The problem of sequencing the movement of a robot so that it can carry out a given task in the minimum required time is of considerable importance, because of the efficiency of such a solution. The problem considered is an application of this idea, as applied to the context of the Navigation Challenge in the International Guided Vehicle Competition (IGVC). The objective is to find a sequence of points and a path in space that the robot has to traverse in order to complete the objective of the competition. A mathematical programming based model and example solution for the Bearcat Robot is given. The challenge in this event is for a robot to autonomously travel, using Differential GPS, from a starting point to a number of target destinations, while recognizing and avoiding the obstacles present, given only a map showing the coordinates of those targets, in the least possible time. The solution can be implemented easily using the Excel Solver, or AMPL. These solutions are practically applicable and easy to run in the competition since they give the sequence of points to be followed. In addition, the program is used together with a heuristic for situations where there are velocity constraints on the robot.