The nurse scheduling model is used to optimize the assignment of nurses to shifts in order to meet the staffing needs of a healthcare facility while also considering the preferences and constraints of the nurses.

There are several advantages to using a model like this to schedule nurses rather than doing it manually:

• Efficiency: A model can quickly generate a schedule that meets all of the constraints and preferences, whereas manually scheduling nurses can be time-consuming and prone to errors.
• Fairness: A model can ensure that nurses are assigned shifts in a fair and equitable manner, whereas manual scheduling may be subject to biases or personal preferences.
• Flexibility: A model can easily handle changes in staffing needs or nurse availability, whereas manually updating a schedule can be difficult and prone to errors.
• Preferences: It is possible to augment the model to include preferences so that the schedules are generated with equity in mind.

Here is a model that represents a basic schedule generator of 5 nurses with 7 shifts, along with typical constraints such as:

• Minimum and maximum shifts per week

• Minimum and maximum consecutive shifts

• All shifts are covered

  ---

  from ortools.linear_solver import pywraplp
    
  def main():
  # Set the number of nurses and the number of shifts.
  num_nurses = 5
  num_shifts = 7
    
  # Set the shift constraints.
  min_shifts_per_week = 3
  max_shifts_per_week = 4
  min_consecutive_shifts = 1
  max_consecutive_shifts = 2
    
  # Create the solver.
  solver = pywraplp.Solver('Nurse Scheduling', pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
    
  # Create the variables.
  x = {}
  for i in range(num_nurses):
    for j in range(num_shifts):
      x[i, j] = solver.IntVar(0, 1, 'x[%i,%i]' % (i, j))
    
  # Set the objective function.
  objective = solver.Minimize(solver.Sum([x[i, j] for i in range(num_nursed) for j in range(num_shifts)]))
    
  # Set the shift constraints.
  for i in range(num_nursed):
    solver.Add(solver.Sum([x[i, j] for j in range(num_shifts)]) >= min_shifts_per_week)
    solver.Add(solver.Sum([x[i, j] for j in range(num_shifts)]) <= max_shifts_per_week)
    for j in range(num_shifts - 1):
      solver.Add(x[i, j] + x[i, j+1] <= max_consecutive_shifts)
    
  # Set the overall shift coverage constraints.
  for j in range(num_shifts):
    solver.Add(solver.Sum([x[i, j] for i in range(num_nursed)]) == 1)
    
  # Solve the problem.
  status = solver.Solve()
    
  # Print the solution.
  if status == pywraplp.Solver.OPTIMAL:
    print('Optimal solution found.')
    for i in range(num_nursed):
      for j in range(num_shifts):
        if x[i, j].solution_value() > 0:
          print('Nurse', i, 'works shift', j)
  else:
    print('Problem could not be solved.')
      
    if name == 'main':
  main()