Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:35:15

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 retail chain wants to optimize the allocation of membership marketing budget across different branches to maximize total purchases by members. The budget allocation should consider the membership levels and historical purchase data.",
  "optimization_problem": "The goal is to maximize the total purchases by members across all branches by optimally allocating a fixed marketing budget. The allocation should be based on historical purchase data and membership levels, ensuring that each branch receives a minimum budget.",
  "objective": "maximize total_purchases = \u2211(purchase_coefficient[branch_id] \u00d7 budget_allocation[branch_id])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine the total marketing budget and minimum budget allocations for each branch",
  "mapping_adequacy_summary": "needs_improvement"
}

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

CREATE TABLE BudgetAllocation (
  branch_id INTEGER,
  amount FLOAT
);

CREATE TABLE Purchase (
  branch_id INTEGER,
  Total_pounds FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "BudgetAllocation": {
      "business_purpose": "Stores budget allocation for each branch",
      "optimization_role": "decision_variables",
      "columns": {
        "branch_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each branch",
          "optimization_purpose": "Index for budget allocation",
          "sample_values": "1, 2, 3"
        },
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "Allocated budget amount for the branch",
          "optimization_purpose": "Decision variable for budget allocation",
          "sample_values": "10000, 15000, 20000"
        }
      }
    },
    "Purchase": {
      "business_purpose": "Stores historical purchase data",
      "optimization_role": "objective_coefficients",
      "columns": {
        "branch_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each branch",
          "optimization_purpose": "Index for purchase coefficient",
          "sample_values": "1, 2, 3"
        },
        "Total_pounds": {
          "data_type": "FLOAT",
          "business_meaning": "Total historical purchases in pounds",
          "optimization_purpose": "Coefficient for budget allocation",
          "sample_values": "50000, 75000, 100000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_budget": {
    "sample_value": "100000",
    "data_type": "FLOAT",
    "business_meaning": "Total marketing budget available for allocation",
    "optimization_role": "Used as a constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  },
  "min_budget": {
    "sample_value": "5000",
    "data_type": "FLOAT",
    "business_meaning": "Minimum budget allocation for each branch",
    "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": "shop_membership",
  "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": "shop_membership",
  "iteration": 1,
  "business_context": "A retail chain wants to optimize the allocation of membership marketing budget across different branches to maximize total purchases by members. The budget allocation should consider the membership levels and historical purchase data.",
  "optimization_problem_description": "Maximize the total purchases by members across all branches by optimally allocating a fixed marketing budget. The allocation should be based on historical purchase data and membership levels, ensuring that each branch receives a minimum budget.",
  "optimization_formulation": {
    "objective": "maximize total_purchases = \u2211(Purchase.Total_pounds[branch_id] \u00d7 BudgetAllocation.amount[branch_id])",
    "decision_variables": "BudgetAllocation.amount[branch_id] for each branch_id, continuous",
    "constraints": [
      "\u2211(BudgetAllocation.amount[branch_id]) \u2264 business_configuration_logic.total_budget",
      "BudgetAllocation.amount[branch_id] \u2265 business_configuration_logic.min_budget for each branch_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Purchase.Total_pounds[branch_id]": {
        "currently_mapped_to": "Purchase.Total_pounds",
        "mapping_adequacy": "good",
        "description": "Total historical purchases in pounds for each branch"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "Total marketing budget available for allocation"
      },
      "min_budget[branch_id]": {
        "currently_mapped_to": "business_configuration_logic.min_budget",
        "mapping_adequacy": "good",
        "description": "Minimum budget allocation for each branch"
      }
    },
    "decision_variables": {
      "BudgetAllocation.amount[branch_id]": {
        "currently_mapped_to": "BudgetAllocation.amount",
        "mapping_adequacy": "good",
        "description": "Allocated budget amount for each branch",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
