THE GROUND CREW WERE NOT USING HEADSETS WHILE PUSHING BACK THE AIRPLANE. THE GROUND CREW DID NOT FOLLOW COMPANY PROCEDURES AND DISCONNECTED THE TOW BAR WITHOUT RECEIVING AN ACKNOWLEDGMENT FROM THE FLIGHT CREW. THE GROUND CREW DID UTILIZE HAND SIGNAL PROCEDURES TWICE, BUT WERE UNABLE TO SEE THE CAPTAIN'S RESPONSE DUE TO THE POOR LIGHTING CONDITIONS. THE FLIGHT CREW WAS STARTING THE ENGINES AND DID NOT SEE NOR ACKNOWLEDGE THE PARKING BRAKE SIGNAL. THEY WERE NOT AWARE THAT THE GROUND CREW DISCONNECTED THE TOW BAR. MOMENTS LATER, THE JET ROLLED FORWARD AND STRUCK THE TUG.