A retirement committee shall be established to supervise the general operation of the retirement system established pursuant to the Police Officers Retirement Act. The city council shall continue to be responsible for the general administration of such retirement system unless specific functions or all functions with regard to the administration of the retirement system are delegated, by ordinance, to the retirement committee. Whenever duties or powers are vested in the city or the retirement committee under the act or whenever the act fails to specifically allocate the duties or powers of administration of the retirement system, such powers or duties shall be vested in the city unless such powers or duties have been delegated by ordinance to the retirement committee. The city and the retirement committee shall have all powers which are necessary for or appropriate to establishing, maintaining, managing, and administering the retirement system.