Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 22:04:33

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 1), 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.Result[artwork_id, festival_id] as binary variables indicating nomination success
- Operational parameters align with expected linear objective: maximize sum(festival_detail.Num_of_Audience * nomination.Result)
- Business configuration includes: Maximum number of nominations allowed per artwork (used for Used as a constraint bound in optimization model), Maximum number of artworks that can be nominated at each festival (used for Used as a 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": 1,
  "business_context": "An entertainment festival aims to maximize the number of successful nominations for artworks across different festivals, considering audience size as a factor for prioritization. The optimization model will ensure that each artwork and festival adheres to their respective nomination limits.",
  "optimization_problem_description": "The objective is to maximize the weighted sum of successful nominations for artworks at various festivals, where the weight is determined by the audience size of each festival. The decision variables indicate whether an artwork is nominated at a particular festival, subject to constraints on the maximum number of nominations per artwork and the maximum capacity of each festival.",
  "optimization_formulation": {
    "objective": "maximize sum(festival_detail.Num_of_Audience * nomination.Result)",
    "decision_variables": "nomination.Result[artwork_id, festival_id] as binary variables indicating nomination success",
    "constraints": [
      "sum(nomination.Result[artwork_id, *]) <= artwork_constraints.max_nominations for each artwork_id",
      "sum(nomination.Result[*, festival_id]) <= festival_constraints.max_capacity 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": "Number of audience members at the festival, used as a weight in the objective function"
      }
    },
    "constraint_bounds": {
      "max_nominations[artwork_id]": {
        "currently_mapped_to": "artwork_constraints.max_nominations",
        "mapping_adequacy": "good",
        "description": "Maximum nominations allowed per artwork"
      },
      "max_capacity[festival_id]": {
        "currently_mapped_to": "festival_constraints.max_capacity",
        "mapping_adequacy": "good",
        "description": "Maximum capacity of nominations per festival"
      }
    },
    "decision_variables": {
      "nomination_success[artwork_id, festival_id]": {
        "currently_mapped_to": "nomination.Result",
        "mapping_adequacy": "good",
        "description": "Indicates if an artwork wins at a festival",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE festival_detail (
  Num_of_Audience INTEGER
);

CREATE TABLE nomination (
  Result BOOLEAN
);

CREATE TABLE artwork_constraints (
  max_nominations INTEGER
);

CREATE TABLE festival_constraints (
  max_capacity INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical festival sizes and artwork nomination limits to ensure a balanced and realistic scenario for optimization.

-- Realistic data for festival_detail
INSERT INTO festival_detail (Num_of_Audience) VALUES (1200);
INSERT INTO festival_detail (Num_of_Audience) VALUES (4500);
INSERT INTO festival_detail (Num_of_Audience) VALUES (9000);

-- Realistic data for nomination
INSERT INTO nomination (Result) VALUES (0);
INSERT INTO nomination (Result) VALUES (1);
INSERT INTO nomination (Result) VALUES (0);
INSERT INTO nomination (Result) VALUES (1);
INSERT INTO nomination (Result) VALUES (0);

-- Realistic data for artwork_constraints
INSERT INTO artwork_constraints (max_nominations) VALUES (3);
INSERT INTO artwork_constraints (max_nominations) VALUES (5);
INSERT INTO artwork_constraints (max_nominations) VALUES (7);

-- Realistic data for festival_constraints
INSERT INTO festival_constraints (max_capacity) VALUES (50);
INSERT INTO festival_constraints (max_capacity) VALUES (100);
INSERT INTO festival_constraints (max_capacity) VALUES (150);


```

DATA DICTIONARY:
{
  "tables": {
    "festival_detail": {
      "business_purpose": "Stores details about each festival",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Num_of_Audience": {
          "data_type": "INTEGER",
          "business_meaning": "Number of audience members at the festival",
          "optimization_purpose": "Used as a weight in the objective function",
          "sample_values": "1000, 5000, 10000"
        }
      }
    },
    "nomination": {
      "business_purpose": "Stores nomination results for artworks at festivals",
      "optimization_role": "decision_variables",
      "columns": {
        "Result": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if an artwork wins at a festival",
          "optimization_purpose": "Represents binary decision variable",
          "sample_values": "0, 1"
        }
      }
    },
    "artwork_constraints": {
      "business_purpose": "Stores constraints related to artworks",
      "optimization_role": "constraint_bounds",
      "columns": {
        "max_nominations": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum nominations allowed per artwork",
          "optimization_purpose": "Constraint bound for nominations",
          "sample_values": "3, 5, 7"
        }
      }
    },
    "festival_constraints": {
      "business_purpose": "Stores constraints related to festivals",
      "optimization_role": "constraint_bounds",
      "columns": {
        "max_capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum capacity of nominations per festival",
          "optimization_purpose": "Constraint bound for festival capacity",
          "sample_values": "50, 100, 150"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "max_nominations_per_artwork": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of nominations allowed per artwork",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 5,
    "business_justification": "This value reflects a typical limit for artworks, balancing exposure and exclusivity."
  },
  "max_capacity_per_festival": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of artworks that can be nominated at each festival",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 100,
    "business_justification": "This value represents a common capacity for medium-sized festivals, ensuring manageability."
  }
}

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.Result[artwork_id, festival_id] as binary variables indicating nomination success
- Operational parameters align with expected linear objective: maximize sum(festival_detail.Num_of_Audience * nomination.Result)
- Business configuration includes: Maximum number of nominations allowed per artwork (used for Used as a constraint bound in optimization model), Maximum number of artworks that can be nominated at each festival (used for Used as a 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 sum(festival_detail.Num_of_Audience * nomination.Result)
- 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: ['sum(nomination.Result[artwork_id, *]) <= artwork_constraints.max_nominations for each artwork_id', 'sum(nomination.Result[*, festival_id]) <= festival_constraints.max_capacity 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 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE festival_detail (
  Num_of_Audience INTEGER
);

CREATE TABLE nomination (
  Result BOOLEAN
);

CREATE TABLE artwork_constraints (
  max_nominations INTEGER
);

CREATE TABLE festival_constraints (
  max_capacity INTEGER
);


```

### 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 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical festival sizes and artwork nomination limits to ensure a balanced and realistic scenario for optimization.

-- Realistic data for festival_detail
INSERT INTO festival_detail (Num_of_Audience) VALUES (1200);
INSERT INTO festival_detail (Num_of_Audience) VALUES (4500);
INSERT INTO festival_detail (Num_of_Audience) VALUES (9000);

-- Realistic data for nomination
INSERT INTO nomination (Result) VALUES (0);
INSERT INTO nomination (Result) VALUES (1);
INSERT INTO nomination (Result) VALUES (0);
INSERT INTO nomination (Result) VALUES (1);
INSERT INTO nomination (Result) VALUES (0);

-- Realistic data for artwork_constraints
INSERT INTO artwork_constraints (max_nominations) VALUES (3);
INSERT INTO artwork_constraints (max_nominations) VALUES (5);
INSERT INTO artwork_constraints (max_nominations) VALUES (7);

-- Realistic data for festival_constraints
INSERT INTO festival_constraints (max_capacity) VALUES (50);
INSERT INTO festival_constraints (max_capacity) VALUES (100);
INSERT INTO festival_constraints (max_capacity) VALUES (150);


```

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 entertainment festival is focused on maximizing the success of artwork nominations across various festivals. Each nomination is a binary decision, indicating whether an artwork is successfully nominated at a specific festival. The primary objective is to prioritize nominations based on the audience size of each festival, thereby maximizing the overall impact and visibility of the artworks. The operational parameters include constraints on the maximum number of nominations allowed per artwork and the maximum number of artworks that can be nominated at each festival. These constraints ensure a balanced distribution of nominations and manageability of the festival events. The business configuration includes specific parameters such as the maximum nominations per artwork, set at a typical limit to balance exposure and exclusivity, and the maximum capacity per festival, reflecting common limits for medium-sized festivals to ensure manageability.

### Goals  
The optimization goal is to maximize the total impact of successful nominations by considering the audience size at each festival. The metric to optimize is the sum of the audience sizes for all successful nominations, which directly correlates to the visibility and reach of the artworks. This goal is achieved by strategically selecting nominations that maximize audience exposure, ensuring that the festival's resources are utilized effectively to promote the most impactful artworks.

## 2. Constraints    

The optimization model is subject to two primary constraints. First, each artwork can only be nominated a limited number of times, as specified by the maximum nominations allowed per artwork. This constraint ensures that no single artwork dominates the nomination process, allowing for a diverse range of artworks to be showcased. Second, each festival has a maximum capacity for nominations, which limits the number of artworks that can be nominated at any given festival. This constraint ensures that the festival remains manageable and that the audience can fully engage with each nominated artwork. These constraints are linear in nature, aligning with the operational parameters and ensuring a straightforward optimization process.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE festival_detail (
  Num_of_Audience INTEGER
);

CREATE TABLE nomination (
  Result BOOLEAN
);

CREATE TABLE artwork_constraints (
  max_nominations INTEGER
);

CREATE TABLE festival_constraints (
  max_capacity INTEGER
);
```

### Data Dictionary  
The data dictionary provides a comprehensive overview of the tables and columns used in the optimization model, highlighting their business purposes and roles in the optimization process:

- **Festival Detail**: This table stores information about each festival, specifically the number of audience members, which serves as a weight in the optimization objective to prioritize nominations based on audience size.

- **Nomination**: This table records the results of artwork nominations at festivals. The result is a binary indicator of whether an artwork is successfully nominated, serving as the decision variable in the optimization model.

- **Artwork Constraints**: This table defines the constraints related to artworks, specifically the maximum number of nominations allowed per artwork. This constraint ensures a balanced representation of artworks across festivals.

- **Festival Constraints**: This table outlines the constraints related to festivals, specifically the maximum capacity of nominations per festival. This constraint ensures that each festival remains manageable and that the audience can engage with the nominated artworks.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical festival sizes and artwork nomination limits to ensure a balanced and realistic scenario for optimization.

-- Realistic data for festival_detail
INSERT INTO festival_detail (Num_of_Audience) VALUES (1200);
INSERT INTO festival_detail (Num_of_Audience) VALUES (4500);
INSERT INTO festival_detail (Num_of_Audience) VALUES (9000);

-- Realistic data for nomination
INSERT INTO nomination (Result) VALUES (0);
INSERT INTO nomination (Result) VALUES (1);
INSERT INTO nomination (Result) VALUES (0);
INSERT INTO nomination (Result) VALUES (1);
INSERT INTO nomination (Result) VALUES (0);

-- Realistic data for artwork_constraints
INSERT INTO artwork_constraints (max_nominations) VALUES (3);
INSERT INTO artwork_constraints (max_nominations) VALUES (5);
INSERT INTO artwork_constraints (max_nominations) VALUES (7);

-- Realistic data for festival_constraints
INSERT INTO festival_constraints (max_capacity) VALUES (50);
INSERT INTO festival_constraints (max_capacity) VALUES (100);
INSERT INTO festival_constraints (max_capacity) VALUES (150);
```
