Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:46:15

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": "Optimizing player scheduling to maximize total ranking points earned across tournaments while respecting player availability and tournament constraints.",
  "optimization_problem": "The goal is to 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": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization requirements, modifying existing tables to better align with OR expert's mapping, and adding business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints and identify additional data sources for missing parameters.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization requirements, modifying existing tables to better align with OR expert's mapping, and adding 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
);


```

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
          ]
        }
      }
    }
  }
}


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": 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": "wta_1",
  "iteration": 1,
  "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] * x[i]) where x[i] is a binary decision variable indicating whether player i participates in a tournament.",
    "decision_variables": "x[i] \u2208 {0, 1} (binary decision variable indicating whether player i participates in a tournament)",
    "constraints": [
      "\u2211(x[i]) \u2264 max_tournaments_per_player for each player i (player participation limit)",
      "\u2211(x[i]) \u2264 max_players_per_tournament for each tournament (tournament capacity limit)",
      "x[i] \u2264 availability[i] for each player i (player availability constraint)",
      "\u2211(ranking_points[i] * x[i]) \u2264 max_total_ranking_points (total ranking points limit)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "ranking_points[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Ranking points earned by player i in a tournament."
      }
    },
    "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": {
        "currently_mapped_to": "matches.max_players_per_tournament",
        "mapping_adequacy": "good",
        "description": "Maximum number of players allowed in a tournament."
      },
      "availability[i]": {
        "currently_mapped_to": "player_availability.availability",
        "mapping_adequacy": "good",
        "description": "Availability of player i to participate in tournaments."
      },
      "max_total_ranking_points": {
        "currently_mapped_to": "business_configuration_logic.max_total_ranking_points",
        "mapping_adequacy": "good",
        "description": "Maximum total ranking points that can be earned in a tournament."
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "player_tournament_participation.participation",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether player i participates in a tournament.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "ranking_points[i] (ranking points earned by player i in a tournament)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify data source for ranking_points[i] to complete the linear formulation."
  }
}
