Dr. Cooper, who will be 62 later this month, continues as chairman and chief executive.
Mr. White continues as chief executive and was named vice chairman.
The other brother, Antoine, is expected to continue as chief executive of the company.
Mr. Anderson, 45, who owns 57 percent of the company's stock, continues as chairman and chief executive.
He will continue as chief executive, but the position of president will be eliminated.
John Carter will continue as president and chief executive.
Jim Mullen, who was president, continues as chief executive.
Mr. Monaghan, 62, continues as chief executive and takes on the position of chairman.
Bernard Herman was named to the new post of chairman and will continue as chief executive.
He will also continue as chief executive at Darlington.