Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:48:08

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "A sports league aims to optimize the allocation of players to clubs to maximize the total points scored across all clubs, while respecting constraints on the number of players per club and the total budget for player salaries.",
  "optimization_problem": "The league seeks to maximize the total points scored by all clubs by optimally assigning players to clubs. The constraints include a maximum number of players per club, a minimum number of players per club, and a total budget limit for player salaries.",
  "objective": "maximize \u2211(Points_ij * X_ij) where Points_ij is the points scored by player i in club j, and X_ij is a binary decision variable indicating whether player i is assigned to club j.",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization requirements (player_points and player_club_assignments) and updating business configuration logic with scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map the missing objective coefficients and decision variables.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization requirements (player_points and player_club_assignments) and updating business configuration logic with scalar parameters and formulas.

CREATE TABLE club_constraints (
  club_id INTEGER,
  max_players INTEGER,
  min_players INTEGER,
  budget FLOAT
);

CREATE TABLE player_salaries (
  player_id INTEGER,
  salary FLOAT
);

CREATE TABLE player_points (
  player_id INTEGER,
  club_id INTEGER,
  points INTEGER
);

CREATE TABLE player_club_assignments (
  player_id INTEGER,
  club_id INTEGER,
  assignment INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "club_constraints": {
      "business_purpose": "Constraints on the number of players and budget for each club",
      "optimization_role": "constraint_bounds",
      "columns": {
        "club_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the club",
          "optimization_purpose": "Identifies the club for which constraints apply",
          "sample_values": "1, 2, 3"
        },
        "max_players": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of players allowed per club",
          "optimization_purpose": "Upper bound for player count constraint",
          "sample_values": "20, 25, 30"
        },
        "min_players": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of players required per club",
          "optimization_purpose": "Lower bound for player count constraint",
          "sample_values": "15, 18, 20"
        },
        "budget": {
          "data_type": "FLOAT",
          "business_meaning": "Total budget available for player salaries per club",
          "optimization_purpose": "Upper bound for budget constraint",
          "sample_values": "1000000, 1500000, 2000000"
        }
      }
    },
    "player_salaries": {
      "business_purpose": "Salaries of players",
      "optimization_role": "business_data",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the player",
          "optimization_purpose": "Identifies the player for salary data",
          "sample_values": "1, 2, 3"
        },
        "salary": {
          "data_type": "FLOAT",
          "business_meaning": "Salary of the player",
          "optimization_purpose": "Used in budget constraint calculation",
          "sample_values": "50000, 75000, 100000"
        }
      }
    },
    "player_points": {
      "business_purpose": "Points scored by players in clubs",
      "optimization_role": "objective_coefficients",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the player",
          "optimization_purpose": "Identifies the player for points data",
          "sample_values": "1, 2, 3"
        },
        "club_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the club",
          "optimization_purpose": "Identifies the club for points data",
          "sample_values": "1, 2, 3"
        },
        "points": {
          "data_type": "INTEGER",
          "business_meaning": "Points scored by player in club",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "10, 15, 20"
        }
      }
    },
    "player_club_assignments": {
      "business_purpose": "Binary decision variable indicating whether player i is assigned to club j",
      "optimization_role": "decision_variables",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the player",
          "optimization_purpose": "Identifies the player for assignment data",
          "sample_values": "1, 2, 3"
        },
        "club_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the club",
          "optimization_purpose": "Identifies the club for assignment data",
          "sample_values": "1, 2, 3"
        },
        "assignment": {
          "data_type": "INTEGER",
          "business_meaning": "Binary decision variable indicating whether player is assigned to club",
          "optimization_purpose": "Decision variable",
          "sample_values": "0, 1"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Points_ij": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Points scored by player i in club j",
    "optimization_role": "Objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "X_ij": {
    "sample_value": 1,
    "data_type": "INTEGER",
    "business_meaning": "Binary decision variable indicating whether player i is assigned to club j",
    "optimization_role": "Decision variable",
    "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": "sports_competition",
  "iteration": 2,
  "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": "sports_competition",
  "iteration": 2,
  "business_context": "A sports league aims to optimize the allocation of players to clubs to maximize the total points scored across all clubs, while respecting constraints on the number of players per club and the total budget for player salaries.",
  "optimization_problem_description": "The league seeks to maximize the total points scored by all clubs by optimally assigning players to clubs. The constraints include a maximum number of players per club, a minimum number of players per club, and a total budget limit for player salaries.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Points_ij * X_ij) where Points_ij is the points scored by player i in club j, and X_ij is a binary decision variable indicating whether player i is assigned to club j.",
    "decision_variables": "X_ij: binary decision variable indicating whether player i is assigned to club j.",
    "constraints": "1. \u2211(X_ij) \u2264 max_players_j for each club j, 2. \u2211(X_ij) \u2265 min_players_j for each club j, 3. \u2211(Salary_i * X_ij) \u2264 budget_j for each club j."
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Points_ij": {
        "currently_mapped_to": "player_points.points",
        "mapping_adequacy": "good",
        "description": "Points scored by player i in club j."
      }
    },
    "constraint_bounds": {
      "max_players_j": {
        "currently_mapped_to": "club_constraints.max_players",
        "mapping_adequacy": "good",
        "description": "Maximum number of players allowed per club j."
      },
      "min_players_j": {
        "currently_mapped_to": "club_constraints.min_players",
        "mapping_adequacy": "good",
        "description": "Minimum number of players required per club j."
      },
      "budget_j": {
        "currently_mapped_to": "club_constraints.budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for player salaries per club j."
      }
    },
    "decision_variables": {
      "X_ij": {
        "currently_mapped_to": "player_club_assignments.assignment",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether player i is assigned to club j.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
