Searching for the complete cover of a compatible relation on non-empty finite sets plays an important role in data mining and management decision-making. In this paper, the complete cover theory of a compatible relation is discussed, and the relevant theorem of merging compatible classes into complete cover is put forward and proved, and a generating algorithm of the complete cover of a compatible relation is proposed, and apply it to find the optimal solution for resource scheduling and allocating and so on. The application results show that the algorithm has the close efficiency to dynamic programming method, and the practical application is simple, feasible and steady.