(A). A retail shop, stocked by a wholesale dealer, and managed by some other person not the owner of the stock. The wholesale dealer appoints the manager.
“There are tied houses in the drapery, grocery, dairy, boot and shoe, hardward, liquor, and book trades. Whiteley's, if rumour is to be trusted, is a tied house; and the majority of Italian restaurants in London begin by being tied to the Gattis.” —Liberty Review, 14th April, 1894, p. 310, col. 1.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Tied House from Infoplease: