Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:50:08

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: loan_1

```sql
CREATE TABLE bank (
  branch_ID NUMBER,
  bname TEXT,
  no_of_customers NUMBER,
  city TEXT,
  state TEXT
);
```

```sql
CREATE TABLE customer (
  cust_ID TEXT,
  cust_name TEXT,
  acc_type TEXT,
  acc_bal NUMBER,
  no_of_loans NUMBER,
  credit_score NUMBER,
  branch_ID NUMBER,
  state TEXT
);
```

```sql
CREATE TABLE loan (
  loan_ID TEXT,
  loan_type TEXT,
  cust_ID TEXT,
  branch_ID TEXT,
  amount NUMBER
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "loan_1",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing", 
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "loan_1",
  "iteration": 0,
  "business_context": "A bank wants to optimize the allocation of loan amounts across different branches to maximize the total credit score of customers receiving loans, while adhering to budget constraints and ensuring a minimum number of loans per branch.",
  "optimization_problem_description": "The bank aims to maximize the total credit score of customers who receive loans, subject to constraints on the total loan budget, minimum number of loans per branch, and maximum loan amount per customer.",
  "optimization_formulation": {
    "objective": "maximize total_credit_score = \u2211(credit_score[cust_ID] \u00d7 loan_amount[cust_ID])",
    "decision_variables": "loan_amount[cust_ID] - continuous variable representing the loan amount allocated to customer cust_ID",
    "constraints": [
      "\u2211(loan_amount[cust_ID]) \u2264 total_budget",
      "loan_amount[cust_ID] \u2264 max_loan_per_customer for all cust_ID",
      "\u2211(loan_amount[cust_ID]) \u2265 min_loans_per_branch for all branch_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "credit_score[cust_ID]": {
        "currently_mapped_to": "customer.credit_score",
        "mapping_adequacy": "good",
        "description": "The credit score of each customer, used to weigh the loan amount in the objective function"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total budget available for loans across all branches"
      },
      "max_loan_per_customer": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum loan amount that can be allocated to a single customer"
      },
      "min_loans_per_branch": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The minimum total loan amount that must be allocated per branch"
      }
    },
    "decision_variables": {
      "loan_amount[cust_ID]": {
        "currently_mapped_to": "loan.amount",
        "mapping_adequacy": "partial",
        "description": "The amount of loan allocated to each customer",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "total_budget",
    "max_loan_per_customer",
    "min_loans_per_branch"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the constraints and ensure all necessary parameters are available for a complete model"
  }
}
