Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:26:22

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 wants to allocate a fixed budget across cities to maximize the total population served while ensuring equitable distribution across districts and respecting budget constraints.",
  "optimization_problem": "The objective is to maximize the total population served by allocating a fixed budget across cities. The allocation must respect district-level equity constraints and ensure the total spending does not exceed the budget.",
  "objective": "maximize \u2211(Population_i \u00d7 Allocation_i)",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating tables for budget allocation, districts, and cities. Configuration logic updates include adding scalar parameters for total budget, minimum allocation per city, and minimum allocation per district."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define budget constraints and district-level equity requirements",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for budget allocation, districts, and cities. Configuration logic updates include adding scalar parameters for total budget, minimum allocation per city, and minimum allocation per district.

CREATE TABLE city (
  CityID INTEGER,
  Population INTEGER,
  DistrictID INTEGER
);

CREATE TABLE district (
  DistrictID INTEGER,
  DistrictName STRING
);

CREATE TABLE budget_allocation (
  CityID INTEGER,
  Allocation FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "city": {
      "business_purpose": "Stores city-specific data including population and district",
      "optimization_role": "business_data",
      "columns": {
        "CityID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Primary key",
          "sample_values": "1, 2, 3"
        },
        "Population": {
          "data_type": "INTEGER",
          "business_meaning": "Population of the city",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "100000, 200000, 300000"
        },
        "DistrictID": {
          "data_type": "INTEGER",
          "business_meaning": "District to which the city belongs",
          "optimization_purpose": "Constraint grouping",
          "sample_values": "1, 2, 3"
        }
      }
    },
    "district": {
      "business_purpose": "Stores district-specific data including minimum budget allocation",
      "optimization_role": "business_data",
      "columns": {
        "DistrictID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each district",
          "optimization_purpose": "Primary key",
          "sample_values": "1, 2, 3"
        },
        "DistrictName": {
          "data_type": "STRING",
          "business_meaning": "Name of the district",
          "optimization_purpose": "Business context",
          "sample_values": "North, South, East"
        }
      }
    },
    "budget_allocation": {
      "business_purpose": "Stores the budget allocated to each city",
      "optimization_role": "decision_variables",
      "columns": {
        "CityID": {
          "data_type": "INTEGER",
          "business_meaning": "City to which the budget is allocated",
          "optimization_purpose": "Foreign key",
          "sample_values": "1, 2, 3"
        },
        "Allocation": {
          "data_type": "FLOAT",
          "business_meaning": "Budget allocated to the city",
          "optimization_purpose": "Decision variable",
          "sample_values": "50000.0, 75000.0, 100000.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "TotalBudget": {
    "sample_value": 1000000,
    "data_type": "INTEGER",
    "business_meaning": "Total budget available for allocation",
    "optimization_role": "Upper bound for total allocation constraint",
    "configuration_type": "scalar_parameter"
  },
  "MinimumAllocation": {
    "sample_value": 50000,
    "data_type": "INTEGER",
    "business_meaning": "Minimum budget allocation per city",
    "optimization_role": "Lower bound for city allocation constraint",
    "configuration_type": "scalar_parameter"
  },
  "DistrictMinimum_j": {
    "sample_value": 200000,
    "data_type": "INTEGER",
    "business_meaning": "Minimum budget allocation per district",
    "optimization_role": "Lower bound for district allocation 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": "world_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": "world_1",
  "iteration": 1,
  "business_context": "A government agency aims to allocate a fixed budget across cities to maximize the total population served while ensuring equitable distribution across districts and respecting budget constraints.",
  "optimization_problem_description": "Maximize the total population served by allocating a fixed budget across cities, subject to district-level equity constraints and total budget limits.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Population_i \u00d7 Allocation_i)",
    "decision_variables": "Allocation_i: continuous variable representing the budget allocated to city i",
    "constraints": [
      "\u2211(Allocation_i) \u2264 TotalBudget",
      "Allocation_i \u2265 MinimumAllocation for all i",
      "\u2211(Allocation_i for i in district j) \u2265 DistrictMinimum_j for all j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Population_i": {
        "currently_mapped_to": "city.Population",
        "mapping_adequacy": "good",
        "description": "Population of city i, used as the coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "TotalBudget": {
        "currently_mapped_to": "business_configuration_logic.TotalBudget",
        "mapping_adequacy": "good",
        "description": "Total budget available for allocation"
      },
      "MinimumAllocation": {
        "currently_mapped_to": "business_configuration_logic.MinimumAllocation",
        "mapping_adequacy": "good",
        "description": "Minimum budget allocation per city"
      },
      "DistrictMinimum_j": {
        "currently_mapped_to": "business_configuration_logic.DistrictMinimum_j",
        "mapping_adequacy": "good",
        "description": "Minimum budget allocation per district j"
      }
    },
    "decision_variables": {
      "Allocation_i": {
        "currently_mapped_to": "budget_allocation.Allocation",
        "mapping_adequacy": "good",
        "description": "Budget allocated to city i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
