The Alexandria City Council unanimously granted permission yesterday to the cruise ship Caribe to dock at the city pier on three occasions next November.

The council will soon consider the cost of dredging the area immediately in front of the Torpedo Factory pier. The captain of the ship requested last year that the area be dredged 21 feet to allow for easier maneuvering of the ship, which regularly carries tourist passengers to the Caribbean.

The anticipated cost of the city, about $6,500 for police and other city services in connection with the ship's docking, will be reimbursed by the Commodore Cruise Lines, which owns the Caribe, according to city manager Douglas Harman.

The Caribe is expected to use the port to launch a "Cruise to Nowhere" on Nov. 24, as well as a six-day Bermuda cruise Nov. 4-10, and a nine-day cruise to the islands of St. Croix, St. Thomas and St. John on Nov. 10-19, the council was told.

The agreement approved yesterday permits the city to back out of the docking arrangement if the eventual costs of the dredging the port proves prohibitive, according to a memo from Harman. No date was set for an analysis of the dredging costs.