Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:46:15

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": "Optimizing player scheduling to maximize total ranking points earned across tournaments while respecting player availability, tournament participation limits, and ranking points allocation.",
  "optimization_problem": "Maximize the total ranking points earned by players across different tournaments, considering constraints such as player availability, tournament participation limits, and ranking points allocation.",
  "objective": "maximize \u2211(ranking_points[i] * x[i]) where x[i] is a binary decision variable indicating whether player i participates in a tournament.",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for ranking points, modifying existing tables to align with OR expert's mapping, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify data source for ranking_points[i] to complete the linear formulation.",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for ranking points, modifying existing tables to align with OR expert's mapping, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE player_availability (
  player_id INTEGER,
  availability BOOLEAN
);

CREATE TABLE player_tournament_participation (
  player_id INTEGER,
  tournament_id INTEGER,
  participation BOOLEAN
);

CREATE TABLE matches (
  match_id INTEGER,
  tournament_id INTEGER,
  draw_size INTEGER,
  max_players_per_tournament INTEGER
);

CREATE TABLE player_tournament_ranking_points (
  player_id INTEGER,
  tournament_id INTEGER,
  ranking_points INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "player_availability": {
      "business_purpose": "The availability of players to participate in tournaments.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a player.",
          "optimization_purpose": "Links availability to specific players.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "availability": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the player is available to participate in tournaments.",
          "optimization_purpose": "Constraint on player participation.",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "player_tournament_participation": {
      "business_purpose": "Binary decision variable indicating player participation in a tournament.",
      "optimization_role": "decision_variables",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a player.",
          "optimization_purpose": "Links participation to specific players.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "tournament_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a tournament.",
          "optimization_purpose": "Links participation to specific tournaments.",
          "sample_values": [
            101,
            102,
            103
          ]
        },
        "participation": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the player participates in the tournament.",
          "optimization_purpose": "Binary decision variable in optimization.",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "matches": {
      "business_purpose": "Details of matches in tournaments.",
      "optimization_role": "business_data",
      "columns": {
        "match_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a match.",
          "optimization_purpose": "Identifies specific matches.",
          "sample_values": [
            1001,
            1002,
            1003
          ]
        },
        "tournament_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a tournament.",
          "optimization_purpose": "Links matches to specific tournaments.",
          "sample_values": [
            101,
            102,
            103
          ]
        },
        "draw_size": {
          "data_type": "INTEGER",
          "business_meaning": "The number of players in the tournament.",
          "optimization_purpose": "Partial constraint on player participation.",
          "sample_values": [
            32,
            64,
            128
          ]
        },
        "max_players_per_tournament": {
          "data_type": "INTEGER",
          "business_meaning": "The maximum number of players allowed in a tournament.",
          "optimization_purpose": "Constraint on player participation.",
          "sample_values": [
            32,
            64,
            128
          ]
        }
      }
    },
    "player_tournament_ranking_points": {
      "business_purpose": "Ranking points earned by players in tournaments.",
      "optimization_role": "objective_coefficients",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a player.",
          "optimization_purpose": "Links ranking points to specific players.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "tournament_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a tournament.",
          "optimization_purpose": "Links ranking points to specific tournaments.",
          "sample_values": [
            101,
            102,
            103
          ]
        },
        "ranking_points": {
          "data_type": "INTEGER",
          "business_meaning": "Ranking points earned by the player in the tournament.",
          "optimization_purpose": "Coefficient in the objective function.",
          "sample_values": [
            100,
            200,
            300
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_tournaments_per_player": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "The maximum number of tournaments a player can participate in.",
    "optimization_role": "Constraint bound for player participation.",
    "configuration_type": "scalar_parameter"
  },
  "max_total_ranking_points": {
    "sample_value": 1000,
    "data_type": "INTEGER",
    "business_meaning": "The maximum total ranking points that can be earned in a tournament.",
    "optimization_role": "Constraint bound for ranking points.",
    "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": "wta_1",
  "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": "wta_1",
  "iteration": 2,
  "business_context": "Optimizing player scheduling to maximize total ranking points earned across tournaments while respecting player availability, tournament participation limits, and ranking points allocation.",
  "optimization_problem_description": "Maximize the total ranking points earned by players across different tournaments, considering constraints such as player availability, tournament participation limits, and ranking points allocation.",
  "optimization_formulation": {
    "objective": "maximize \u2211(ranking_points[i,j] * x[i,j]) where x[i,j] is a binary decision variable indicating whether player i participates in tournament j.",
    "decision_variables": "x[i,j] = binary decision variable indicating whether player i participates in tournament j.",
    "constraints": "1. \u2211(x[i,j]) <= max_tournaments_per_player for each player i. 2. \u2211(x[i,j]) <= max_players_per_tournament[j] for each tournament j. 3. x[i,j] <= availability[i] for each player i and tournament j."
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "ranking_points[i,j]": {
        "currently_mapped_to": "player_tournament_ranking_points.ranking_points",
        "mapping_adequacy": "good",
        "description": "Ranking points earned by player i in tournament j."
      }
    },
    "constraint_bounds": {
      "max_tournaments_per_player": {
        "currently_mapped_to": "business_configuration_logic.max_tournaments_per_player",
        "mapping_adequacy": "good",
        "description": "Maximum number of tournaments a player can participate in."
      },
      "max_players_per_tournament[j]": {
        "currently_mapped_to": "matches.max_players_per_tournament",
        "mapping_adequacy": "good",
        "description": "Maximum number of players allowed in tournament j."
      },
      "availability[i]": {
        "currently_mapped_to": "player_availability.availability",
        "mapping_adequacy": "good",
        "description": "Availability of player i to participate in tournaments."
      }
    },
    "decision_variables": {
      "x[i,j]": {
        "currently_mapped_to": "player_tournament_participation.participation",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether player i participates in tournament j.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
