Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-25 22:24:49

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: investment_i: continuous variable representing the amount allocated to entrepreneur i
- Operational parameters align with expected linear objective: maximize ∑(return_rate_i × investment_i)
- Business configuration includes: Total available budget for investment (used for Constraint bound for total investment), Maximum amount that can be allocated to each entrepreneur (used for Constraint bound for individual investment)
- 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": "entrepreneur",
  "iteration": 1,
  "business_context": "An investor aims to allocate a fixed budget across multiple entrepreneurs to maximize the total expected return on investment, while ensuring that no single entrepreneur receives more than a specified maximum amount and that the total investment does not exceed the budget.",
  "optimization_problem_description": "Maximize the total expected return on investment by deciding how much money to allocate to each entrepreneur, subject to constraints on the total budget and maximum investment per entrepreneur.",
  "optimization_formulation": {
    "objective": "maximize \u2211(return_rate_i \u00d7 investment_i)",
    "decision_variables": "investment_i: continuous variable representing the amount allocated to entrepreneur i",
    "constraints": [
      "\u2211(investment_i) \u2264 Total_Budget",
      "investment_i \u2264 Max_Investment_i for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "return_rate_i": {
        "currently_mapped_to": "entrepreneurs.return_rate",
        "mapping_adequacy": "good",
        "description": "Expected return rate for each entrepreneur"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total available budget for investment"
      },
      "Max_Investment_i": {
        "currently_mapped_to": "business_configuration_logic.Max_Investment_i",
        "mapping_adequacy": "good",
        "description": "Maximum amount that can be allocated to each entrepreneur"
      }
    },
    "decision_variables": {
      "investment_i": {
        "currently_mapped_to": "entrepreneurs.investment",
        "mapping_adequacy": "good",
        "description": "Amount of money allocated to each entrepreneur",
        "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 and configuration logic updates implemented to address missing optimization requirements and mapping gaps identified by the OR expert.

CREATE TABLE entrepreneurs (
  entrepreneur_id INTEGER,
  return_rate FLOAT,
  investment FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic investment scenarios, considering typical return rates and budget constraints for small to medium-sized ventures.

-- Realistic data for entrepreneurs
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (1, 0.12, 150000);
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (2, 0.18, 200000);
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (3, 0.1, 100000);


```

DATA DICTIONARY:
{
  "tables": {
    "entrepreneurs": {
      "business_purpose": "List of entrepreneurs with their expected return rates and investment allocations",
      "optimization_role": "business_data",
      "columns": {
        "entrepreneur_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each entrepreneur",
          "optimization_purpose": "Index for decision variables and constraints",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "return_rate": {
          "data_type": "FLOAT",
          "business_meaning": "Expected return rate for the entrepreneur",
          "optimization_purpose": "Objective coefficient for optimization",
          "sample_values": [
            0.1,
            0.15,
            0.2
          ]
        },
        "investment": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of money allocated to the entrepreneur",
          "optimization_purpose": "Decision variable for optimization",
          "sample_values": [
            100000,
            150000,
            200000
          ]
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "Total_Budget": {
    "data_type": "FLOAT",
    "business_meaning": "Total available budget for investment",
    "optimization_role": "Constraint bound for total investment",
    "configuration_type": "scalar_parameter",
    "value": 1000000,
    "business_justification": "A realistic total budget for a diversified investment portfolio across multiple entrepreneurs."
  },
  "Max_Investment_i": {
    "data_type": "FLOAT",
    "business_meaning": "Maximum amount that can be allocated to each entrepreneur",
    "optimization_role": "Constraint bound for individual investment",
    "configuration_type": "scalar_parameter",
    "value": 200000,
    "business_justification": "A reasonable maximum investment per entrepreneur to ensure risk management and diversification."
  }
}

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: entrepreneur

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: investment_i: continuous variable representing the amount allocated to entrepreneur i
- Operational parameters align with expected linear objective: maximize ∑(return_rate_i × investment_i)
- Business configuration includes: Total available budget for investment (used for Constraint bound for total investment), Maximum amount that can be allocated to each entrepreneur (used for Constraint bound for individual investment)
- 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 ∑(return_rate_i × investment_i)
- 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: ['∑(investment_i) ≤ Total_Budget', 'investment_i ≤ Max_Investment_i for all i'] (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 and configuration logic updates implemented to address missing optimization requirements and mapping gaps identified by the OR expert.

CREATE TABLE entrepreneurs (
  entrepreneur_id INTEGER,
  return_rate FLOAT,
  investment 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 realistic investment scenarios, considering typical return rates and budget constraints for small to medium-sized ventures.

-- Realistic data for entrepreneurs
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (1, 0.12, 150000);
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (2, 0.18, 200000);
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (3, 0.1, 100000);


```

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

Response:
# Complete Optimization Problem and Solution: entrepreneur

## 1. Problem Context and Goals

### Context  
An investor is tasked with allocating a fixed budget across multiple entrepreneurs to maximize the total expected return on investment. The investor must decide how much money to allocate to each entrepreneur, ensuring that the total investment does not exceed the available budget and that no single entrepreneur receives more than a specified maximum amount. The available budget for investment is set at one million dollars, and the maximum amount that can be allocated to any single entrepreneur is two hundred thousand dollars. These parameters are designed to ensure risk management and diversification across the investment portfolio. The expected return rate for each entrepreneur is a key factor in determining the optimal allocation, as it directly influences the total return on investment.

### Goals  
The primary goal of this optimization problem is to maximize the total expected return on investment by strategically allocating the available budget across the entrepreneurs. Success is measured by the total return generated from the investments, which is calculated by multiplying the amount allocated to each entrepreneur by their respective expected return rate and summing these values across all entrepreneurs. The optimization process ensures that the allocation decisions are made in a way that respects the budget and individual investment limits while maximizing the overall return.

## 2. Constraints    

The optimization problem is subject to two key constraints:  
1. **Total Budget Constraint**: The sum of all investments allocated to the entrepreneurs must not exceed the total available budget of one million dollars. This ensures that the investor does not overspend and stays within the financial limits.  
2. **Individual Investment Limit**: The amount allocated to any single entrepreneur must not exceed two hundred thousand dollars. This constraint ensures that the investment portfolio remains diversified and that no single entrepreneur receives an disproportionately large share of the budget.  

These constraints are designed to align with the investor's risk management strategy and ensure that the allocation decisions are both financially sound and operationally feasible.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes and configuration logic updates implemented to address missing optimization requirements and mapping gaps identified by the OR expert.

CREATE TABLE entrepreneurs (
  entrepreneur_id INTEGER,
  return_rate FLOAT,
  investment FLOAT
);
```

### Data Dictionary  
The `entrepreneurs` table contains the following columns, each with a specific business purpose and optimization role:  
- **entrepreneur_id**: A unique identifier for each entrepreneur, used to index the decision variables and constraints in the optimization problem.  
- **return_rate**: The expected return rate for each entrepreneur, which serves as the coefficient in the objective function to maximize the total return on investment.  
- **investment**: The amount of money allocated to each entrepreneur, which is the decision variable in the optimization problem.  

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic investment scenarios, considering typical return rates and budget constraints for small to medium-sized ventures.

-- Realistic data for entrepreneurs
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (1, 0.12, 150000);
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (2, 0.18, 200000);
INSERT INTO entrepreneurs (entrepreneur_id, return_rate, investment) VALUES (3, 0.1, 100000);
```
