Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 23:09:50

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: credit_limit[account_id] for each account_id, continuous
- Operational parameters align with expected linear objective: maximize ∑(expected_volume[account_id] × credit_limit[account_id])
- Business configuration includes: Total credit available for allocation across all accounts (used for Used as a constraint in the optimization model), Minimum credit limit required for an account to be considered active (used for Used as a 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": "customers_card_transactions",
  "iteration": 1,
  "business_context": "A financial institution aims to optimize credit limit allocations to maximize expected transaction volumes while adhering to risk management constraints, ensuring efficient use of available credit resources.",
  "optimization_problem_description": "Maximize the total expected transaction volume by optimally allocating credit limits to customer accounts, subject to constraints on total available credit, individual account risk limits, and minimum credit requirements for active accounts.",
  "optimization_formulation": {
    "objective": "maximize \u2211(expected_volume[account_id] \u00d7 credit_limit[account_id])",
    "decision_variables": "credit_limit[account_id] for each account_id, continuous",
    "constraints": [
      "\u2211(credit_limit[account_id]) \u2264 total_available_credit",
      "credit_limit[account_id] \u2264 max_credit_limit[account_id] for each account_id",
      "credit_limit[account_id] \u2265 min_credit_limit_for_active_account if is_active[account_id] is true"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "expected_volume[account_id]": {
        "currently_mapped_to": "account_expected_transaction_volume.expected_volume",
        "mapping_adequacy": "good",
        "description": "Expected transaction volume for each account, used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "total_available_credit": {
        "currently_mapped_to": "business_configuration_logic.total_available_credit",
        "mapping_adequacy": "good",
        "description": "Total credit available for allocation across all accounts"
      },
      "max_credit_limit[account_id]": {
        "currently_mapped_to": "account_credit_limits.max_credit_limit",
        "mapping_adequacy": "good",
        "description": "Maximum allowable credit limit for each account"
      },
      "min_credit_limit_for_active_account": {
        "currently_mapped_to": "business_configuration_logic.min_credit_limit_for_active_account",
        "mapping_adequacy": "good",
        "description": "Minimum credit limit required for an account to be considered active"
      }
    },
    "decision_variables": {
      "credit_limit[account_id]": {
        "currently_mapped_to": "account_credit_limits.credit_limit",
        "mapping_adequacy": "good",
        "description": "Credit limit allocated to each account, decision variable in the optimization model",
        "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, modifying existing tables to fill mapping gaps, and moving certain parameters to configuration logic for better management.

CREATE TABLE account_expected_transaction_volume (
  account_id INTEGER,
  expected_volume FLOAT
);

CREATE TABLE account_credit_limits (
  account_id INTEGER,
  credit_limit FLOAT,
  max_credit_limit FLOAT,
  is_active BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical credit limits and transaction volumes observed in financial institutions, ensuring a balance between risk management and business growth objectives.

-- Realistic data for account_expected_transaction_volume
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (1, 1200.0);
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (2, 1800.0);
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (3, 2200.0);

-- Realistic data for account_credit_limits
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (1, 800.0, 2000.0, True);
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (2, 1500.0, 2500.0, True);
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (3, 1800.0, 3000.0, True);


```

DATA DICTIONARY:
{
  "tables": {
    "account_expected_transaction_volume": {
      "business_purpose": "Stores expected transaction volume for each account",
      "optimization_role": "objective_coefficients",
      "columns": {
        "account_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each account",
          "optimization_purpose": "Index for expected transaction volume",
          "sample_values": "1, 2, 3"
        },
        "expected_volume": {
          "data_type": "FLOAT",
          "business_meaning": "Expected transaction volume for the account",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "1000.0, 1500.0, 2000.0"
        }
      }
    },
    "account_credit_limits": {
      "business_purpose": "Stores credit limits and status for each account",
      "optimization_role": "constraint_bounds",
      "columns": {
        "account_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each account",
          "optimization_purpose": "Index for credit limits",
          "sample_values": "1, 2, 3"
        },
        "credit_limit": {
          "data_type": "FLOAT",
          "business_meaning": "Credit limit allocated to the account",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "500.0, 1000.0, 1500.0"
        },
        "max_credit_limit": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum allowable credit limit for the account",
          "optimization_purpose": "Constraint bound",
          "sample_values": "2000.0, 2500.0, 3000.0"
        },
        "is_active": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the account is active",
          "optimization_purpose": "Determines if credit limit can be greater than zero",
          "sample_values": "true, false"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "total_available_credit": {
    "data_type": "FLOAT",
    "business_meaning": "Total credit available for allocation across all accounts",
    "optimization_role": "Used as a constraint in the optimization model",
    "configuration_type": "scalar_parameter",
    "value": 500000.0,
    "business_justification": "This value ensures sufficient credit is available to support active accounts while managing overall risk."
  },
  "min_credit_limit_for_active_account": {
    "data_type": "FLOAT",
    "business_meaning": "Minimum credit limit required for an account to be considered active",
    "optimization_role": "Used as a constraint in the optimization model",
    "configuration_type": "scalar_parameter",
    "value": 500.0,
    "business_justification": "This minimum ensures that active accounts have enough credit to facilitate meaningful transactions."
  }
}

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: customers_card_transactions

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: credit_limit[account_id] for each account_id, continuous
- Operational parameters align with expected linear objective: maximize ∑(expected_volume[account_id] × credit_limit[account_id])
- Business configuration includes: Total credit available for allocation across all accounts (used for Used as a constraint in the optimization model), Minimum credit limit required for an account to be considered active (used for Used as a 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 ∑(expected_volume[account_id] × credit_limit[account_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: ['∑(credit_limit[account_id]) ≤ total_available_credit', 'credit_limit[account_id] ≤ max_credit_limit[account_id] for each account_id', 'credit_limit[account_id] ≥ min_credit_limit_for_active_account if is_active[account_id] is true'] (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, modifying existing tables to fill mapping gaps, and moving certain parameters to configuration logic for better management.

CREATE TABLE account_expected_transaction_volume (
  account_id INTEGER,
  expected_volume FLOAT
);

CREATE TABLE account_credit_limits (
  account_id INTEGER,
  credit_limit FLOAT,
  max_credit_limit FLOAT,
  is_active 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 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical credit limits and transaction volumes observed in financial institutions, ensuring a balance between risk management and business growth objectives.

-- Realistic data for account_expected_transaction_volume
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (1, 1200.0);
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (2, 1800.0);
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (3, 2200.0);

-- Realistic data for account_credit_limits
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (1, 800.0, 2000.0, True);
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (2, 1500.0, 2500.0, True);
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (3, 1800.0, 3000.0, True);


```

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

Response:
# Complete Optimization Problem and Solution: customers_card_transactions

## 1. Problem Context and Goals

### Context  
A financial institution is focused on optimizing the allocation of credit limits to customer accounts. The primary decision involves determining the appropriate credit limit for each account, which is treated as a continuous variable. The institution aims to maximize the total expected transaction volume, which is directly influenced by the credit limits assigned to each account. This objective aligns with the operational goal of maximizing the sum of expected transaction volumes across all accounts, where each account's expected volume acts as a coefficient in the optimization process.

The business configuration includes critical parameters such as the total credit available for allocation across all accounts, which serves as a constraint to ensure that the total assigned credit does not exceed this limit. Additionally, there is a minimum credit limit requirement for an account to be considered active, ensuring that accounts have sufficient credit to facilitate meaningful transactions. These parameters are essential for maintaining a balance between business growth and risk management.

The data used in this optimization process reflects current operational information, ensuring that decisions are based on realistic and up-to-date insights. The constraints are designed to be linear, avoiding any nonlinear relationships such as variable products or divisions, and are directly tied to the business configuration parameters.

### Goals  
The primary goal of this optimization problem is to maximize the total expected transaction volume across all customer accounts. This is achieved by strategically allocating credit limits to each account, with the objective of maximizing the sum of the products of expected transaction volumes and their respective credit limits. Success in this optimization is measured by the increase in total expected transaction volume, which is directly linked to the coefficients derived from the expected volumes of each account. The optimization goal is clearly defined in linear terms, ensuring a straightforward and efficient solution process.

## 2. Constraints    

The optimization problem is subject to several linear constraints that ensure the solution is both feasible and aligned with business objectives:

- The total credit allocated across all accounts must not exceed the total available credit. This constraint ensures that the institution operates within its financial capacity and manages risk effectively.
- Each account's credit limit must not exceed its maximum allowable credit limit. This constraint is crucial for maintaining individual account risk limits and preventing overexposure.
- For an account to be considered active, its credit limit must meet or exceed the minimum credit limit requirement. This ensures that active accounts have enough credit to support meaningful transactions and contribute to the overall transaction volume.

These constraints are expressed in business terms that naturally lead to linear mathematical forms, facilitating a straightforward optimization process.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data, modifying existing tables to fill mapping gaps, and moving certain parameters to configuration logic for better management.

CREATE TABLE account_expected_transaction_volume (
  account_id INTEGER,
  expected_volume FLOAT
);

CREATE TABLE account_credit_limits (
  account_id INTEGER,
  credit_limit FLOAT,
  max_credit_limit FLOAT,
  is_active BOOLEAN
);
```

### Data Dictionary  
The data dictionary provides a comprehensive mapping of tables and columns to their business purposes and optimization roles:

- **account_expected_transaction_volume**: This table stores the expected transaction volume for each account. The expected volume serves as a coefficient in the optimization objective, representing the potential transaction activity associated with each account.

  - **account_id**: A unique identifier for each account, used to index expected transaction volumes.
  - **expected_volume**: The anticipated transaction volume for the account, acting as a coefficient in the objective function.

- **account_credit_limits**: This table contains information about the credit limits and status of each account. It plays a crucial role in defining the constraints of the optimization problem.

  - **account_id**: A unique identifier for each account, used to index credit limits.
  - **credit_limit**: The credit limit allocated to the account, which is the decision variable in the optimization model.
  - **max_credit_limit**: The maximum allowable credit limit for the account, serving as a constraint bound.
  - **is_active**: A boolean indicator of whether the account is active, determining if the credit limit can be greater than zero.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical credit limits and transaction volumes observed in financial institutions, ensuring a balance between risk management and business growth objectives.

-- Realistic data for account_expected_transaction_volume
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (1, 1200.0);
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (2, 1800.0);
INSERT INTO account_expected_transaction_volume (account_id, expected_volume) VALUES (3, 2200.0);

-- Realistic data for account_credit_limits
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (1, 800.0, 2000.0, True);
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (2, 1500.0, 2500.0, True);
INSERT INTO account_credit_limits (account_id, credit_limit, max_credit_limit, is_active) VALUES (3, 1800.0, 3000.0, True);
```
