and objectives
- Align constraint descriptions with expected mathematical constraints
- Ensure data descriptions map clearly to expected coefficient sources
- Maintain business authenticity while fixing mathematical consistency issues
- Avoid business scenarios that would naturally require nonlinear relationships (variable products, divisions, etc.)

AUTO-EXTRACTED CONTEXT REQUIREMENTS:
- Business decisions match expected decision variables: Nomination_Decision[Artwork_ID, Festival_ID] ∈ {0, 1}
- Operational parameters align with expected linear objective: maximize ∑(Engagement_Score[Artwork_ID, Festival_ID] × Nomination_Decision[Artwork_ID, Festival_ID])
- Business configuration includes: Minimum required diversity score for nominated artworks (used for Constraint bound in optimization model)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate

FINAL OR ANALYSIS:
{
  "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"
  }
}

FINAL DATABASE 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 STORED VALUES:
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic film festival scenarios, ensuring diversity in artwork types and engagement scores that reflect audience preferences. Constraints were respected to ensure the optimization problem remains solvable.

-- Realistic data for engagement_scores
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (1, 1, 0.85);
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (2, 1, 0.75);
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (3, 1, 0.65);

-- Realistic data for festival_nominations
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (1, 5);
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (2, 6);
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (3, 4);

-- Realistic data for artwork_types
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Film', 0.9);
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Short', 0.8);
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Documentary', 0.7);

-- Realistic data for nomination_decisions
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (1, 1, True);
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (2, 1, False);
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (3, 1, True);


```

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"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "minimum_diversity_score": {
    "data_type": "FLOAT",
    "business_meaning": "Minimum required diversity score for nominated artworks",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 0.75,
    "business_justification": "A moderate diversity score ensures a balanced selection of artwork types while maintaining audience engagement."
  }
}

Business Configuration Design: 
Our system separates business logic design from value determination:
- Configuration Logic (business_configuration_logic.json): Templates designed by data engineers with sample_value for scalars and actual formulas for business logic
- Configuration Values (business_configuration.json): Realistic values determined by domain experts for scalar parameters only
- Design Rationale: Ensures business logic consistency while allowing flexible parameter tuning


TASK: Create structured markdown documentation for SECTIONS 1-3 ONLY (Problem Description).

EXACT MARKDOWN STRUCTURE TO FOLLOW:

# Complete Optimization Problem and Solution: entertainment_awards

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: Nomination_Decision[Artwork_ID, Festival_ID] ∈ {0, 1}
- Operational parameters align with expected linear objective: maximize ∑(Engagement_Score[Artwork_ID, Festival_ID] × Nomination_Decision[Artwork_ID, Festival_ID])
- Business configuration includes: Minimum required diversity score for nominated artworks (used for Constraint bound in optimization model)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate
- CRITICAL: Include ALL business configuration information (scalar parameters AND business logic formulas) in natural business language

### Goals  
[Regenerate goals that clearly lead to LINEAR mathematical objective:]
- Optimization goal: maximize
- Metric to optimize: maximize ∑(Engagement_Score[Artwork_ID, Festival_ID] × Nomination_Decision[Artwork_ID, Festival_ID])
- Success measurement aligned with expected coefficient sources
- Use natural language to precisely describe linear optimization goal
- NO mathematical formulas, equations, or symbolic notation

## 2. Constraints    

[Regenerate constraints that directly match expected LINEAR mathematical constraints:]
- Expected constraint: ['∑(Nomination_Decision[Artwork_ID, Festival_ID]) ≤ max_nominations[Festival_ID] for each Festival_ID', '∑(diversity_score[Type] × Nomination_Decision[Artwork_ID, Festival_ID]) ≥ minimum_diversity_score for each Festival_ID'] (Form: Standard constraint form based on business requirements)

[Each constraint should be described in business terms that naturally lead to LINEAR mathematical forms (no variable products or divisions)]

## 3. Available Data  

### Database 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
);


```

### Data Dictionary  
[Create comprehensive business-oriented data dictionary mapping tables and columns to their business purposes and optimization roles - NOT technical database terms. Base this on the data_dictionary provided but rewrite in business language that clearly connects to the expected linear mathematical formulation]

### Current Stored Values  
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic film festival scenarios, ensuring diversity in artwork types and engagement scores that reflect audience preferences. Constraints were respected to ensure the optimization problem remains solvable.

-- Realistic data for engagement_scores
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (1, 1, 0.85);
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (2, 1, 0.75);
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (3, 1, 0.65);

-- Realistic data for festival_nominations
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (1, 5);
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (2, 6);
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (3, 4);

-- Realistic data for artwork_types
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Film', 0.9);
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Short', 0.8);
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Documentary', 0.7);

-- Realistic data for nomination_decisions
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (1, 1, True);
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (2, 1, False);
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (3, 1, True);


```

STOP HERE - Do not include section 4 (Mathematical Optimization Formulation).

Response:
# Complete Optimization Problem and Solution: entertainment_awards

## 1. Problem Context and Goals

### Context  
The film festival aims to maximize audience engagement by selecting a subset of artworks to nominate for each festival. The decision to nominate an artwork is binary, meaning each artwork can either be nominated or not for a specific festival. The engagement score for each artwork at a festival reflects its potential to attract and engage the audience. The festival must also adhere to two key operational constraints:  
1. **Maximum Nominations per Festival**: Each festival has a predefined limit on the number of artworks that can be nominated.  
2. **Minimum Diversity Requirement**: The nominated artworks must collectively meet a minimum diversity score, ensuring a balanced representation of different artwork types.  

The business configuration includes a scalar parameter, the minimum required diversity score, which is set to 0.75. This ensures that the selection of artworks maintains a moderate level of diversity while maximizing audience engagement.  

### Goals  
The primary goal of this optimization problem is to maximize the total audience engagement across all festivals. This is achieved by selecting the optimal set of artworks to nominate, considering their engagement scores and adhering to the operational constraints. Success is measured by the sum of engagement scores for the nominated artworks, ensuring that the festival’s audience engagement is as high as possible while respecting the nomination limits and diversity requirements.  

## 2. Constraints  

The optimization problem is subject to the following constraints:  
1. **Maximum Nominations per Festival**: For each festival, the total number of nominated artworks cannot exceed the predefined maximum number of nominations allowed for that festival.  
2. **Minimum Diversity Requirement**: For each festival, the combined diversity score of the nominated artworks must meet or exceed the minimum required diversity score of 0.75. This ensures a balanced selection of artwork types.  

These constraints are designed to ensure that the festival’s operational limits and diversity goals are met while maximizing audience engagement.  

## 3. Available Data  

### Database 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
);
```

### Data Dictionary  
- **engagement_scores**: Contains the engagement scores for artworks at specific festivals.  
  - *Artwork_ID*: Unique identifier for the artwork.  
  - *Festival_ID*: Unique identifier for the festival.  
  - *score*: Engagement score for the artwork at the festival, used as the coefficient in the optimization objective.  

- **festival_nominations**: Defines the maximum number of nominations allowed per festival.  
  - *Festival_ID*: Unique identifier for the festival.  
  - *max_nominations*: Maximum number of nominations allowed for the festival, used as a constraint bound.  

- **artwork_types**: Lists the types of artworks and their associated diversity scores.  
  - *Type*: Type of artwork (e.g., Film, Short, Documentary).  
  - *diversity_score*: Diversity score for the artwork type, used in the diversity constraint.  

- **nomination_decisions**: Represents the binary decision variable indicating whether an artwork is nominated at a festival.  
  - *Artwork_ID*: Unique identifier for the artwork.  
  - *Festival_ID*: Unique identifier for the festival.  
  - *decision*: Binary decision (True/False) indicating whether the artwork is nominated.  

### Current Stored Values  
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic film festival scenarios, ensuring diversity in artwork types and engagement scores that reflect audience preferences. Constraints were respected to ensure the optimization problem remains solvable.

-- Realistic data for engagement_scores
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (1, 1, 0.85);
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (2, 1, 0.75);
INSERT INTO engagement_scores (Artwork_ID, Festival_ID, score) VALUES (3, 1, 0.65);

-- Realistic data for festival_nominations
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (1, 5);
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (2, 6);
INSERT INTO festival_nominations (Festival_ID, max_nominations) VALUES (3, 4);

-- Realistic data for artwork_types
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Film', 0.9);
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Short', 0.8);
INSERT INTO artwork_types (Type, diversity_score) VALUES ('Documentary', 0.7);

-- Realistic data for nomination_decisions
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (1, 1, True);
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (2, 1, False);
INSERT INTO nomination_decisions (Artwork_ID, Festival_ID, decision) VALUES (3, 1, True);
```
