Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 22:48:45

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: x_i, a binary variable for each photo i indicating selection (0 or 1)
- Operational parameters align with expected linear objective: maximize sum(d_i * x_i) where d_i is the diversity score of photo i and x_i is a binary variable indicating if photo i is selected
- Business configuration includes: Maximum number of photos that can be selected for the book (used for Constraint on the total number of selected photos), Maximum number of photos that can be selected from each mountain (used for Constraint on the number of selected photos per mountain)
- 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": "mountain_photos",
  "iteration": 1,
  "business_context": "A photography company is optimizing the selection of photos for a new mountain photography book. The goal is to maximize the visual diversity of the book by selecting photos with different colors and mountains, while considering constraints on the number of photos that can be included from each mountain and the total number of photos.",
  "optimization_problem_description": "The company aims to maximize the diversity of selected photos by choosing a set of photos that includes a variety of colors and mountains. The objective is to maximize the sum of selected photos' diversity scores, subject to constraints on the maximum number of photos per mountain and the total number of photos.",
  "optimization_formulation": {
    "objective": "maximize sum(d_i * x_i) where d_i is the diversity score of photo i and x_i is a binary variable indicating if photo i is selected",
    "decision_variables": "x_i, a binary variable for each photo i indicating selection (0 or 1)",
    "constraints": [
      "sum(x_i) <= Total_Photos_Limit",
      "sum(x_i for photos from mountain j) <= Max_Photos_Per_Mountain for each mountain j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "d_i": {
        "currently_mapped_to": "photo_diversity_scores.diversity_score",
        "mapping_adequacy": "good",
        "description": "Diversity score of photo i used in the objective function"
      }
    },
    "constraint_bounds": {
      "Total_Photos_Limit": {
        "currently_mapped_to": "business_configuration_logic.Total_Photos_Limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of photos that can be selected for the book"
      },
      "Max_Photos_Per_Mountain": {
        "currently_mapped_to": "business_configuration_logic.Max_Photos_Per_Mountain",
        "mapping_adequacy": "good",
        "description": "Maximum number of photos that can be selected from each mountain"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "photos.id",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if photo i is selected",
        "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 a new table for diversity scores and updating business configuration logic for constraints. These changes address the OR expert's mapping gaps and missing requirements.

CREATE TABLE photos (
  id INTEGER,
  diversity_score FLOAT
);

CREATE TABLE photo_diversity_scores (
  photo_id INTEGER,
  diversity_score FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical constraints and diversity requirements for a photography book, ensuring a balance between diversity and selection limits.

-- Realistic data for photos
INSERT INTO photos (id, diversity_score) VALUES (1, 0.85);
INSERT INTO photos (id, diversity_score) VALUES (2, 0.75);
INSERT INTO photos (id, diversity_score) VALUES (3, 0.9);
INSERT INTO photos (id, diversity_score) VALUES (4, 0.65);
INSERT INTO photos (id, diversity_score) VALUES (5, 0.8);

-- Realistic data for photo_diversity_scores
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (1, 0.85);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (2, 0.75);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (3, 0.9);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (4, 0.65);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (5, 0.8);


```

DATA DICTIONARY:
{
  "tables": {
    "photos": {
      "business_purpose": "Stores information about each photo",
      "optimization_role": "decision_variables",
      "columns": {
        "id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each photo",
          "optimization_purpose": "Used as a decision variable in optimization",
          "sample_values": "1, 2, 3"
        },
        "diversity_score": {
          "data_type": "FLOAT",
          "business_meaning": "Diversity score of the photo based on color and mountain",
          "optimization_purpose": "Objective coefficient in optimization",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    },
    "photo_diversity_scores": {
      "business_purpose": "Stores diversity scores for each photo",
      "optimization_role": "objective_coefficients",
      "columns": {
        "photo_id": {
          "data_type": "INTEGER",
          "business_meaning": "Reference to the photo ID",
          "optimization_purpose": "Links diversity score to photo",
          "sample_values": "1, 2, 3"
        },
        "diversity_score": {
          "data_type": "FLOAT",
          "business_meaning": "Diversity score of the photo",
          "optimization_purpose": "Used in the objective function",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "Total_Photos_Limit": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of photos that can be selected for the book",
    "optimization_role": "Constraint on the total number of selected photos",
    "configuration_type": "scalar_parameter",
    "value": 15,
    "business_justification": "Allows for a diverse selection while keeping the book manageable in size."
  },
  "Max_Photos_Per_Mountain": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of photos that can be selected from each mountain",
    "optimization_role": "Constraint on the number of selected photos per mountain",
    "configuration_type": "scalar_parameter",
    "value": 5,
    "business_justification": "Ensures no single mountain dominates the book, promoting diversity."
  }
}

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: mountain_photos

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: x_i, a binary variable for each photo i indicating selection (0 or 1)
- Operational parameters align with expected linear objective: maximize sum(d_i * x_i) where d_i is the diversity score of photo i and x_i is a binary variable indicating if photo i is selected
- Business configuration includes: Maximum number of photos that can be selected for the book (used for Constraint on the total number of selected photos), Maximum number of photos that can be selected from each mountain (used for Constraint on the number of selected photos per mountain)
- 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(d_i * x_i) where d_i is the diversity score of photo i and x_i is a binary variable indicating if photo i is selected
- 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(x_i) <= Total_Photos_Limit', 'sum(x_i for photos from mountain j) <= Max_Photos_Per_Mountain for each mountain j'] (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 a new table for diversity scores and updating business configuration logic for constraints. These changes address the OR expert's mapping gaps and missing requirements.

CREATE TABLE photos (
  id INTEGER,
  diversity_score FLOAT
);

CREATE TABLE photo_diversity_scores (
  photo_id INTEGER,
  diversity_score FLOAT
);


```

### 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 constraints and diversity requirements for a photography book, ensuring a balance between diversity and selection limits.

-- Realistic data for photos
INSERT INTO photos (id, diversity_score) VALUES (1, 0.85);
INSERT INTO photos (id, diversity_score) VALUES (2, 0.75);
INSERT INTO photos (id, diversity_score) VALUES (3, 0.9);
INSERT INTO photos (id, diversity_score) VALUES (4, 0.65);
INSERT INTO photos (id, diversity_score) VALUES (5, 0.8);

-- Realistic data for photo_diversity_scores
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (1, 0.85);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (2, 0.75);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (3, 0.9);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (4, 0.65);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (5, 0.8);


```

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

Response:
# Complete Optimization Problem and Solution: mountain_photos

## 1. Problem Context and Goals

### Context  
A photography company is in the process of curating a selection of photos for a new mountain photography book. The primary objective is to enhance the visual diversity of the book by selecting photos that showcase a variety of colors and different mountains. The decision-making process involves selecting photos, where each photo is represented by a binary decision variable. This variable indicates whether a photo is included in the final selection or not. The operational goal is to maximize the total diversity score of the selected photos. Each photo has an associated diversity score, which reflects its contribution to the overall diversity of the book.

The business configuration includes specific constraints: the total number of photos that can be included in the book is limited, and there is also a restriction on the number of photos that can be selected from each individual mountain. These constraints ensure that the book remains manageable in size and that no single mountain dominates the content, thereby promoting a balanced representation of different mountains.

### Goals  
The optimization goal is to maximize the diversity of the selected photos. This is achieved by focusing on the sum of the diversity scores of the photos that are chosen for inclusion in the book. The success of this optimization is measured by the total diversity score, which is derived from the diversity scores of the individual photos selected. The aim is to select photos in such a way that the overall diversity score is maximized, while adhering to the constraints on the total number of photos and the number of photos per mountain.

## 2. Constraints    

The selection process is subject to two primary constraints. First, there is a limit on the total number of photos that can be included in the book. This ensures that the book remains concise and focused. Second, there is a constraint on the number of photos that can be selected from each mountain. This constraint is in place to ensure that the book features a diverse range of mountains, preventing any single mountain from being overrepresented. These constraints are designed to naturally align with linear mathematical formulations, ensuring a straightforward optimization process.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for diversity scores and updating business configuration logic for constraints. These changes address the OR expert's mapping gaps and missing requirements.

CREATE TABLE photos (
  id INTEGER,
  diversity_score FLOAT
);

CREATE TABLE photo_diversity_scores (
  photo_id INTEGER,
  diversity_score FLOAT
);
```

### Data Dictionary  
The data is organized into tables that serve specific business purposes and optimization roles:

- **Photos Table**: This table contains information about each photo. It includes:
  - **ID**: A unique identifier for each photo, used as a decision variable in the optimization process.
  - **Diversity Score**: A numerical value representing the diversity of the photo, based on its color and the mountain it depicts. This score is used as an objective coefficient in the optimization.

- **Photo Diversity Scores Table**: This table stores the diversity scores for each photo, linking them to their respective photo IDs. The diversity score is crucial for determining the contribution of each photo to the overall diversity of the book.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical constraints and diversity requirements for a photography book, ensuring a balance between diversity and selection limits.

-- Realistic data for photos
INSERT INTO photos (id, diversity_score) VALUES (1, 0.85);
INSERT INTO photos (id, diversity_score) VALUES (2, 0.75);
INSERT INTO photos (id, diversity_score) VALUES (3, 0.9);
INSERT INTO photos (id, diversity_score) VALUES (4, 0.65);
INSERT INTO photos (id, diversity_score) VALUES (5, 0.8);

-- Realistic data for photo_diversity_scores
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (1, 0.85);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (2, 0.75);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (3, 0.9);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (4, 0.65);
INSERT INTO photo_diversity_scores (photo_id, diversity_score) VALUES (5, 0.8);
```
