Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:30:39

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 government agency aims to optimize the allocation of its budget across departments to maximize overall efficiency, considering factors like department ranking, number of employees, and budget constraints.",
  "optimization_problem": "The goal is to maximize the total efficiency score of all departments, where efficiency is a weighted sum of department ranking and the number of employees. The optimization must respect the total budget available and ensure that each department receives a minimum budget to function.",
  "objective": "maximize \u2211(w1 * Ranking[d] + w2 * Num_Employees[d]) * Budget_Allocation[d]",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating tables for department budgets and efficiency weights, and moving scalar parameters like total budget and weights to business_configuration_logic.json."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define weights for efficiency calculation and gather budget constraints for each department",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for department budgets and efficiency weights, and moving scalar parameters like total budget and weights to business_configuration_logic.json.

CREATE TABLE department_budgets (
  department_id INTEGER,
  minimum_budget FLOAT,
  maximum_budget FLOAT,
  allocated_budget FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "department_budgets": {
      "business_purpose": "Minimum and maximum budget constraints for each department",
      "optimization_role": "constraint_bounds",
      "columns": {
        "department_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each department",
          "optimization_purpose": "Index for budget constraints",
          "sample_values": "1, 2, 3"
        },
        "minimum_budget": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum budget required for department",
          "optimization_purpose": "Lower bound for budget allocation",
          "sample_values": "10000, 15000, 20000"
        },
        "maximum_budget": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum budget that can be allocated to department",
          "optimization_purpose": "Upper bound for budget allocation",
          "sample_values": "50000, 60000, 70000"
        },
        "allocated_budget": {
          "data_type": "FLOAT",
          "business_meaning": "Budget allocated to department",
          "optimization_purpose": "Decision variable for budget allocation",
          "sample_values": "30000, 35000, 40000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "w1": {
    "sample_value": 0.6,
    "data_type": "FLOAT",
    "business_meaning": "weight for department ranking in efficiency calculation",
    "optimization_role": "objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "w2": {
    "sample_value": 0.4,
    "data_type": "FLOAT",
    "business_meaning": "weight for number of employees in efficiency calculation",
    "optimization_role": "objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "Total_Budget": {
    "sample_value": 1000000,
    "data_type": "FLOAT",
    "business_meaning": "total budget available for allocation",
    "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": "department_management",
  "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": "department_management",
  "iteration": 1,
  "business_context": "A government agency aims to optimize the allocation of its budget across departments to maximize overall efficiency, considering factors like department ranking, number of employees, and budget constraints.",
  "optimization_problem_description": "Maximize the total efficiency score of all departments, where efficiency is a weighted sum of department ranking and the number of employees, while respecting the total budget available and ensuring each department receives a minimum budget to function.",
  "optimization_formulation": {
    "objective": "maximize \u2211(w1 * Ranking[d] + w2 * Num_Employees[d]) * Budget_Allocation[d]",
    "decision_variables": "Budget_Allocation[d] (continuous)",
    "constraints": "\u2211 Budget_Allocation[d] \u2264 Total_Budget, minimum_budget[d] \u2264 Budget_Allocation[d] \u2264 maximum_budget[d] for all departments d"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "w1": {
        "currently_mapped_to": "business_configuration_logic.w1",
        "mapping_adequacy": "good",
        "description": "weight for department ranking in efficiency calculation"
      },
      "w2": {
        "currently_mapped_to": "business_configuration_logic.w2",
        "mapping_adequacy": "good",
        "description": "weight for number of employees in efficiency calculation"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "total budget available for allocation"
      },
      "minimum_budget[d]": {
        "currently_mapped_to": "department_budgets.minimum_budget",
        "mapping_adequacy": "good",
        "description": "minimum budget required for department d"
      },
      "maximum_budget[d]": {
        "currently_mapped_to": "department_budgets.maximum_budget",
        "mapping_adequacy": "good",
        "description": "maximum budget that can be allocated to department d"
      }
    },
    "decision_variables": {
      "Budget_Allocation[d]": {
        "currently_mapped_to": "department_budgets.allocated_budget",
        "mapping_adequacy": "good",
        "description": "budget allocated to department d",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
