Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:42:22

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


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



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "business_context": "A small bank wants to optimize the allocation of funds between savings and checking accounts to maximize the total interest earned, subject to certain constraints on minimum balances and total funds available.",
  "optimization_problem": "The bank needs to decide how much money to allocate to each customer's savings and checking accounts to maximize the total interest earned, while ensuring that each account maintains a minimum balance and the total allocation does not exceed the available funds.",
  "objective": "maximize total_interest = sum(savings_interest_rate * savings_balance[custid] + checking_interest_rate * checking_balance[custid])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for interest rates and minimum balances, and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine interest rates and minimum balance requirements for optimization",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for interest rates and minimum balances, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE SAVINGS (
  balance FLOAT,
  interest_rate FLOAT
);

CREATE TABLE CHECKING (
  balance FLOAT,
  interest_rate FLOAT
);

CREATE TABLE CUSTOMER_FUNDS (
  total_funds FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "SAVINGS": {
      "business_purpose": "Stores savings account balances and interest rates for customers",
      "optimization_role": "decision_variables/objective_coefficients",
      "columns": {
        "balance": {
          "data_type": "FLOAT",
          "business_meaning": "amount allocated to savings for each customer",
          "optimization_purpose": "decision variable",
          "sample_values": "1000.0, 2000.0, 3000.0"
        },
        "interest_rate": {
          "data_type": "FLOAT",
          "business_meaning": "interest rate applied to savings balances",
          "optimization_purpose": "objective coefficient",
          "sample_values": "0.01, 0.015, 0.02"
        }
      }
    },
    "CHECKING": {
      "business_purpose": "Stores checking account balances and interest rates for customers",
      "optimization_role": "decision_variables/objective_coefficients",
      "columns": {
        "balance": {
          "data_type": "FLOAT",
          "business_meaning": "amount allocated to checking for each customer",
          "optimization_purpose": "decision variable",
          "sample_values": "500.0, 1500.0, 2500.0"
        },
        "interest_rate": {
          "data_type": "FLOAT",
          "business_meaning": "interest rate applied to checking balances",
          "optimization_purpose": "objective coefficient",
          "sample_values": "0.005, 0.01, 0.015"
        }
      }
    },
    "CUSTOMER_FUNDS": {
      "business_purpose": "Stores total funds available for allocation for each customer",
      "optimization_role": "constraint_bounds",
      "columns": {
        "total_funds": {
          "data_type": "FLOAT",
          "business_meaning": "total funds available for allocation for each customer",
          "optimization_purpose": "constraint bound",
          "sample_values": "5000.0, 10000.0, 15000.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "minimum_savings_balance": {
    "sample_value": "1000",
    "data_type": "FLOAT",
    "business_meaning": "minimum required balance for savings accounts",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "minimum_checking_balance": {
    "sample_value": "500",
    "data_type": "FLOAT",
    "business_meaning": "minimum required balance for checking accounts",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "small_bank_1",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "small_bank_1",
  "iteration": 1,
  "business_context": "A small bank is optimizing the allocation of customer funds between savings and checking accounts to maximize interest earned, ensuring minimum balances and not exceeding total available funds.",
  "optimization_problem_description": "The bank aims to allocate funds between savings and checking accounts for each customer to maximize total interest earned, subject to constraints on minimum balances and total funds available.",
  "optimization_formulation": {
    "objective": "maximize total_interest = sum(savings_interest_rate * savings_balance[custid] + checking_interest_rate * checking_balance[custid])",
    "decision_variables": {
      "savings_balance[custid]": {
        "description": "Amount allocated to savings for each customer",
        "variable_type": "continuous"
      },
      "checking_balance[custid]": {
        "description": "Amount allocated to checking for each customer",
        "variable_type": "continuous"
      }
    },
    "constraints": {
      "total_funds_constraint[custid]": {
        "expression": "savings_balance[custid] + checking_balance[custid] <= total_funds[custid]",
        "description": "Total allocation does not exceed available funds"
      },
      "minimum_savings_balance_constraint[custid]": {
        "expression": "savings_balance[custid] >= minimum_savings_balance",
        "description": "Savings balance meets minimum requirement"
      },
      "minimum_checking_balance_constraint[custid]": {
        "expression": "checking_balance[custid] >= minimum_checking_balance",
        "description": "Checking balance meets minimum requirement"
      }
    }
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "savings_interest_rate[custid]": {
        "currently_mapped_to": "SAVINGS.interest_rate",
        "mapping_adequacy": "good",
        "description": "Interest rate applied to savings balances"
      },
      "checking_interest_rate[custid]": {
        "currently_mapped_to": "CHECKING.interest_rate",
        "mapping_adequacy": "good",
        "description": "Interest rate applied to checking balances"
      }
    },
    "constraint_bounds": {
      "total_funds[custid]": {
        "currently_mapped_to": "CUSTOMER_FUNDS.total_funds",
        "mapping_adequacy": "good",
        "description": "Total funds available for allocation"
      },
      "minimum_savings_balance": {
        "currently_mapped_to": "business_configuration_logic.minimum_savings_balance",
        "mapping_adequacy": "good",
        "description": "Minimum required balance for savings accounts"
      },
      "minimum_checking_balance": {
        "currently_mapped_to": "business_configuration_logic.minimum_checking_balance",
        "mapping_adequacy": "good",
        "description": "Minimum required balance for checking accounts"
      }
    },
    "decision_variables": {
      "savings_balance[custid]": {
        "currently_mapped_to": "SAVINGS.balance",
        "mapping_adequacy": "good",
        "description": "Amount allocated to savings for each customer",
        "variable_type": "continuous"
      },
      "checking_balance[custid]": {
        "currently_mapped_to": "CHECKING.balance",
        "mapping_adequacy": "good",
        "description": "Amount allocated to checking for each customer",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
