Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:38:53

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 league wants to optimize the selection of players for a season to maximize the overall team performance based on draft picks and player statistics.",
  "optimization_problem": "The goal is to maximize the total performance score of selected players for a team within a season, considering constraints on draft picks and team composition.",
  "objective": "maximize total_performance_score = \u2211(performance_coefficient[i] * x[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for performance coefficients and constraint bounds, modifying existing tables to include necessary columns, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data for performance scores and team composition constraints",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for performance coefficients and constraint bounds, modifying existing tables to include necessary columns, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Player (
  player_id INTEGER,
  performance_coefficient FLOAT,
  selected BOOLEAN
);

CREATE TABLE PerformanceCoefficients (
  player_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE ConstraintBounds (
  constraint_name STRING,
  value INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Player": {
      "business_purpose": "Stores information about players",
      "optimization_role": "decision_variables",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each player",
          "optimization_purpose": "Identifies players in optimization model",
          "sample_values": "1, 2, 3"
        },
        "performance_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Performance score of the player",
          "optimization_purpose": "Used in objective function to maximize performance",
          "sample_values": "0.85, 0.9, 0.95"
        },
        "selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the player is selected",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    },
    "PerformanceCoefficients": {
      "business_purpose": "Stores performance coefficients for players",
      "optimization_role": "objective_coefficients",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each player",
          "optimization_purpose": "Links to Player table",
          "sample_values": "1, 2, 3"
        },
        "coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Performance coefficient for optimization",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.85, 0.9, 0.95"
        }
      }
    },
    "ConstraintBounds": {
      "business_purpose": "Stores constraint bounds for team composition",
      "optimization_role": "constraint_bounds",
      "columns": {
        "constraint_name": {
          "data_type": "STRING",
          "business_meaning": "Name of the constraint",
          "optimization_purpose": "Identifies constraint in optimization model",
          "sample_values": "max_players_per_team, max_draft_pick_sum"
        },
        "value": {
          "data_type": "INTEGER",
          "business_meaning": "Value of the constraint",
          "optimization_purpose": "Used in constraint formulation",
          "sample_values": "25, 100"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_players_per_team": {
    "sample_value": 25,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of players allowed in a team",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "max_draft_pick_sum": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum allowable sum of draft pick numbers",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "min_defenders": {
    "sample_value": 4,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of defenders required in the team",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "min_midfielders": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of midfielders required in the team",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "min_forwards": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of forwards required in the team",
    "optimization_role": "Used as a constraint 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": "match_season",
  "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": "match_season",
  "iteration": 1,
  "business_context": "A sports league is optimizing player selection for a season to maximize team performance, considering constraints on team composition and draft picks.",
  "optimization_problem_description": "Maximize the total performance score of selected players while adhering to constraints on the number of players, draft pick limits, and team composition requirements.",
  "optimization_formulation": {
    "objective": "maximize total_performance_score = \u2211(PerformanceCoefficients.coefficient[i] * Player.selected[i])",
    "decision_variables": "Player.selected[i] for each player i, where selected is a binary variable indicating if a player is chosen",
    "constraints": [
      "\u2211(Player.selected[i]) <= business_configuration_logic.max_players_per_team",
      "\u2211(DraftPickNumber[i] * Player.selected[i]) <= business_configuration_logic.max_draft_pick_sum",
      "\u2211(Defender.selected[i]) >= business_configuration_logic.min_defenders",
      "\u2211(Midfielder.selected[i]) >= business_configuration_logic.min_midfielders",
      "\u2211(Forward.selected[i]) >= business_configuration_logic.min_forwards"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "performance_coefficient[i]": {
        "currently_mapped_to": "PerformanceCoefficients.coefficient",
        "mapping_adequacy": "good",
        "description": "Performance coefficient for each player used in the objective function"
      }
    },
    "constraint_bounds": {
      "max_players_per_team": {
        "currently_mapped_to": "business_configuration_logic.max_players_per_team",
        "mapping_adequacy": "good",
        "description": "Maximum number of players allowed in a team"
      },
      "max_draft_pick_sum": {
        "currently_mapped_to": "business_configuration_logic.max_draft_pick_sum",
        "mapping_adequacy": "good",
        "description": "Maximum allowable sum of draft pick numbers"
      },
      "min_defenders": {
        "currently_mapped_to": "business_configuration_logic.min_defenders",
        "mapping_adequacy": "good",
        "description": "Minimum number of defenders required in the team"
      },
      "min_midfielders": {
        "currently_mapped_to": "business_configuration_logic.min_midfielders",
        "mapping_adequacy": "good",
        "description": "Minimum number of midfielders required in the team"
      },
      "min_forwards": {
        "currently_mapped_to": "business_configuration_logic.min_forwards",
        "mapping_adequacy": "good",
        "description": "Minimum number of forwards required in the team"
      }
    },
    "decision_variables": {
      "selected[i]": {
        "currently_mapped_to": "Player.selected",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if a player is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
