Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:29:33

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 bank aims to optimize the allocation of funds between savings and checking accounts to maximize interest income while ensuring liquidity and regulatory compliance.",
  "optimization_problem": "The bank wants to maximize the total interest income from savings and checking accounts, subject to constraints on minimum balances, total funds, and regulatory requirements.",
  "objective": "maximize \u2211(interest_rate_savings \u00d7 balance_savings + interest_rate_checking \u00d7 balance_checking)",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating tables for missing optimization requirements and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing coefficients and constraint bounds to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for missing optimization requirements and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE CUSTOMER_FUNDS (
  custid INTEGER,
  total_funds FLOAT
);

CREATE TABLE SAVINGS (
  custid INTEGER,
  balance FLOAT
);

CREATE TABLE CHECKING (
  custid INTEGER,
  balance FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "CUSTOMER_FUNDS": {
      "business_purpose": "Total funds available per customer for allocation between savings and checking accounts",
      "optimization_role": "constraint_bounds",
      "columns": {
        "custid": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each customer",
          "optimization_purpose": "Index for decision variables and constraints",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "total_funds": {
          "data_type": "FLOAT",
          "business_meaning": "Total funds available for the customer",
          "optimization_purpose": "Upper bound constraint for total account balances",
          "sample_values": [
            1000.0,
            1500.0,
            2000.0
          ]
        }
      }
    },
    "SAVINGS": {
      "business_purpose": "Savings account balances for each customer",
      "optimization_role": "decision_variables",
      "columns": {
        "custid": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each customer",
          "optimization_purpose": "Index for decision variables",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "balance": {
          "data_type": "FLOAT",
          "business_meaning": "Balance in savings account",
          "optimization_purpose": "Decision variable for savings account allocation",
          "sample_values": [
            500.0,
            750.0,
            1000.0
          ]
        }
      }
    },
    "CHECKING": {
      "business_purpose": "Checking account balances for each customer",
      "optimization_role": "decision_variables",
      "columns": {
        "custid": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each customer",
          "optimization_purpose": "Index for decision variables",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "balance": {
          "data_type": "FLOAT",
          "business_meaning": "Balance in checking account",
          "optimization_purpose": "Decision variable for checking account allocation",
          "sample_values": [
            300.0,
            450.0,
            600.0
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "interest_rate_savings": {
    "sample_value": 0.03,
    "data_type": "FLOAT",
    "business_meaning": "Interest rate for savings accounts",
    "optimization_role": "Objective coefficient for savings account balances",
    "configuration_type": "scalar_parameter"
  },
  "interest_rate_checking": {
    "sample_value": 0.01,
    "data_type": "FLOAT",
    "business_meaning": "Interest rate for checking accounts",
    "optimization_role": "Objective coefficient for checking account balances",
    "configuration_type": "scalar_parameter"
  },
  "min_balance_savings": {
    "sample_value": 100.0,
    "data_type": "FLOAT",
    "business_meaning": "Minimum balance required for savings accounts",
    "optimization_role": "Lower bound constraint for savings account balances",
    "configuration_type": "scalar_parameter"
  },
  "min_balance_checking": {
    "sample_value": 50.0,
    "data_type": "FLOAT",
    "business_meaning": "Minimum balance required for checking accounts",
    "optimization_role": "Lower bound constraint for checking account balances",
    "configuration_type": "scalar_parameter"
  },
  "total_bank_funds": {
    "sample_value": 1000000.0,
    "data_type": "FLOAT",
    "business_meaning": "Total funds available in the bank",
    "optimization_role": "Upper bound constraint for total account balances",
    "configuration_type": "scalar_parameter"
  },
  "max_balance_savings": {
    "sample_value": 50000.0,
    "data_type": "FLOAT",
    "business_meaning": "Maximum balance allowed for savings accounts",
    "optimization_role": "Upper bound constraint for savings account balances",
    "configuration_type": "scalar_parameter"
  },
  "max_balance_checking": {
    "sample_value": 30000.0,
    "data_type": "FLOAT",
    "business_meaning": "Maximum balance allowed for checking accounts",
    "optimization_role": "Upper bound constraint for checking account balances",
    "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 bank aims to optimize the allocation of funds between savings and checking accounts to maximize interest income while ensuring liquidity and regulatory compliance. The optimization must maintain a linear structure to ensure computational efficiency and scalability.",
  "optimization_problem_description": "Maximize the total interest income from savings and checking accounts, subject to constraints on minimum balances, total funds, and regulatory requirements. The problem is formulated as a linear programming (LP) model.",
  "optimization_formulation": {
    "objective": "maximize \u2211(interest_rate_savings \u00d7 balance_savings[custid] + interest_rate_checking \u00d7 balance_checking[custid])",
    "decision_variables": "balance_savings[custid] (continuous), balance_checking[custid] (continuous)",
    "constraints": [
      "balance_savings[custid] + balance_checking[custid] \u2264 total_funds[custid] (total funds constraint)",
      "balance_savings[custid] \u2265 min_balance_savings (minimum savings balance constraint)",
      "balance_checking[custid] \u2265 min_balance_checking (minimum checking balance constraint)",
      "balance_savings[custid] \u2264 max_balance_savings (maximum savings balance constraint)",
      "balance_checking[custid] \u2264 max_balance_checking (maximum checking balance constraint)",
      "\u2211(balance_savings[custid] + balance_checking[custid]) \u2264 total_bank_funds (total bank funds constraint)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "interest_rate_savings": {
        "currently_mapped_to": "business_configuration_logic.interest_rate_savings",
        "mapping_adequacy": "good",
        "description": "Interest rate for savings accounts"
      },
      "interest_rate_checking": {
        "currently_mapped_to": "business_configuration_logic.interest_rate_checking",
        "mapping_adequacy": "good",
        "description": "Interest rate for checking accounts"
      }
    },
    "constraint_bounds": {
      "total_funds[custid]": {
        "currently_mapped_to": "CUSTOMER_FUNDS.total_funds",
        "mapping_adequacy": "good",
        "description": "Total funds available per customer"
      },
      "min_balance_savings": {
        "currently_mapped_to": "business_configuration_logic.min_balance_savings",
        "mapping_adequacy": "good",
        "description": "Minimum balance required for savings accounts"
      },
      "min_balance_checking": {
        "currently_mapped_to": "business_configuration_logic.min_balance_checking",
        "mapping_adequacy": "good",
        "description": "Minimum balance required for checking accounts"
      },
      "max_balance_savings": {
        "currently_mapped_to": "business_configuration_logic.max_balance_savings",
        "mapping_adequacy": "good",
        "description": "Maximum balance allowed for savings accounts"
      },
      "max_balance_checking": {
        "currently_mapped_to": "business_configuration_logic.max_balance_checking",
        "mapping_adequacy": "good",
        "description": "Maximum balance allowed for checking accounts"
      },
      "total_bank_funds": {
        "currently_mapped_to": "business_configuration_logic.total_bank_funds",
        "mapping_adequacy": "good",
        "description": "Total funds available in the bank"
      }
    },
    "decision_variables": {
      "balance_savings[custid]": {
        "currently_mapped_to": "SAVINGS.balance",
        "mapping_adequacy": "good",
        "description": "Balance in savings account",
        "variable_type": "continuous"
      },
      "balance_checking[custid]": {
        "currently_mapped_to": "CHECKING.balance",
        "mapping_adequacy": "good",
        "description": "Balance in checking account",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
