Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:30:28

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 sports organization wants to optimize the selection of host cities for matches in a given year, considering factors like regional population, GDP, and average temperature during the match month.",
  "optimization_problem": "The goal is to maximize the overall benefit of selecting host cities for matches, where the benefit is a weighted sum of regional population, GDP, and average temperature during the match month. The selection must respect constraints such as the maximum number of matches per city and the total budget allocated for hosting.",
  "objective": "maximize \u2211(w1 * Population_i + w2 * GDP_i + w3 * Temperature_i) * x_i",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating tables for city data, match constraints, and objective coefficients. Configuration logic updates include scalar parameters for weights and constraints, and formulas for benefit calculation."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define the weights for the objective function and gather data for the constraints (Total_Matches, Total_Budget, Max_Matches_Per_City, Cost_i).",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for city data, match constraints, and objective coefficients. Configuration logic updates include scalar parameters for weights and constraints, and formulas for benefit calculation.

CREATE TABLE city_data (
  city_id INTEGER,
  population INTEGER,
  gdp FLOAT,
  avg_temperature FLOAT,
  hosting_cost FLOAT
);

CREATE TABLE match_constraints (
  constraint_id INTEGER,
  max_matches_per_city INTEGER,
  total_budget FLOAT
);

CREATE TABLE objective_coefficients (
  coefficient_id INTEGER,
  weight_population FLOAT,
  weight_gdp FLOAT,
  weight_temperature FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "city_data": {
      "business_purpose": "Contains data about potential host cities, including population, GDP, and average temperature during match month.",
      "optimization_role": "business_data",
      "columns": {
        "city_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Decision variable identifier",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "population": {
          "data_type": "INTEGER",
          "business_meaning": "Regional population of the city",
          "optimization_purpose": "Objective function component",
          "sample_values": [
            500000,
            1000000,
            1500000
          ]
        },
        "gdp": {
          "data_type": "FLOAT",
          "business_meaning": "GDP of the city",
          "optimization_purpose": "Objective function component",
          "sample_values": [
            50000.0,
            100000.0,
            150000.0
          ]
        },
        "avg_temperature": {
          "data_type": "FLOAT",
          "business_meaning": "Average temperature during the match month",
          "optimization_purpose": "Objective function component",
          "sample_values": [
            20.0,
            25.0,
            30.0
          ]
        },
        "hosting_cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost of hosting a match in the city",
          "optimization_purpose": "Constraint component",
          "sample_values": [
            100000.0,
            150000.0,
            200000.0
          ]
        }
      }
    },
    "match_constraints": {
      "business_purpose": "Stores constraints related to hosting matches, such as maximum number of matches per city and total budget.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "constraint_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each constraint",
          "optimization_purpose": "Constraint identifier",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "max_matches_per_city": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of matches per city",
          "optimization_purpose": "Constraint bound",
          "sample_values": [
            2,
            2,
            2
          ]
        },
        "total_budget": {
          "data_type": "FLOAT",
          "business_meaning": "Total budget constraint for hosting",
          "optimization_purpose": "Constraint bound",
          "sample_values": [
            1000000.0,
            1000000.0,
            1000000.0
          ]
        }
      }
    },
    "objective_coefficients": {
      "business_purpose": "Stores the weights for the objective function components (population, GDP, temperature).",
      "optimization_role": "objective_coefficients",
      "columns": {
        "coefficient_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each coefficient",
          "optimization_purpose": "Coefficient identifier",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "weight_population": {
          "data_type": "FLOAT",
          "business_meaning": "Weight for regional population in the objective function",
          "optimization_purpose": "Objective coefficient",
          "sample_values": [
            0.4,
            0.4,
            0.4
          ]
        },
        "weight_gdp": {
          "data_type": "FLOAT",
          "business_meaning": "Weight for GDP in the objective function",
          "optimization_purpose": "Objective coefficient",
          "sample_values": [
            0.3,
            0.3,
            0.3
          ]
        },
        "weight_temperature": {
          "data_type": "FLOAT",
          "business_meaning": "Weight for average temperature in the objective function",
          "optimization_purpose": "Objective coefficient",
          "sample_values": [
            0.3,
            0.3,
            0.3
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "w1": {
    "sample_value": 0.4,
    "data_type": "FLOAT",
    "business_meaning": "Weight for regional population in the objective function",
    "optimization_role": "Objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "w2": {
    "sample_value": 0.3,
    "data_type": "FLOAT",
    "business_meaning": "Weight for GDP in the objective function",
    "optimization_role": "Objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "w3": {
    "sample_value": 0.3,
    "data_type": "FLOAT",
    "business_meaning": "Weight for average temperature in the objective function",
    "optimization_role": "Objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "Total_Matches": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Total number of matches to be hosted",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Total_Budget": {
    "sample_value": 1000000,
    "data_type": "FLOAT",
    "business_meaning": "Total budget constraint for hosting",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Max_Matches_Per_City": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of matches per city",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Benefit_Calculation": {
    "formula_expression": "w1 * Population_i + w2 * GDP_i + w3 * Temperature_i",
    "data_type": "STRING",
    "business_meaning": "Calculation of the benefit for selecting a city as a host",
    "optimization_role": "Objective function component",
    "configuration_type": "business_logic_formula"
  }
}


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

JSON STRUCTURE REQUIRED:

{
  "database_id": "city_record",
  "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": "city_record",
  "iteration": 1,
  "business_context": "A sports organization aims to optimize the selection of host cities for matches in a given year, considering factors like regional population, GDP, and average temperature during the match month. The optimization must respect constraints such as the maximum number of matches per city and the total budget allocated for hosting.",
  "optimization_problem_description": "The goal is to maximize the overall benefit of selecting host cities for matches, where the benefit is a weighted sum of regional population, GDP, and average temperature during the match month. The selection must respect constraints such as the maximum number of matches per city and the total budget allocated for hosting.",
  "optimization_formulation": {
    "objective": "maximize \u2211(w1 * Population_i + w2 * GDP_i + w3 * Temperature_i) * x_i",
    "decision_variables": "x_i: binary decision variable indicating whether city i is selected as a host",
    "constraints": [
      "\u2211(x_i) \u2264 Total_Matches",
      "\u2211(hosting_cost_i * x_i) \u2264 Total_Budget",
      "x_i \u2264 Max_Matches_Per_City for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "w1": {
        "currently_mapped_to": "objective_coefficients.weight_population",
        "mapping_adequacy": "good",
        "description": "Weight for regional population in the objective function"
      },
      "w2": {
        "currently_mapped_to": "objective_coefficients.weight_gdp",
        "mapping_adequacy": "good",
        "description": "Weight for GDP in the objective function"
      },
      "w3": {
        "currently_mapped_to": "objective_coefficients.weight_temperature",
        "mapping_adequacy": "good",
        "description": "Weight for average temperature in the objective function"
      }
    },
    "constraint_bounds": {
      "Total_Matches": {
        "currently_mapped_to": "business_configuration_logic.Total_Matches",
        "mapping_adequacy": "good",
        "description": "Total number of matches to be hosted"
      },
      "Total_Budget": {
        "currently_mapped_to": "match_constraints.total_budget",
        "mapping_adequacy": "good",
        "description": "Total budget constraint for hosting"
      },
      "Max_Matches_Per_City": {
        "currently_mapped_to": "match_constraints.max_matches_per_city",
        "mapping_adequacy": "good",
        "description": "Maximum number of matches per city"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "city_data.city_id",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether city i is selected as a host",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
