Which commercial lodging type is located on or near U.S. installations, is operated by a commercial lodging company, and is corporately branded?

The correct choice reflects the features of commercial lodging specifically designed for military personnel and their families. DoD Privatized lodging is a unique category that involves lodging facilities which, while not owned by the Department of Defense, are operated by a commercial company under a privatization agreement. This means they are typically located on or near military installations, offering convenience for service members.

These establishments are corporately branded, which denotes that they follow the branding guidelines of the corporate entity operating them. This ensures consistency in quality and service standards, much like other commercial hotels in the hospitality industry.

The other types of lodging mentioned, such as Military Family Housing and Government-Contracted Beds, do not align with the specific criteria of being operated by a commercial lodging company or being corporately branded in the same manner. Military Family Housing refers to government-managed accommodations for military families, while Government-Contracted Beds are typically temporary lodging facilities contracted by the government but not exclusively linked to commercial brands. Institutional Lodging usually pertains to facilities that serve a specific purpose beyond typical lodging, such as dormitories or communal living spaces and do not fit the commercial lodging definition. Thus, DoD Privatized lodging stands out as the most accurate answer based on its operational model and branding characteristics.