Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:38:03

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 allocation of matches to cities to maximize the total GDP impact while considering temperature constraints for each month.",
  "optimization_problem": "The goal is to allocate a set of matches to different cities such that the total GDP impact is maximized. Each city has a specific GDP contribution per match, and matches can only be held in cities where the temperature is within a suitable range for that month.",
  "objective": "maximize total_GDP_impact = sum(GDP_contribution_per_match[city_id] * x[match_id, city_id])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for decision variables, modifying existing tables to include temperature suitability ranges, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine temperature suitability range and refine GDP contribution per match",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for decision variables, modifying existing tables to include temperature suitability ranges, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE city (
  city_id INTEGER,
  GDP FLOAT
);

CREATE TABLE temperature (
  city_id INTEGER,
  month STRING,
  min_temp FLOAT,
  max_temp FLOAT
);

CREATE TABLE match_allocation (
  match_id INTEGER,
  city_id INTEGER,
  is_allocated BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "city": {
      "business_purpose": "Stores information about cities including GDP",
      "optimization_role": "objective_coefficients",
      "columns": {
        "city_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Used to index cities in optimization",
          "sample_values": "1, 2, 3"
        },
        "GDP": {
          "data_type": "FLOAT",
          "business_meaning": "GDP contribution of the city per match",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "1000.0, 2000.0, 3000.0"
        }
      }
    },
    "temperature": {
      "business_purpose": "Stores monthly temperature data for each city",
      "optimization_role": "constraint_bounds",
      "columns": {
        "city_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Used to index cities in optimization",
          "sample_values": "1, 2, 3"
        },
        "month": {
          "data_type": "STRING",
          "business_meaning": "Month of the year",
          "optimization_purpose": "Used to index temperature data",
          "sample_values": "Jan, Feb, Mar"
        },
        "min_temp": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum suitable temperature for matches",
          "optimization_purpose": "Lower bound in temperature constraints",
          "sample_values": "15.0, 16.0, 17.0"
        },
        "max_temp": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum suitable temperature for matches",
          "optimization_purpose": "Upper bound in temperature constraints",
          "sample_values": "25.0, 26.0, 27.0"
        }
      }
    },
    "match_allocation": {
      "business_purpose": "Stores decision variables for match allocations",
      "optimization_role": "decision_variables",
      "columns": {
        "match_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each match",
          "optimization_purpose": "Used to index matches in optimization",
          "sample_values": "1, 2, 3"
        },
        "city_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Used to index cities in optimization",
          "sample_values": "1, 2, 3"
        },
        "is_allocated": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a match is allocated to a city",
          "optimization_purpose": "Binary decision variable",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "temperature_suitability_range": {
    "sample_value": "15-25",
    "data_type": "STRING",
    "business_meaning": "Temperature range suitable for holding matches",
    "optimization_role": "Used to ensure matches are held in cities with suitable temperatures",
    "configuration_type": "scalar_parameter"
  },
  "gdp_contribution_formula": {
    "formula_expression": "city.GDP * match_importance_factor",
    "data_type": "STRING",
    "business_meaning": "Calculates GDP contribution per match based on city GDP and match importance",
    "optimization_role": "Used to calculate objective coefficients for GDP impact",
    "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 is optimizing the allocation of matches to cities to maximize GDP impact while ensuring matches are held in cities with suitable temperatures for each month.",
  "optimization_problem_description": "Allocate matches to cities to maximize total GDP impact, ensuring temperature suitability for each month.",
  "optimization_formulation": {
    "objective": "maximize total_GDP_impact = sum(city.GDP * is_allocated[match_id, city_id])",
    "decision_variables": "is_allocated[match_id, city_id] - binary variable indicating if a match is allocated to a city",
    "constraints": [
      "sum(is_allocated[match_id, city_id]) <= 1 for each match_id",
      "min_temp <= current_month_temp <= max_temp for each city_id and month"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "GDP_contribution[city_id]": {
        "currently_mapped_to": "city.GDP",
        "mapping_adequacy": "good",
        "description": "GDP contribution of the city per match"
      }
    },
    "constraint_bounds": {
      "temperature_suitability[city_id, month]": {
        "currently_mapped_to": "temperature.min_temp and temperature.max_temp",
        "mapping_adequacy": "good",
        "description": "Temperature suitability range for each city and month"
      }
    },
    "decision_variables": {
      "is_allocated[match_id, city_id]": {
        "currently_mapped_to": "match_allocation.is_allocated",
        "mapping_adequacy": "good",
        "description": "Indicates if a match is allocated to a city",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
