Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:38:53

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: match_season

```sql
CREATE TABLE country (
  Country_id NUMBER,
  Country_name TEXT,
  Capital TEXT,
  Official_native_language TEXT
);
```

```sql
CREATE TABLE team (
  Team_id NUMBER,
  Name TEXT
);
```

```sql
CREATE TABLE match_season (
  Season NUMBER,
  Player TEXT,
  Position TEXT,
  Country NUMBER,
  Team NUMBER,
  Draft_Pick_Number NUMBER,
  Draft_Class TEXT,
  College TEXT
);
```

```sql
CREATE TABLE player (
  Player_ID NUMBER,
  Player TEXT,
  Years_Played TEXT,
  Total_WL TEXT,
  Singles_WL TEXT,
  Doubles_WL TEXT,
  Team 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": "match_season",
  "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": "match_season",
  "iteration": 0,
  "business_context": "A sports league wants to optimize the selection of players for a season to maximize the overall team performance based on draft picks and player statistics.",
  "optimization_problem_description": "The goal is to maximize the total performance score of selected players for a team within a season, considering constraints on draft picks and team composition.",
  "optimization_formulation": {
    "objective": "maximize total_performance_score = \u2211(performance_coefficient[i] * x[i])",
    "decision_variables": "x[i] = 1 if player i is selected, 0 otherwise (binary)",
    "constraints": [
      "\u2211(x[i]) \u2264 max_players_per_team",
      "\u2211(draft_pick_number[i] * x[i]) \u2264 max_draft_pick_sum",
      "\u2211(x[i] | position[i] = 'Goalkeeper') = 1",
      "\u2211(x[i] | position[i] = 'Defender') \u2265 min_defenders",
      "\u2211(x[i] | position[i] = 'Midfielder') \u2265 min_midfielders",
      "\u2211(x[i] | position[i] = 'Forward') \u2265 min_forwards"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "performance_coefficient[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the performance score of player i"
      }
    },
    "constraint_bounds": {
      "max_players_per_team": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of players allowed in a team"
      },
      "max_draft_pick_sum": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum allowable sum of draft pick numbers for selected players"
      },
      "min_defenders": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum number of defenders required in the team"
      },
      "min_midfielders": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum number of midfielders required in the team"
      },
      "min_forwards": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum number of forwards required in the team"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "match_season.Player",
        "mapping_adequacy": "partial",
        "description": "binary variable indicating if player i is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Performance scores for each player",
    "Maximum number of players per team",
    "Maximum allowable sum of draft pick numbers",
    "Minimum number of players required for each position"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data for performance scores and team composition constraints"
  }
}
