This paper presents a mission system and the therein implemented algorithms for path planning in a time-varying environment based on graph methods. The basic task of the introduced path planning algorithms is to find a time-optimal path from a defined start position to a goal position with consideration of the time-varying ocean current for an autonomous underwater vehicle (AUV). Building on this, additional practice-oriented considerations in planning are discussed in this paper. Such points are the discussion of possible methods to accelerate the algorithms and the determination of the optimal departure time. The solutions and algorithms presented in this paper are focused on path planning requirements for the AUV ``SLOCUM Glider''. These algorithms are equally applicable to other AUVs or aerial mobile autonomous systems.