In this paper, we propose an algorithm which is based on many things: the notions well-known of the simplex network method, Ford Fulkerson’s algorithm and our new idea, which is << the gain cycles >>, applied on a bi-objective minimum cost flow problem. This algorithm permits us to have a good order of many criteria in a rapid and an efficient way; because this classification permits us to structure the optimal area, in which we can choose the best action among the others which exist in the objective space. From this one, we distinguish, that the resolution of this problem comes to find an under set of good actions, among which the decider can select an action of best compromise, or make a decision, in the case where reference indications of the deciders may change. A didactic example is done to illustrate our algorithm.