Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-25 22:50:52

Prompt:
You are a business analyst creating structured optimization problem documentation.

DATA SOURCES EXPLANATION:
- FINAL OR ANALYSIS: Final converged optimization problem from alternating process (iteration 1), contains business context and schema mapping evaluation
- DATABASE SCHEMA: Current database structure after iterative adjustments  
- DATA DICTIONARY: Business meanings and optimization roles of tables and columns
- CURRENT STORED VALUES: Realistic business data generated by triple expert (business + data + optimization)
- BUSINESS CONFIGURATION: Scalar parameters and business logic formulas separated from table data

CRITICAL REQUIREMENTS: 
- Ensure problem description naturally leads to LINEAR or MIXED-INTEGER optimization formulation
- Make business context consistent with the intended decision variables and objectives
- Align constraint descriptions with expected mathematical constraints
- Ensure data descriptions map clearly to expected coefficient sources
- Maintain business authenticity while fixing mathematical consistency issues
- Avoid business scenarios that would naturally require nonlinear relationships (variable products, divisions, etc.)

AUTO-EXTRACTED CONTEXT REQUIREMENTS:
- Business decisions match expected decision variables: assign[player_id, school_id] (binary)
- Operational parameters align with expected linear objective: maximize ∑(performance_weight[school_id, position] × assign[player_id, school_id])
- Business configuration includes: Minimum number of players required to form a team (used for Used in team size constraint), Minimum number of players required in a specific position (used for Used in position constraints), Maximum number of players allowed in a specific position (used for Used in position constraints)
- Business logic formulas to express in natural language: Calculation of performance weight based on historical performance and position weight (calculation method for Used in objective function)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate

FINAL OR ANALYSIS:
{
  "database_id": "school_player",
  "iteration": 1,
  "business_context": "Optimize the allocation of players to schools based on school performance and player positions to maximize overall team performance while adhering to school enrollment limits and position constraints.",
  "optimization_problem_description": "Maximize the overall performance of teams by assigning players to schools in a way that aligns with the schools' historical performance and the players' positions, subject to school enrollment limits and position constraints.",
  "optimization_formulation": {
    "objective": "maximize \u2211(performance_weight[school_id, position] \u00d7 assign[player_id, school_id])",
    "decision_variables": "assign[player_id, school_id] (binary)",
    "constraints": [
      "\u2211(assign[player_id, school_id]) \u2264 school.enrollment for each school_id",
      "min_players[position] \u2264 \u2211(assign[player_id, school_id]) \u2264 max_players[position] for each position and school_id",
      "\u2211(assign[player_id, school_id]) \u2265 min_team_size for each school_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "performance_weight[school_id, position]": {
        "currently_mapped_to": "performance_weight.weight",
        "mapping_adequacy": "good",
        "description": "Performance weight for a school in a specific position"
      }
    },
    "constraint_bounds": {
      "school.enrollment": {
        "currently_mapped_to": "school.enrollment",
        "mapping_adequacy": "good",
        "description": "Maximum number of players a school can enroll"
      },
      "min_players[position]": {
        "currently_mapped_to": "position_constraints.min_players",
        "mapping_adequacy": "good",
        "description": "Minimum number of players required in a specific position"
      },
      "max_players[position]": {
        "currently_mapped_to": "position_constraints.max_players",
        "mapping_adequacy": "good",
        "description": "Maximum number of players allowed in a specific position"
      },
      "min_team_size": {
        "currently_mapped_to": "business_configuration_logic.min_team_size",
        "mapping_adequacy": "good",
        "description": "Minimum number of players required to form a team"
      }
    },
    "decision_variables": {
      "assign[player_id, school_id]": {
        "currently_mapped_to": "player_assignment.assigned",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if a player is assigned to a school",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for performance weights, position constraints, and team size requirements. Configuration logic updates include scalar parameters for minimum team size and position constraints, and formulas for performance weight calculations.

CREATE TABLE performance_weight (
  school_id INTEGER,
  position STRING,
  weight FLOAT
);

CREATE TABLE position_constraints (
  position STRING,
  min_players INTEGER,
  max_players INTEGER
);

CREATE TABLE school (
  school_id INTEGER,
  enrollment INTEGER,
  historical_performance FLOAT
);

CREATE TABLE player_assignment (
  player_id INTEGER,
  school_id INTEGER,
  assigned BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic school sports team sizes, historical performance data, and typical position constraints in team sports. The data ensures that the optimization problem is meaningful and solvable by aligning with real-world scenarios.

-- Realistic data for performance_weight
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Forward', 0.9);
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Midfielder', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Defender', 0.7);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Forward', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Midfielder', 0.9);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Defender', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Forward', 0.7);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Midfielder', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Defender', 0.9);

-- Realistic data for position_constraints
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Forward', 2, 4);
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Midfielder', 3, 5);
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Defender', 3, 5);

-- Realistic data for school
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (1, 25, 0.9);
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (2, 20, 0.8);
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (3, 30, 0.7);

-- Realistic data for player_assignment
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (1, 1, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (2, 2, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (3, 3, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (4, 1, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (5, 2, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (6, 3, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (7, 1, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (8, 2, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (9, 3, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (10, 1, True);


```

DATA DICTIONARY:
{
  "tables": {
    "performance_weight": {
      "business_purpose": "Stores performance weights for schools based on positions",
      "optimization_role": "objective_coefficients",
      "columns": {
        "school_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the school",
          "optimization_purpose": "Used to map performance weight to school",
          "sample_values": "1, 2, 3"
        },
        "position": {
          "data_type": "STRING",
          "business_meaning": "Player position",
          "optimization_purpose": "Used to map performance weight to position",
          "sample_values": "Forward, Midfielder, Defender"
        },
        "weight": {
          "data_type": "FLOAT",
          "business_meaning": "Performance weight for the school in the specified position",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.8, 0.9, 1.0"
        }
      }
    },
    "position_constraints": {
      "business_purpose": "Stores minimum and maximum number of players allowed in each position",
      "optimization_role": "constraint_bounds",
      "columns": {
        "position": {
          "data_type": "STRING",
          "business_meaning": "Player position",
          "optimization_purpose": "Used to map constraints to position",
          "sample_values": "Forward, Midfielder, Defender"
        },
        "min_players": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of players required in the position",
          "optimization_purpose": "Used in position constraints",
          "sample_values": "2, 3, 4"
        },
        "max_players": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of players allowed in the position",
          "optimization_purpose": "Used in position constraints",
          "sample_values": "4, 5, 6"
        }
      }
    },
    "school": {
      "business_purpose": "Stores school information including enrollment capacity and historical performance",
      "optimization_role": "business_data",
      "columns": {
        "school_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the school",
          "optimization_purpose": "Used to map school to performance weight and enrollment",
          "sample_values": "1, 2, 3"
        },
        "enrollment": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of players a school can enroll",
          "optimization_purpose": "Used in enrollment constraint",
          "sample_values": "20, 25, 30"
        },
        "historical_performance": {
          "data_type": "FLOAT",
          "business_meaning": "Historical performance score of the school",
          "optimization_purpose": "Used in performance weight calculation",
          "sample_values": "0.8, 0.9, 1.0"
        }
      }
    },
    "player_assignment": {
      "business_purpose": "Stores assignment of players to schools",
      "optimization_role": "decision_variables",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the player",
          "optimization_purpose": "Used to map player to school",
          "sample_values": "1, 2, 3"
        },
        "school_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the school",
          "optimization_purpose": "Used to map player to school",
          "sample_values": "1, 2, 3"
        },
        "assigned": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the player is assigned to the school",
          "optimization_purpose": "Used in decision variable",
          "sample_values": "true, false"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "min_team_size": {
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of players required to form a team",
    "optimization_role": "Used in team size constraint",
    "configuration_type": "scalar_parameter",
    "value": 11,
    "business_justification": "A typical sports team requires at least 11 players to form a complete team."
  },
  "min_positions": {
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of players required in a specific position",
    "optimization_role": "Used in position constraints",
    "configuration_type": "scalar_parameter",
    "value": 2,
    "business_justification": "Teams typically require at least 2 players in each position to ensure coverage."
  },
  "max_positions": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of players allowed in a specific position",
    "optimization_role": "Used in position constraints",
    "configuration_type": "scalar_parameter",
    "value": 5,
    "business_justification": "Teams typically allow up to 5 players in each position to maintain flexibility."
  },
  "performance_weight_formula": {
    "data_type": "STRING",
    "business_meaning": "Calculation of performance weight based on historical performance and position weight",
    "optimization_role": "Used in objective function",
    "configuration_type": "business_logic_formula",
    "formula_expression": "historical_performance * position_weight"
  }
}

Business Configuration Design: 
Our system separates business logic design from value determination:
- Configuration Logic (business_configuration_logic.json): Templates designed by data engineers with sample_value for scalars and actual formulas for business logic
- Configuration Values (business_configuration.json): Realistic values determined by domain experts for scalar parameters only
- Design Rationale: Ensures business logic consistency while allowing flexible parameter tuning


TASK: Create structured markdown documentation for SECTIONS 1-3 ONLY (Problem Description).

EXACT MARKDOWN STRUCTURE TO FOLLOW:

# Complete Optimization Problem and Solution: school_player

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: assign[player_id, school_id] (binary)
- Operational parameters align with expected linear objective: maximize ∑(performance_weight[school_id, position] × assign[player_id, school_id])
- Business configuration includes: Minimum number of players required to form a team (used for Used in team size constraint), Minimum number of players required in a specific position (used for Used in position constraints), Maximum number of players allowed in a specific position (used for Used in position constraints)
- Business logic formulas to express in natural language: Calculation of performance weight based on historical performance and position weight (calculation method for Used in objective function)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate
- CRITICAL: Include ALL business configuration information (scalar parameters AND business logic formulas) in natural business language

### Goals  
[Regenerate goals that clearly lead to LINEAR mathematical objective:]
- Optimization goal: maximize
- Metric to optimize: maximize ∑(performance_weight[school_id, position] × assign[player_id, school_id])
- Success measurement aligned with expected coefficient sources
- Use natural language to precisely describe linear optimization goal
- NO mathematical formulas, equations, or symbolic notation

## 2. Constraints    

[Regenerate constraints that directly match expected LINEAR mathematical constraints:]
- Expected constraint: ['∑(assign[player_id, school_id]) ≤ school.enrollment for each school_id', 'min_players[position] ≤ ∑(assign[player_id, school_id]) ≤ max_players[position] for each position and school_id', '∑(assign[player_id, school_id]) ≥ min_team_size for each school_id'] (Form: Standard constraint form based on business requirements)

[Each constraint should be described in business terms that naturally lead to LINEAR mathematical forms (no variable products or divisions)]

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for performance weights, position constraints, and team size requirements. Configuration logic updates include scalar parameters for minimum team size and position constraints, and formulas for performance weight calculations.

CREATE TABLE performance_weight (
  school_id INTEGER,
  position STRING,
  weight FLOAT
);

CREATE TABLE position_constraints (
  position STRING,
  min_players INTEGER,
  max_players INTEGER
);

CREATE TABLE school (
  school_id INTEGER,
  enrollment INTEGER,
  historical_performance FLOAT
);

CREATE TABLE player_assignment (
  player_id INTEGER,
  school_id INTEGER,
  assigned BOOLEAN
);


```

### Data Dictionary  
[Create comprehensive business-oriented data dictionary mapping tables and columns to their business purposes and optimization roles - NOT technical database terms. Base this on the data_dictionary provided but rewrite in business language that clearly connects to the expected linear mathematical formulation]

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic school sports team sizes, historical performance data, and typical position constraints in team sports. The data ensures that the optimization problem is meaningful and solvable by aligning with real-world scenarios.

-- Realistic data for performance_weight
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Forward', 0.9);
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Midfielder', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Defender', 0.7);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Forward', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Midfielder', 0.9);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Defender', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Forward', 0.7);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Midfielder', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Defender', 0.9);

-- Realistic data for position_constraints
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Forward', 2, 4);
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Midfielder', 3, 5);
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Defender', 3, 5);

-- Realistic data for school
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (1, 25, 0.9);
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (2, 20, 0.8);
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (3, 30, 0.7);

-- Realistic data for player_assignment
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (1, 1, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (2, 2, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (3, 3, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (4, 1, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (5, 2, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (6, 3, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (7, 1, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (8, 2, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (9, 3, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (10, 1, True);


```

STOP HERE - Do not include section 4 (Mathematical Optimization Formulation).

Response:
# Complete Optimization Problem and Solution: school_player

## 1. Problem Context and Goals

### Context  
The optimization problem focuses on allocating players to schools in a way that maximizes the overall performance of school sports teams. Each school has specific enrollment limits, and each team must adhere to position constraints to ensure balanced and effective team compositions. The decision to assign a player to a school is binary, meaning a player is either assigned to a school or not.  

The performance weight for each school and position is calculated based on the school's historical performance and the importance of the position. This weight is used to evaluate the contribution of assigning a player to a school. The business configuration includes:  
- A minimum team size of 11 players, ensuring that each school has enough players to form a complete team.  
- Minimum and maximum player requirements for each position, ensuring that teams have adequate coverage and flexibility. For example, a team must have at least 2 players and no more than 5 players in the "Forward" position.  

The performance weight is derived by multiplying the school's historical performance score by the position weight, ensuring that the objective function reflects both the school's capabilities and the strategic importance of each position.  

### Goals  
The primary goal of this optimization is to maximize the overall performance of all school teams. This is achieved by assigning players to schools in a way that aligns with the schools' historical performance and the players' positions. Success is measured by the total performance weight across all assignments, ensuring that the best possible team compositions are achieved while adhering to enrollment limits and position constraints.  

## 2. Constraints  

The optimization problem must adhere to the following constraints:  
1. **School Enrollment Limits**: The total number of players assigned to a school cannot exceed the school's enrollment capacity. For example, if a school can enroll up to 25 players, the sum of all player assignments to that school must be less than or equal to 25.  
2. **Position Constraints**: Each school must have a minimum and maximum number of players in each position. For instance, a school must have at least 2 players and no more than 5 players in the "Forward" position.  
3. **Minimum Team Size**: Each school must have at least 11 players assigned to form a complete team.  

These constraints ensure that the team compositions are feasible, balanced, and aligned with operational requirements.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for performance weights, position constraints, and team size requirements. Configuration logic updates include scalar parameters for minimum team size and position constraints, and formulas for performance weight calculations.

CREATE TABLE performance_weight (
  school_id INTEGER,
  position STRING,
  weight FLOAT
);

CREATE TABLE position_constraints (
  position STRING,
  min_players INTEGER,
  max_players INTEGER
);

CREATE TABLE school (
  school_id INTEGER,
  enrollment INTEGER,
  historical_performance FLOAT
);

CREATE TABLE player_assignment (
  player_id INTEGER,
  school_id INTEGER,
  assigned BOOLEAN
);
```

### Data Dictionary  
- **performance_weight**: Stores the performance weights for schools based on positions.  
  - `school_id`: Unique identifier for the school.  
  - `position`: Player position (e.g., Forward, Midfielder, Defender).  
  - `weight`: Performance weight for the school in the specified position, used in the objective function.  
- **position_constraints**: Stores the minimum and maximum number of players allowed in each position.  
  - `position`: Player position.  
  - `min_players`: Minimum number of players required in the position, used in position constraints.  
  - `max_players`: Maximum number of players allowed in the position, used in position constraints.  
- **school**: Stores school information, including enrollment capacity and historical performance.  
  - `school_id`: Unique identifier for the school.  
  - `enrollment`: Maximum number of players a school can enroll, used in enrollment constraints.  
  - `historical_performance`: Historical performance score of the school, used in performance weight calculation.  
- **player_assignment**: Stores the assignment of players to schools.  
  - `player_id`: Unique identifier for the player.  
  - `school_id`: Unique identifier for the school.  
  - `assigned`: Indicates if the player is assigned to the school, used as the decision variable.  

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic school sports team sizes, historical performance data, and typical position constraints in team sports. The data ensures that the optimization problem is meaningful and solvable by aligning with real-world scenarios.

-- Realistic data for performance_weight
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Forward', 0.9);
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Midfielder', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (1, 'Defender', 0.7);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Forward', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Midfielder', 0.9);
INSERT INTO performance_weight (school_id, position, weight) VALUES (2, 'Defender', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Forward', 0.7);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Midfielder', 0.8);
INSERT INTO performance_weight (school_id, position, weight) VALUES (3, 'Defender', 0.9);

-- Realistic data for position_constraints
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Forward', 2, 4);
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Midfielder', 3, 5);
INSERT INTO position_constraints (position, min_players, max_players) VALUES ('Defender', 3, 5);

-- Realistic data for school
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (1, 25, 0.9);
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (2, 20, 0.8);
INSERT INTO school (school_id, enrollment, historical_performance) VALUES (3, 30, 0.7);

-- Realistic data for player_assignment
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (1, 1, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (2, 2, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (3, 3, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (4, 1, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (5, 2, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (6, 3, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (7, 1, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (8, 2, True);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (9, 3, False);
INSERT INTO player_assignment (player_id, school_id, assigned) VALUES (10, 1, True);
```
