Upon the written petition of the city council of Charleston or of any of the patrons of any person owning or operating a wharf, warehouse or terminal facility for public uses or for hire, alleging that the plant or equipment in Charleston County of such person is inadequate or unsuited to the public need, the Authority shall fix a time and place for a hearing upon such petition and shall mail notice thereof to the parties in interest and give due public notice thereof at least one week prior to such hearing. Upon such hearing the Authority may, if it finds the wharf, warehouse or terminal facility to be inadequate or unsuited to the public need, order and prescribe such wharf, warehouse or terminal facility as shall be adequate and suitable and fix a time within which such person owning or operating the same shall construct such additions or improvements. Such person shall thereupon construct such additions or improvements to its plant or equipment within the time so fixed.