Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:31:00

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 poker tournament organizer wants to maximize the total earnings of selected poker players while ensuring diversity in nationalities and limiting the number of players with low money ranks.",
  "optimization_problem": "The organizer needs to select a subset of poker players to maximize their total earnings, ensuring that the selected players represent at least three different nationalities and that no more than 20% of the selected players have a money rank below 50.",
  "objective": "maximize \u2211(Earnings_i \u00d7 x_i) where x_i is a binary decision variable indicating whether player i is selected",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for decision variables and adding a configuration parameter for the maximum number of players. Business configuration logic updated to include scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints related to nationality diversity and ensure all required data is available",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for decision variables and adding a configuration parameter for the maximum number of players. Business configuration logic updated to include scalar parameters and formulas.

CREATE TABLE poker_player (
  Earnings FLOAT,
  Money_Rank INTEGER,
  Selected BOOLEAN
);

CREATE TABLE player_selection (
  Player_ID INTEGER,
  Selected BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "poker_player": {
      "business_purpose": "Stores information about poker players",
      "optimization_role": "objective_coefficients/constraint_bounds/business_data",
      "columns": {
        "Earnings": {
          "data_type": "FLOAT",
          "business_meaning": "Earnings of each poker player",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "1000.0, 1500.0, 2000.0"
        },
        "Money_Rank": {
          "data_type": "INTEGER",
          "business_meaning": "Money rank of each poker player",
          "optimization_purpose": "Used in constraint to limit players with money rank below 50",
          "sample_values": "45, 55, 60"
        },
        "Selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary decision variable indicating whether player is selected",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "true, false"
        }
      }
    },
    "player_selection": {
      "business_purpose": "Binary decision variables indicating whether each player is selected",
      "optimization_role": "decision_variables",
      "columns": {
        "Player_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each player",
          "optimization_purpose": "Links to poker_player table",
          "sample_values": "1, 2, 3"
        },
        "Selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary decision variable indicating whether player is selected",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_players": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of players to select",
    "optimization_role": "Upper bound for total players constraint",
    "configuration_type": "scalar_parameter"
  },
  "money_rank_threshold": {
    "sample_value": 50,
    "data_type": "INTEGER",
    "business_meaning": "Threshold for money rank to limit players",
    "optimization_role": "Used in constraint to limit players with money rank below 50",
    "configuration_type": "scalar_parameter"
  },
  "money_rank_percentage_limit": {
    "formula_expression": "SUM(IF(Money_Rank < money_rank_threshold, 1, 0)) / COUNT(*) <= 0.2",
    "data_type": "STRING",
    "business_meaning": "Formula to ensure no more than 20% of selected players have a money rank below 50",
    "optimization_role": "Constraint to limit players with money rank below 50",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "poker_player",
  "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": "poker_player",
  "iteration": 1,
  "business_context": "A poker tournament organizer wants to maximize the total earnings of selected poker players while ensuring diversity in nationalities and limiting the number of players with low money ranks.",
  "optimization_problem_description": "Select a subset of poker players to maximize their total earnings, ensuring that the selected players represent at least three different nationalities and that no more than 20% of the selected players have a money rank below 50.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Earnings_i \u00d7 x_i) where x_i is a binary decision variable indicating whether player i is selected",
    "decision_variables": "x_i \u2208 {0, 1} for each player i, indicating whether player i is selected",
    "constraints": [
      "\u2211(x_i) \u2264 max_players",
      "\u2211(IF(Money_Rank_i < money_rank_threshold, x_i, 0)) \u2264 0.2 \u00d7 \u2211(x_i)",
      "\u2211(IF(Nationality_i = nationality_j, x_i, 0)) \u2265 1 for at least three different nationalities j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Earnings_i": {
        "currently_mapped_to": "poker_player.Earnings",
        "mapping_adequacy": "good",
        "description": "Earnings of each poker player used as coefficients in the objective function"
      }
    },
    "constraint_bounds": {
      "max_players": {
        "currently_mapped_to": "business_configuration_logic.max_players",
        "mapping_adequacy": "good",
        "description": "Maximum number of players to select"
      },
      "money_rank_threshold": {
        "currently_mapped_to": "business_configuration_logic.money_rank_threshold",
        "mapping_adequacy": "good",
        "description": "Threshold for money rank to limit players"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "player_selection.Selected",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether player i is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Nationality data for each player to enforce diversity constraint"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Add nationality data to the schema to enforce the diversity constraint"
  }
}
