The commissioner of each respective department shall be and hereby is vested with the right, power and authority to appoint all heads of departments, officers and employees under his charge, control or supervision, unless otherwise provided in this code; provided, that all such appointments, except day laborers and temporary employees, shall be subject to the approval of the council, and no such appointment shall take effect or be valid without such approval. The commissioner of each respective department shall be and hereby is vested with the right, power and authority to discharge at all times, without the approval thereof by the council, any person so appointed by him, whenever, in the judgment of said commissioner, the efficient conduct of the city's affairs shall demand it, except as otherwise provided herein. (1968 Code, sec. 1-105)