Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:29:13

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 wants to minimize the total transaction fees incurred by its customers while ensuring that each customer's transaction volume does not exceed their account limits.",
  "optimization_problem": "The bank aims to minimize the total transaction fees by optimizing the allocation of transactions across different card types, each with different fee structures, while ensuring that the total transaction amount per customer does not exceed their account limits.",
  "objective": "minimize \u2211(fee_per_card_type[card_type_code] \u00d7 transaction_amount[card_id])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for card fees and account limits, and updating business configuration logic to include scalar parameters for fees and account limits."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data for fee_per_card_type and account_limit",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for card fees and account limits, and updating business configuration logic to include scalar parameters for fees and account limits.

CREATE TABLE Card_Fees (
  card_type_code STRING,
  fee FLOAT
);

CREATE TABLE Account_Limits (
  customer_id INTEGER,
  account_limit FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Card_Fees": {
      "business_purpose": "fee associated with each card type",
      "optimization_role": "objective_coefficients",
      "columns": {
        "card_type_code": {
          "data_type": "STRING",
          "business_meaning": "code representing the card type",
          "optimization_purpose": "identifier for the card type fee",
          "sample_values": "VISA, MASTERCARD"
        },
        "fee": {
          "data_type": "FLOAT",
          "business_meaning": "fee associated with the card type",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": "0.02, 0.03"
        }
      }
    },
    "Account_Limits": {
      "business_purpose": "maximum transaction amount allowed per customer",
      "optimization_role": "constraint_bounds",
      "columns": {
        "customer_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the customer",
          "optimization_purpose": "identifier for the account limit",
          "sample_values": "1, 2, 3"
        },
        "account_limit": {
          "data_type": "FLOAT",
          "business_meaning": "maximum transaction amount allowed",
          "optimization_purpose": "bound in the constraint",
          "sample_values": "1000, 1500, 2000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "fee_per_card_type": {
    "sample_value": 0.02,
    "data_type": "FLOAT",
    "business_meaning": "fee associated with each card type",
    "optimization_role": "coefficient in the objective function",
    "configuration_type": "scalar_parameter"
  },
  "account_limit": {
    "sample_value": 1000,
    "data_type": "FLOAT",
    "business_meaning": "maximum transaction amount allowed per customer",
    "optimization_role": "bound in the constraint",
    "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 bank aims to minimize the total transaction fees incurred by its customers by optimizing the allocation of transactions across different card types, each with different fee structures, while ensuring that the total transaction amount per customer does not exceed their account limits.",
  "optimization_problem_description": "Minimize the total transaction fees by allocating transactions across card types with different fees, subject to the constraint that the total transaction amount per customer does not exceed their account limits.",
  "optimization_formulation": {
    "objective": "minimize \u2211(fee_per_card_type[card_type_code] \u00d7 transaction_amount[card_id])",
    "decision_variables": "transaction_amount[card_id] (continuous)",
    "constraints": "\u2211(transaction_amount[card_id]) \u2264 account_limit[customer_id] for each customer_id"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "fee_per_card_type[card_type_code]": {
        "currently_mapped_to": "Card_Fees.fee",
        "mapping_adequacy": "good",
        "description": "fee associated with each card type"
      }
    },
    "constraint_bounds": {
      "account_limit[customer_id]": {
        "currently_mapped_to": "Account_Limits.account_limit",
        "mapping_adequacy": "good",
        "description": "maximum transaction amount allowed per customer"
      }
    },
    "decision_variables": {
      "transaction_amount[card_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "amount of transaction allocated to each card type",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "transaction_amount[card_id]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map missing data for transaction_amount[card_id]"
  }
}
