Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-25 22:34:08

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: amount[loan_ID]: continuous
- Operational parameters align with expected linear objective: maximize ∑(amount[loan_ID])
- Business configuration includes: Maximum loan amount per customer (used for Constraint bound in optimization model), Maximum loan amount per credit score unit (used for Constraint bound in optimization model), Maximum total loan amount per customer (used for 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": "loan_1",
  "iteration": 1,
  "business_context": "A bank aims to optimize its loan allocation across branches to maximize total loan disbursement while ensuring that no branch exceeds its customer capacity and that each customer's credit score is respected.",
  "optimization_problem_description": "Maximize the total loan amount disbursed across all branches, subject to constraints on branch customer capacity, individual customer credit scores, and the number of loans per customer.",
  "optimization_formulation": {
    "objective": "maximize \u2211(amount[loan_ID])",
    "decision_variables": "amount[loan_ID]: continuous",
    "constraints": [
      "\u2211(amount[loan_ID] for each branch) \u2264 no_of_customers[branch_ID] * max_loan_per_customer",
      "amount[loan_ID] \u2264 credit_score[customer_ID] * max_loan_per_credit_score",
      "\u2211(amount[loan_ID] for each customer) \u2264 max_total_loan_per_customer"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "amount[loan_ID]": {
        "currently_mapped_to": "loan.amount",
        "mapping_adequacy": "good",
        "description": "The loan amount to be disbursed"
      }
    },
    "constraint_bounds": {
      "no_of_customers[branch_ID]": {
        "currently_mapped_to": "bank.no_of_customers",
        "mapping_adequacy": "good",
        "description": "The number of customers in a branch"
      },
      "credit_score[customer_ID]": {
        "currently_mapped_to": "customer.credit_score",
        "mapping_adequacy": "good",
        "description": "The credit score of a customer"
      },
      "max_loan_per_customer": {
        "currently_mapped_to": "business_configuration_logic.max_loan_per_customer",
        "mapping_adequacy": "good",
        "description": "Maximum loan amount per customer"
      },
      "max_loan_per_credit_score": {
        "currently_mapped_to": "business_configuration_logic.max_loan_per_credit_score",
        "mapping_adequacy": "good",
        "description": "Maximum loan amount per credit score unit"
      },
      "max_total_loan_per_customer": {
        "currently_mapped_to": "business_configuration_logic.max_total_loan_per_customer",
        "mapping_adequacy": "good",
        "description": "Maximum total loan amount per customer"
      }
    },
    "decision_variables": {
      "amount[loan_ID]": {
        "currently_mapped_to": "loan.amount",
        "mapping_adequacy": "good",
        "description": "The loan amount to be disbursed",
        "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 adding missing parameters to business_configuration_logic.json and ensuring all tables meet the 3-row minimum rule. Configuration logic updates address scalar parameters and formulas identified as missing in the OR expert analysis.

CREATE TABLE loan (
  amount FLOAT
);

CREATE TABLE bank (
  no_of_customers INTEGER
);

CREATE TABLE customer (
  credit_score INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical banking practices, ensuring that loan amounts, customer capacities, and credit scores are realistic and align with the optimization constraints.

-- Realistic data for loan
INSERT INTO loan (amount) VALUES (5000.0);
INSERT INTO loan (amount) VALUES (10000.0);
INSERT INTO loan (amount) VALUES (7500.0);

-- Realistic data for bank
INSERT INTO bank (no_of_customers) VALUES (150);
INSERT INTO bank (no_of_customers) VALUES (250);
INSERT INTO bank (no_of_customers) VALUES (200);

-- Realistic data for customer
INSERT INTO customer (credit_score) VALUES (720);
INSERT INTO customer (credit_score) VALUES (780);
INSERT INTO customer (credit_score) VALUES (750);


```

DATA DICTIONARY:
{
  "tables": {
    "loan": {
      "business_purpose": "Stores loan details for optimization",
      "optimization_role": "decision_variables",
      "columns": {
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "The loan amount to be disbursed",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "1000.0, 5000.0, 7500.0"
        }
      }
    },
    "bank": {
      "business_purpose": "Stores branch details for optimization",
      "optimization_role": "constraint_bounds",
      "columns": {
        "no_of_customers": {
          "data_type": "INTEGER",
          "business_meaning": "The number of customers in a branch",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "customer": {
      "business_purpose": "Stores customer details for optimization",
      "optimization_role": "constraint_bounds",
      "columns": {
        "credit_score": {
          "data_type": "INTEGER",
          "business_meaning": "The credit score of a customer",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": "700, 750, 800"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "max_loan_per_customer": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum loan amount per customer",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 15000,
    "business_justification": "This value ensures that no single customer can take an excessively large loan, maintaining risk control."
  },
  "max_loan_per_credit_score": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum loan amount per credit score unit",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 600,
    "business_justification": "This value allows higher loan amounts for customers with better credit scores, incentivizing good credit behavior."
  },
  "max_total_loan_per_customer": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum total loan amount per customer",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 60000,
    "business_justification": "This value ensures that the total loan amount per customer is capped, preventing overexposure to any single customer."
  }
}

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: loan_1

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: amount[loan_ID]: continuous
- Operational parameters align with expected linear objective: maximize ∑(amount[loan_ID])
- Business configuration includes: Maximum loan amount per customer (used for Constraint bound in optimization model), Maximum loan amount per credit score unit (used for Constraint bound in optimization model), Maximum total loan amount per customer (used for 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 ∑(amount[loan_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: ['∑(amount[loan_ID] for each branch) ≤ no_of_customers[branch_ID] * max_loan_per_customer', 'amount[loan_ID] ≤ credit_score[customer_ID] * max_loan_per_credit_score', '∑(amount[loan_ID] for each customer) ≤ max_total_loan_per_customer'] (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 adding missing parameters to business_configuration_logic.json and ensuring all tables meet the 3-row minimum rule. Configuration logic updates address scalar parameters and formulas identified as missing in the OR expert analysis.

CREATE TABLE loan (
  amount FLOAT
);

CREATE TABLE bank (
  no_of_customers INTEGER
);

CREATE TABLE customer (
  credit_score 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 banking practices, ensuring that loan amounts, customer capacities, and credit scores are realistic and align with the optimization constraints.

-- Realistic data for loan
INSERT INTO loan (amount) VALUES (5000.0);
INSERT INTO loan (amount) VALUES (10000.0);
INSERT INTO loan (amount) VALUES (7500.0);

-- Realistic data for bank
INSERT INTO bank (no_of_customers) VALUES (150);
INSERT INTO bank (no_of_customers) VALUES (250);
INSERT INTO bank (no_of_customers) VALUES (200);

-- Realistic data for customer
INSERT INTO customer (credit_score) VALUES (720);
INSERT INTO customer (credit_score) VALUES (780);
INSERT INTO customer (credit_score) VALUES (750);


```

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

Response:
# Complete Optimization Problem and Solution: loan_1

## 1. Problem Context and Goals

### Context  
A bank is focused on optimizing its loan allocation strategy across its branches to maximize the total loan amount disbursed. The bank must ensure that its loan allocation adheres to several operational constraints to maintain financial stability and risk control. Specifically, the bank must respect the capacity of each branch in terms of the number of customers it can serve, the creditworthiness of each customer as reflected by their credit score, and the total loan exposure per customer.  

The bank has established specific operational parameters to guide this process:  
- **Maximum loan amount per customer**: No single customer can receive a loan exceeding $15,000.  
- **Maximum loan amount per credit score unit**: For every unit of a customer’s credit score, the loan amount cannot exceed $600. This ensures that customers with higher credit scores are eligible for larger loans.  
- **Maximum total loan amount per customer**: The cumulative loan amount for any single customer across all branches cannot exceed $60,000, preventing overexposure to any individual customer.  

The decision variable in this optimization is the loan amount to be disbursed, which is a continuous value. The bank aims to allocate these loan amounts in a way that maximizes the total disbursement while adhering to the above constraints.  

### Goals  
The primary goal of this optimization is to maximize the total loan amount disbursed across all branches. Success is measured by the sum of all loan amounts allocated, ensuring that the bank’s resources are utilized effectively while maintaining compliance with the established operational constraints.  

## 2. Constraints  

The optimization must respect the following constraints:  
1. **Branch customer capacity**: The total loan amount allocated to a branch cannot exceed the product of the number of customers in that branch and the maximum loan amount per customer. This ensures that each branch operates within its customer service capacity.  
2. **Customer credit score**: The loan amount allocated to a customer cannot exceed the product of their credit score and the maximum loan amount per credit score unit. This ensures that loan amounts are proportional to the customer’s creditworthiness.  
3. **Total loan exposure per customer**: The sum of all loan amounts allocated to a single customer across all branches cannot exceed the maximum total loan amount per customer. This prevents overexposure to any individual customer.  

These constraints are designed to ensure that the bank’s loan allocation strategy is both efficient and risk-controlled, aligning with its operational and financial goals.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding missing parameters to business_configuration_logic.json and ensuring all tables meet the 3-row minimum rule. Configuration logic updates address scalar parameters and formulas identified as missing in the OR expert analysis.

CREATE TABLE loan (
  amount FLOAT
);

CREATE TABLE bank (
  no_of_customers INTEGER
);

CREATE TABLE customer (
  credit_score INTEGER
);
```

### Data Dictionary  
- **Loan Table**:  
  - **Purpose**: Stores details about the loans to be disbursed.  
  - **Optimization Role**: Contains the decision variable for the optimization model.  
  - **Columns**:  
    - **amount**: The loan amount to be disbursed. This is the primary decision variable in the optimization.  

- **Bank Table**:  
  - **Purpose**: Stores information about each branch’s customer capacity.  
  - **Optimization Role**: Provides data for the branch customer capacity constraint.  
  - **Columns**:  
    - **no_of_customers**: The number of customers in a branch, used to calculate the maximum loan allocation per branch.  

- **Customer Table**:  
  - **Purpose**: Stores customer-specific details, particularly their credit scores.  
  - **Optimization Role**: Provides data for the credit score-based loan allocation constraint.  
  - **Columns**:  
    - **credit_score**: The credit score of a customer, used to determine the maximum loan amount they are eligible for.  

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical banking practices, ensuring that loan amounts, customer capacities, and credit scores are realistic and align with the optimization constraints.

-- Realistic data for loan
INSERT INTO loan (amount) VALUES (5000.0);
INSERT INTO loan (amount) VALUES (10000.0);
INSERT INTO loan (amount) VALUES (7500.0);

-- Realistic data for bank
INSERT INTO bank (no_of_customers) VALUES (150);
INSERT INTO bank (no_of_customers) VALUES (250);
INSERT INTO bank (no_of_customers) VALUES (200);

-- Realistic data for customer
INSERT INTO customer (credit_score) VALUES (720);
INSERT INTO customer (credit_score) VALUES (780);
INSERT INTO customer (credit_score) VALUES (750);
```
