Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 23:34:23

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: budget_allocation[mID] for each movie mID, continuous
- Operational parameters align with expected linear objective: maximize sum(promotion_sensitivity[mID] * budget_allocation[mID])
- Business configuration includes: the total promotional budget available for allocation (used for used as an upper bound constraint in the optimization model), the minimum promotional budget that must be allocated to each movie (used for used as a lower bound constraint in the 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": "movie_1",
  "iteration": 1,
  "business_context": "A movie streaming service aims to optimize the allocation of its promotional budget across various movies to maximize the expected improvement in their average ratings, considering budget constraints and minimum promotional requirements for each movie.",
  "optimization_problem_description": "Determine the optimal allocation of a fixed promotional budget to different movies to maximize the expected increase in their average ratings. Each movie has a different sensitivity to promotional spending, and there are minimum promotional requirements for each movie.",
  "optimization_formulation": {
    "objective": "maximize sum(promotion_sensitivity[mID] * budget_allocation[mID])",
    "decision_variables": "budget_allocation[mID] for each movie mID, continuous",
    "constraints": [
      "sum(budget_allocation[mID]) <= total_budget",
      "budget_allocation[mID] >= min_promotion_requirement for each movie mID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "promotion_sensitivity[mID]": {
        "currently_mapped_to": "promotion_sensitivity.sensitivity_value",
        "mapping_adequacy": "good",
        "description": "sensitivity of each movie's rating to promotional spending"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "the total promotional budget available for allocation"
      },
      "min_promotion_requirement": {
        "currently_mapped_to": "business_configuration_logic.min_promotion_requirement",
        "mapping_adequacy": "good",
        "description": "the minimum promotional budget that must be allocated to each movie"
      }
    },
    "decision_variables": {
      "budget_allocation[mID]": {
        "currently_mapped_to": "budget_allocation.amount",
        "mapping_adequacy": "good",
        "description": "amount of budget allocated to each movie",
        "variable_type": "continuous"
      }
    }
  },
  "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 optimization data and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE promotion_sensitivity (
  mID INTEGER,
  sensitivity_value FLOAT
);

CREATE TABLE budget_allocation (
  mID INTEGER,
  amount FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical promotional budget allocations and expected sensitivity of movie ratings to promotional efforts, ensuring a balanced distribution across movies.

-- Realistic data for promotion_sensitivity
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (1, 0.15);
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (2, 0.25);
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (3, 0.1);

-- Realistic data for budget_allocation
INSERT INTO budget_allocation (mID, amount) VALUES (1, 20000);
INSERT INTO budget_allocation (mID, amount) VALUES (2, 30000);
INSERT INTO budget_allocation (mID, amount) VALUES (3, 15000);


```

DATA DICTIONARY:
{
  "tables": {
    "promotion_sensitivity": {
      "business_purpose": "represents the sensitivity of each movie's rating to promotional spending",
      "optimization_role": "objective_coefficients",
      "columns": {
        "mID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each movie",
          "optimization_purpose": "index for sensitivity values",
          "sample_values": "1, 2, 3"
        },
        "sensitivity_value": {
          "data_type": "FLOAT",
          "business_meaning": "sensitivity of the movie's rating to promotional spending",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": "0.1, 0.2, 0.3"
        }
      }
    },
    "budget_allocation": {
      "business_purpose": "represents the allocation of promotional budget to each movie",
      "optimization_role": "decision_variables",
      "columns": {
        "mID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each movie",
          "optimization_purpose": "index for budget allocation",
          "sample_values": "1, 2, 3"
        },
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "amount of budget allocated to the movie",
          "optimization_purpose": "decision variable in the optimization model",
          "sample_values": "10000, 15000, 20000"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "total_budget": {
    "data_type": "FLOAT",
    "business_meaning": "the total promotional budget available for allocation",
    "optimization_role": "used as an upper bound constraint in the optimization model",
    "configuration_type": "scalar_parameter",
    "value": 65000,
    "business_justification": "Reflects a realistic promotional budget for a small to medium-sized streaming service."
  },
  "min_promotion_requirement": {
    "data_type": "FLOAT",
    "business_meaning": "the minimum promotional budget that must be allocated to each movie",
    "optimization_role": "used as a lower bound constraint in the optimization model",
    "configuration_type": "scalar_parameter",
    "value": 10000,
    "business_justification": "Ensures each movie receives a minimum level of promotion to be effective."
  }
}

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: movie_1

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: budget_allocation[mID] for each movie mID, continuous
- Operational parameters align with expected linear objective: maximize sum(promotion_sensitivity[mID] * budget_allocation[mID])
- Business configuration includes: the total promotional budget available for allocation (used for used as an upper bound constraint in the optimization model), the minimum promotional budget that must be allocated to each movie (used for used as a lower bound constraint in the 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(promotion_sensitivity[mID] * budget_allocation[mID])
- 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(budget_allocation[mID]) <= total_budget', 'budget_allocation[mID] >= min_promotion_requirement for each movie mID'] (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 optimization data and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE promotion_sensitivity (
  mID INTEGER,
  sensitivity_value FLOAT
);

CREATE TABLE budget_allocation (
  mID INTEGER,
  amount 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 promotional budget allocations and expected sensitivity of movie ratings to promotional efforts, ensuring a balanced distribution across movies.

-- Realistic data for promotion_sensitivity
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (1, 0.15);
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (2, 0.25);
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (3, 0.1);

-- Realistic data for budget_allocation
INSERT INTO budget_allocation (mID, amount) VALUES (1, 20000);
INSERT INTO budget_allocation (mID, amount) VALUES (2, 30000);
INSERT INTO budget_allocation (mID, amount) VALUES (3, 15000);


```

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

Response:
# Complete Optimization Problem and Solution: movie_1

## 1. Problem Context and Goals

### Context  
A movie streaming service is focused on optimizing how it allocates its promotional budget across various movies. The primary decision involves determining the amount of budget to allocate to each movie, represented by the decision variable budget_allocation[mID], which is continuous for each movie identified by mID. The service aims to enhance the average ratings of its movies by leveraging promotional spending. Each movie has a unique sensitivity to promotional efforts, which influences how effectively the budget impacts its ratings. The operational goal is to maximize the overall expected improvement in movie ratings by strategically distributing the promotional budget.

The business configuration includes a total promotional budget that serves as the upper limit for allocation. Additionally, there is a minimum promotional budget requirement for each movie to ensure that every movie receives a baseline level of promotion. These constraints are critical to maintaining a balanced promotional strategy that aligns with the service's operational and financial objectives.

### Goals  
The optimization goal is to maximize the expected increase in movie ratings by effectively allocating the promotional budget. The metric to optimize is the sum of the product of each movie's sensitivity to promotional spending and the allocated budget for that movie. Success is measured by the extent to which the promotional budget allocation enhances the overall ratings, with the sensitivity values serving as the coefficients that guide the optimization process. The objective is clearly defined in linear terms, focusing on maximizing the impact of promotional spending within the given constraints.

## 2. Constraints    

The optimization problem is subject to the following constraints:

- The total amount of budget allocated across all movies must not exceed the total promotional budget available. This ensures that the promotional spending remains within the financial limits set by the service.
- Each movie must receive at least a minimum promotional budget. This constraint guarantees that every movie benefits from a baseline level of promotion, which is essential for maintaining a consistent promotional strategy.

These constraints are expressed in linear terms, aligning with the business requirements and ensuring that the optimization problem remains within the realm of linear programming.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE promotion_sensitivity (
  mID INTEGER,
  sensitivity_value FLOAT
);

CREATE TABLE budget_allocation (
  mID INTEGER,
  amount FLOAT
);


```

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

- **Promotion Sensitivity Table**: This table captures the sensitivity of each movie's rating to promotional spending. It includes:
  - **mID**: A unique identifier for each movie, serving as an index for sensitivity values.
  - **Sensitivity Value**: Represents how responsive a movie's rating is to promotional efforts, acting as a coefficient in the optimization objective.

- **Budget Allocation Table**: This table details the allocation of the promotional budget to each movie. It includes:
  - **mID**: A unique identifier for each movie, serving as an index for budget allocation.
  - **Amount**: The amount of budget allocated to each movie, functioning as a decision variable in the optimization model.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical promotional budget allocations and expected sensitivity of movie ratings to promotional efforts, ensuring a balanced distribution across movies.

-- Realistic data for promotion_sensitivity
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (1, 0.15);
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (2, 0.25);
INSERT INTO promotion_sensitivity (mID, sensitivity_value) VALUES (3, 0.1);

-- Realistic data for budget_allocation
INSERT INTO budget_allocation (mID, amount) VALUES (1, 20000);
INSERT INTO budget_allocation (mID, amount) VALUES (2, 30000);
INSERT INTO budget_allocation (mID, amount) VALUES (3, 15000);


```
