Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:27:47

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 bodybuilding competition organizer wants to select a team of bodybuilders to maximize the total score based on their Snatch and Clean & Jerk performances, while ensuring the team meets certain diversity and physical criteria.",
  "optimization_problem": "The goal is to maximize the total score of the selected team, which is the sum of the Snatch and Clean & Jerk scores of the chosen bodybuilders. The selection must respect constraints on the total number of bodybuilders, their average height, and their average weight.",
  "objective": "maximize \u2211(Snatch_i + Clean_Jerk_i) * x_i, where x_i is a binary decision variable indicating whether bodybuilder i is selected",
  "table_count": 1,
  "key_changes": [
    "Schema changes include adding a table for decision variables and updating configuration logic to handle team size constraints and business metrics."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints and ensure all necessary decision variables are included",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a table for decision variables and updating configuration logic to handle team size constraints and business metrics.

CREATE TABLE body_builder (
  Snatch FLOAT,
  Clean_Jerk FLOAT
);

CREATE TABLE people (
  Height FLOAT,
  Weight FLOAT
);

CREATE TABLE team_selection (
  is_selected BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "body_builder": {
      "business_purpose": "Stores performance scores of bodybuilders",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Snatch": {
          "data_type": "FLOAT",
          "business_meaning": "Snatch score of the bodybuilder",
          "optimization_purpose": "Used in the objective function",
          "sample_values": "150.5, 160.0, 170.5"
        },
        "Clean_Jerk": {
          "data_type": "FLOAT",
          "business_meaning": "Clean & Jerk score of the bodybuilder",
          "optimization_purpose": "Used in the objective function",
          "sample_values": "200.0, 210.5, 220.0"
        }
      }
    },
    "people": {
      "business_purpose": "Stores physical attributes of bodybuilders",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Height": {
          "data_type": "FLOAT",
          "business_meaning": "Height of the bodybuilder in cm",
          "optimization_purpose": "Used in the average height constraint",
          "sample_values": "175.0, 180.0, 185.0"
        },
        "Weight": {
          "data_type": "FLOAT",
          "business_meaning": "Weight of the bodybuilder in kg",
          "optimization_purpose": "Used in the average weight constraint",
          "sample_values": "90.0, 95.0, 100.0"
        }
      }
    },
    "team_selection": {
      "business_purpose": "Indicates whether a bodybuilder is selected for the team",
      "optimization_role": "decision_variables",
      "columns": {
        "is_selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the bodybuilder is selected for the team",
          "optimization_purpose": "Binary decision variable in the optimization model",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "team_size_limit": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of bodybuilders allowed in the team",
    "optimization_role": "Constraint on the total number of bodybuilders",
    "configuration_type": "scalar_parameter"
  },
  "average_height_constraint": {
    "formula_expression": "\u2211(Height_i * x_i) / \u2211x_i \u2265 170",
    "data_type": "STRING",
    "business_meaning": "Minimum average height requirement for the team",
    "optimization_role": "Constraint on the average height of the team",
    "configuration_type": "business_logic_formula"
  },
  "average_weight_constraint": {
    "formula_expression": "\u2211(Weight_i * x_i) / \u2211x_i \u2264 100",
    "data_type": "STRING",
    "business_meaning": "Maximum average weight requirement for the team",
    "optimization_role": "Constraint on the average weight of the team",
    "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": "body_builder",
  "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": "body_builder",
  "iteration": 1,
  "business_context": "A bodybuilding competition organizer wants to select a team of bodybuilders to maximize the total score based on their Snatch and Clean & Jerk performances, while ensuring the team meets certain diversity and physical criteria. The selection must respect constraints on the total number of bodybuilders, their average height, and their average weight.",
  "optimization_problem_description": "The goal is to maximize the total score of the selected team, which is the sum of the Snatch and Clean & Jerk scores of the chosen bodybuilders. The selection must respect constraints on the total number of bodybuilders, their average height, and their average weight.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Snatch_i + Clean_Jerk_i) * x_i, where x_i is a binary decision variable indicating whether bodybuilder i is selected",
    "decision_variables": "x_i: binary decision variable indicating whether bodybuilder i is selected",
    "constraints": [
      "\u2211x_i \u2264 team_size_limit: Total number of bodybuilders in the team must not exceed the limit",
      "\u2211(Height_i * x_i) \u2265 170 * \u2211x_i: Average height of the team must be at least 170 cm",
      "\u2211(Weight_i * x_i) \u2264 100 * \u2211x_i: Average weight of the team must not exceed 100 kg"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Snatch_i": {
        "currently_mapped_to": "body_builder.Snatch",
        "mapping_adequacy": "good",
        "description": "Snatch score of bodybuilder i"
      },
      "Clean_Jerk_i": {
        "currently_mapped_to": "body_builder.Clean_Jerk",
        "mapping_adequacy": "good",
        "description": "Clean & Jerk score of bodybuilder i"
      }
    },
    "constraint_bounds": {
      "team_size_limit": {
        "currently_mapped_to": "business_configuration_logic.team_size_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of bodybuilders allowed in the team"
      },
      "Height_i": {
        "currently_mapped_to": "people.Height",
        "mapping_adequacy": "good",
        "description": "Height of bodybuilder i"
      },
      "Weight_i": {
        "currently_mapped_to": "people.Weight",
        "mapping_adequacy": "good",
        "description": "Weight of bodybuilder i"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "team_selection.is_selected",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether bodybuilder i is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
