In this paper, we have done a rapid and very simple algorithm that resolves the multiple objective combinatorial optimization problem. This is done by determining a basic optimal solution, which is a strong spanning tree constructed, according to a well-chosen criterion. Consequently, our algorithm uses notions of Bellman’s algorithm to determine the best path of the network, and Ford Fulkerson’s algorithm to maximise the flow value. The two algorithms are manipulated by the Simplex Network Method, which permits to reach the optimality conditions. In short, the interest of our work is the optimization of many criteria taking into account the strong spanning tree that represents the central angular stone of the network. To illustrate that, we propose to optimize a bi-objective distribution problem.