For my thesis I have to solve the 'Marathon Supporters Problem':
A supporter wants to see 'his runners' as many times as possible during the race. The race track is one big ellips, with many supporting points. The supporter can travel between these points with a deterministic speed. The speed of the runner is stochastic. The objective is the maximize the number of times a supporter can see the runner. At every point the runner is only visible during a specific time window (depending of the running speed).
Has anyone an idea how I can solve this problem with Dynamic Programming? Which states do you suggest? And how to split this problem in subproblems?