Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:32:05

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 gymnastics competition requires selecting a team of gymnasts to maximize the total points scored across all events, while ensuring that each gymnast does not exceed a maximum number of events they can participate in.",
  "optimization_problem": "The goal is to maximize the total points scored by the team across all events, subject to constraints on the number of events each gymnast can participate in and the total number of gymnasts on the team.",
  "objective": "maximize \u2211(Floor_Exercise_Points * x1 + Pommel_Horse_Points * x2 + Rings_Points * x3 + Vault_Points * x4 + Parallel_Bars_Points * x5 + Horizontal_Bar_Points * x6)",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for decision variables and constraint bounds, and updating business configuration logic to handle scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define constraints on the number of events per gymnast and the total number of gymnasts on the team",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, and updating business configuration logic to handle scalar parameters and formulas.

CREATE TABLE gymnast (
  Floor_Exercise_Points FLOAT,
  Pommel_Horse_Points FLOAT,
  Rings_Points FLOAT,
  Vault_Points FLOAT,
  Parallel_Bars_Points FLOAT,
  Horizontal_Bar_Points FLOAT
);

CREATE TABLE gymnast_event_participation (
  floor_exercise BOOLEAN,
  pommel_horse BOOLEAN,
  rings BOOLEAN,
  vault BOOLEAN,
  parallel_bars BOOLEAN,
  horizontal_bar BOOLEAN
);

CREATE TABLE team_constraints (
  max_events_per_gymnast INTEGER,
  max_gymnasts_on_team INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "gymnast": {
      "business_purpose": "Stores gymnast performance data across events",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Floor_Exercise_Points": {
          "data_type": "FLOAT",
          "business_meaning": "Points scored by a gymnast in the floor exercise",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "9.5"
        },
        "Pommel_Horse_Points": {
          "data_type": "FLOAT",
          "business_meaning": "Points scored by a gymnast in the pommel horse event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "8.7"
        },
        "Rings_Points": {
          "data_type": "FLOAT",
          "business_meaning": "Points scored by a gymnast in the rings event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "9.0"
        },
        "Vault_Points": {
          "data_type": "FLOAT",
          "business_meaning": "Points scored by a gymnast in the vault event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "9.2"
        },
        "Parallel_Bars_Points": {
          "data_type": "FLOAT",
          "business_meaning": "Points scored by a gymnast in the parallel bars event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "8.9"
        },
        "Horizontal_Bar_Points": {
          "data_type": "FLOAT",
          "business_meaning": "Points scored by a gymnast in the horizontal bar event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "9.1"
        }
      }
    },
    "gymnast_event_participation": {
      "business_purpose": "Binary decision variables for event participation",
      "optimization_role": "decision_variables",
      "columns": {
        "floor_exercise": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the gymnast participates in the floor exercise",
          "optimization_purpose": "Decision variable x1",
          "sample_values": "true"
        },
        "pommel_horse": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the gymnast participates in the pommel horse event",
          "optimization_purpose": "Decision variable x2",
          "sample_values": "false"
        },
        "rings": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the gymnast participates in the rings event",
          "optimization_purpose": "Decision variable x3",
          "sample_values": "true"
        },
        "vault": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the gymnast participates in the vault event",
          "optimization_purpose": "Decision variable x4",
          "sample_values": "false"
        },
        "parallel_bars": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the gymnast participates in the parallel bars event",
          "optimization_purpose": "Decision variable x5",
          "sample_values": "true"
        },
        "horizontal_bar": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the gymnast participates in the horizontal bar event",
          "optimization_purpose": "Decision variable x6",
          "sample_values": "false"
        }
      }
    },
    "team_constraints": {
      "business_purpose": "Constraints on the number of events per gymnast and the total number of gymnasts on the team",
      "optimization_role": "constraint_bounds",
      "columns": {
        "max_events_per_gymnast": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of events a gymnast can participate in",
          "optimization_purpose": "Constraint bound",
          "sample_values": "3"
        },
        "max_gymnasts_on_team": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of gymnasts on the team",
          "optimization_purpose": "Constraint bound",
          "sample_values": "10"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_events_per_gymnast": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of events a gymnast can participate in",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "max_gymnasts_on_team": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of gymnasts on the team",
    "optimization_role": "Constraint bound in optimization model",
    "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": "gymnast",
  "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": "gymnast",
  "iteration": 1,
  "business_context": "A gymnastics competition requires selecting a team of gymnasts to maximize the total points scored across all events, while ensuring that each gymnast does not exceed a maximum number of events they can participate in and the total number of gymnasts on the team does not exceed a specified limit.",
  "optimization_problem_description": "The goal is to maximize the total points scored by the team across all events, subject to constraints on the number of events each gymnast can participate in and the total number of gymnasts on the team.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Floor_Exercise_Points * x1 + Pommel_Horse_Points * x2 + Rings_Points * x3 + Vault_Points * x4 + Parallel_Bars_Points * x5 + Horizontal_Bar_Points * x6)",
    "decision_variables": "x1, x2, x3, x4, x5, x6 (binary variables indicating participation in each event)",
    "constraints": "x1 + x2 + x3 + x4 + x5 + x6 \u2264 max_events_per_gymnast (for each gymnast), \u2211(x1 + x2 + x3 + x4 + x5 + x6) \u2264 max_gymnasts_on_team"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Floor_Exercise_Points": {
        "currently_mapped_to": "gymnast.Floor_Exercise_Points",
        "mapping_adequacy": "good",
        "description": "Coefficient for floor exercise participation in the objective function"
      },
      "Pommel_Horse_Points": {
        "currently_mapped_to": "gymnast.Pommel_Horse_Points",
        "mapping_adequacy": "good",
        "description": "Coefficient for pommel horse participation in the objective function"
      },
      "Rings_Points": {
        "currently_mapped_to": "gymnast.Rings_Points",
        "mapping_adequacy": "good",
        "description": "Coefficient for rings participation in the objective function"
      },
      "Vault_Points": {
        "currently_mapped_to": "gymnast.Vault_Points",
        "mapping_adequacy": "good",
        "description": "Coefficient for vault participation in the objective function"
      },
      "Parallel_Bars_Points": {
        "currently_mapped_to": "gymnast.Parallel_Bars_Points",
        "mapping_adequacy": "good",
        "description": "Coefficient for parallel bars participation in the objective function"
      },
      "Horizontal_Bar_Points": {
        "currently_mapped_to": "gymnast.Horizontal_Bar_Points",
        "mapping_adequacy": "good",
        "description": "Coefficient for horizontal bar participation in the objective function"
      }
    },
    "constraint_bounds": {
      "max_events_per_gymnast": {
        "currently_mapped_to": "team_constraints.max_events_per_gymnast",
        "mapping_adequacy": "good",
        "description": "Maximum number of events a gymnast can participate in"
      },
      "max_gymnasts_on_team": {
        "currently_mapped_to": "team_constraints.max_gymnasts_on_team",
        "mapping_adequacy": "good",
        "description": "Maximum number of gymnasts on the team"
      }
    },
    "decision_variables": {
      "x1": {
        "currently_mapped_to": "gymnast_event_participation.floor_exercise",
        "mapping_adequacy": "good",
        "description": "Decision variable for floor exercise participation",
        "variable_type": "binary"
      },
      "x2": {
        "currently_mapped_to": "gymnast_event_participation.pommel_horse",
        "mapping_adequacy": "good",
        "description": "Decision variable for pommel horse participation",
        "variable_type": "binary"
      },
      "x3": {
        "currently_mapped_to": "gymnast_event_participation.rings",
        "mapping_adequacy": "good",
        "description": "Decision variable for rings participation",
        "variable_type": "binary"
      },
      "x4": {
        "currently_mapped_to": "gymnast_event_participation.vault",
        "mapping_adequacy": "good",
        "description": "Decision variable for vault participation",
        "variable_type": "binary"
      },
      "x5": {
        "currently_mapped_to": "gymnast_event_participation.parallel_bars",
        "mapping_adequacy": "good",
        "description": "Decision variable for parallel bars participation",
        "variable_type": "binary"
      },
      "x6": {
        "currently_mapped_to": "gymnast_event_participation.horizontal_bar",
        "mapping_adequacy": "good",
        "description": "Decision variable for horizontal bar participation",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
