=== Problem Context ===
# Complete Optimization Problem and Solution: company_employee

## 1. Problem Context and Goals

### Context  
The company is focused on optimizing its workforce allocation to maximize the overall employee experience while ensuring efficient resource utilization. The decision involves assigning employees to different companies based on their years of experience and the financial performance of the companies. Each employee can be assigned to only one company, and each company has a maximum capacity for the number of employees it can hire.  

The business configuration includes two key weights:  
- **Weight for years of experience (0.7)**: This reflects the importance of employee experience in the overall employee experience score.  
- **Weight for company profits (0.3)**: This represents the contribution of a company's financial performance to the employee experience score.  

Additionally, each company has a predefined maximum number of employees it can hire, ensuring a balanced distribution of workforce across companies.  

### Goals  
The primary goal is to maximize the total employee experience score, which is calculated as a weighted combination of the employees' years of experience and the financial performance of the companies they are assigned to. Success is measured by achieving the highest possible score while adhering to the constraints of employee assignments and company hiring capacities.  

## 2. Constraints  

The optimization problem is subject to the following constraints:  
1. **Employee Assignment Constraint**: Each employee must be assigned to exactly one company. This ensures that all employees are allocated without duplication.  
2. **Company Capacity Constraint**: The total number of employees assigned to each company cannot exceed its predefined maximum capacity. This ensures that companies do not exceed their hiring limits.  

These constraints ensure that the workforce allocation is both feasible and aligned with operational capabilities.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for employee assignments and company capacities, and updating business configuration logic to include weights and maximum employee capacities.

CREATE TABLE employee_assignment (
  employee_id INTEGER,
  company_id INTEGER,
  assignment_status BOOLEAN
);

CREATE TABLE company_capacity (
  company_id INTEGER,
  max_employees INTEGER
);
```

### Data Dictionary  
- **employee_assignment**:  
  - **employee_id**: Unique identifier for each employee. Used to track individual employees in the optimization process.  
  - **company_id**: Unique identifier for each company. Used to track the companies employees are assigned to.  
  - **assignment_status**: Indicates whether an employee is assigned to a specific company. This is the binary decision variable in the optimization model.  

- **company_capacity**:  
  - **company_id**: Unique identifier for each company. Used to track the companies in the optimization process.  
  - **max_employees**: The maximum number of employees each company can hire. This serves as the constraint bound in the optimization model.  


=== Schema ===
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for employee assignments and company capacities, and updating business configuration logic to include weights and maximum employee capacities.

CREATE TABLE employee_assignment (
  employee_id INTEGER,
  company_id INTEGER,
  assignment_status BOOLEAN
);

CREATE TABLE company_capacity (
  company_id INTEGER,
  max_employees INTEGER
);



=== LLM Response ===
```sql
-- Query Description: Retrieve the current assignment status of employees to companies.
-- This is crucial for understanding the initial state of employee assignments, which serves as the decision variable in the optimization model.
SELECT employee_id, company_id, assignment_status
FROM employee_assignment;

-- Query Description: Retrieve the maximum capacity of each company.
-- This data is essential for enforcing the company capacity constraint in the optimization model.
SELECT company_id, max_employees
FROM company_capacity;

-- Query Description: Retrieve the total number of employees currently assigned to each company.
-- This helps in understanding the current load on each company and ensures that the company capacity constraint is not violated.
SELECT company_id, COUNT(employee_id) AS current_employees
FROM employee_assignment
WHERE assignment_status = TRUE
GROUP BY company_id;

-- Query Description: Retrieve the list of employees who are not currently assigned to any company.
-- This data is important for identifying employees who are available for assignment, which is necessary for the employee assignment constraint.
SELECT employee_id
FROM employee_assignment
WHERE assignment_status = FALSE;

-- Query Description: Retrieve the list of companies that have not yet reached their maximum capacity.
-- This helps in identifying companies that can still accept more employees, which is crucial for the company capacity constraint.
SELECT cc.company_id, cc.max_employees, COUNT(ea.employee_id) AS current_employees
FROM company_capacity cc
LEFT JOIN employee_assignment ea ON cc.company_id = ea.company_id AND ea.assignment_status = TRUE
GROUP BY cc.company_id, cc.max_employees
HAVING COUNT(ea.employee_id) < cc.max_employees;

-- Query Description: Retrieve the total number of employees and the total capacity across all companies.
-- This provides an overview of the workforce and capacity, which is useful for understanding the overall feasibility of the optimization problem.
SELECT SUM(cc.max_employees) AS total_capacity, COUNT(ea.employee_id) AS total_employees
FROM company_capacity cc
LEFT JOIN employee_assignment ea ON cc.company_id = ea.company_id AND ea.assignment_status = TRUE;

-- Query Description: Retrieve the list of employees along with their current assignment status and the company's maximum capacity.
-- This data is useful for understanding the relationship between employees and companies, and for ensuring that the company capacity constraint is not violated.
SELECT ea.employee_id, ea.company_id, ea.assignment_status, cc.max_employees
FROM employee_assignment ea
LEFT JOIN company_capacity cc ON ea.company_id = cc.company_id;

-- Query Description: Retrieve the list of companies along with their current number of assigned employees and their maximum capacity.
-- This helps in understanding the current state of each company in terms of employee assignments and capacity.
SELECT cc.company_id, cc.max_employees, COUNT(ea.employee_id) AS current_employees
FROM company_capacity cc
LEFT JOIN employee_assignment ea ON cc.company_id = ea.company_id AND ea.assignment_status = TRUE
GROUP BY cc.company_id, cc.max_employees;
```

These queries are designed to retrieve the most relevant data for the optimization problem, including the current state of employee assignments, company capacities, and the relationships between employees and companies. This data is essential for formulating and solving the optimization problem while adhering to the given constraints.
