Yes, Melbourne Airport is equipped with the necessary navigational and physical infrastructure to allow aircraft to continue to land and take-off in adverse weather conditions. Melbourne Airport is Category IIIb rated allowing aircraft to land in poor visibility and has an ILS on both the northern and western approach runways.
Each airline must apply to CASA for approval to conduct Category IIIb operations and pilots need to be qualified in a Category III B approach.
For more information about Category IIIb visit the Airservices Australia website.
For more information on how fog may affect flights, click here.