Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:38:38

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either 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
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: poker_player

```sql
CREATE TABLE poker_player (
  Poker_Player_ID NUMBER,
  People_ID NUMBER,
  Final_Table_Made NUMBER,
  Best_Finish NUMBER,
  Money_Rank NUMBER,
  Earnings NUMBER
);
```

```sql
CREATE TABLE people (
  People_ID NUMBER,
  Nationality TEXT,
  Name TEXT,
  Birth_Date TEXT,
  Height NUMBER
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "poker_player",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 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 needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "poker_player",
  "iteration": 0,
  "business_context": "A poker tournament organizer wants to optimize the allocation of prize money to players based on their performance metrics to maximize the overall satisfaction of players while staying within a budget.",
  "optimization_problem_description": "The goal is to maximize the total satisfaction of players by allocating prize money based on their performance metrics such as Final_Table_Made, Best_Finish, and Money_Rank, while ensuring the total prize money does not exceed the budget.",
  "optimization_formulation": {
    "objective": "maximize total_satisfaction = \u2211(satisfaction_coefficient[i] * prize_money[i])",
    "decision_variables": "prize_money[i] for each player i, representing the prize money allocated to player i (continuous)",
    "constraints": [
      "\u2211(prize_money[i]) \u2264 total_budget",
      "prize_money[i] \u2265 0 for all i",
      "prize_money[i] \u2264 max_prize_limit for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "satisfaction_coefficient[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the satisfaction derived from the prize money allocated to player i based on their performance"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "the total budget available for prize money allocation"
      },
      "max_prize_limit": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "the maximum prize money that can be allocated to any single player"
      }
    },
    "decision_variables": {
      "prize_money[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "the amount of prize money allocated to player i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "satisfaction coefficients for each player based on performance metrics",
    "total budget for prize money allocation",
    "maximum prize limit for individual players"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine satisfaction coefficients and budget constraints for a complete model"
  }
}
