Alexander Muir was born on April 26, 1819 on a farm near the town of Stevenston, Ayrshire in Scotland. He left home in 1832 and went to sea as an apprentice seaman. He sailed between the Far East and Great Britain. In 1836 he left Scotland as a sailor and headed for Quebec, where he met with family near Howick, Quebec in July. Between 1837 and 1847 Alexander sailed the Great Lakes, rising to the rank of Captain. Muir built his house on Queen Street, Port Dalhousie, Ontario in 1841. On February 12, 1845 he was married to Jane Lang of Kingston.

Muir began building a floating dry dock at Port Dalhousie in 1850. Eventually Alexander was joined by is four brothers to form Muir Bros. By 1866, Muir Bros. had built a permanent dry dock next to the floating dock.

The brothers also bought timberlands to control their own supply of timber for shipbuilding, dry docks construction and freight. The first Muir Bros. ship was launched on March 3, 1855. It was called “Ayr” after their hometown. Ships from Muir fleet travelled far and wide, including Scotland, Duluth and Liverpool. The third dry dock was built in Port Huron, USA.  Alexander Muir worked at the dry docks for the rest of his life. He died on January 2, 1910.  After the death of all Muir Brothers, the company was passed on to remaining family members. Muir Bros. were the last dry dock to operate in Port Dalhousie.