Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:09:50

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 financial institution wants to optimize the allocation of credit limits across different customer accounts to maximize the expected transaction volume while adhering to risk management constraints.",
  "optimization_problem": "The goal is to 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.",
  "objective": "maximize \u2211(expected_transaction_volume[account_id] \u00d7 credit_limit[account_id])",
  "table_count": 2,
  "key_changes": [
    "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."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data and parameters to fully define the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT 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 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"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_available_credit": {
    "sample_value": "1000000",
    "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"
  },
  "min_credit_limit_for_active_account": {
    "sample_value": "500",
    "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"
  }
}


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

JSON STRUCTURE REQUIRED:

{
  "database_id": "customers_card_transactions",
  "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": "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"
  }
}
