This paper introduces a network flow method for manpower scheduling and resource allocation. The network formulation of the problem permits the development of an algorithm that determines the minimal flow of resources through the network. The method presented here corresponds to the Simplex method, for in both methods the value of the objective function is optimized while the capacity limitations are preserved. The procedure proposed here, however, uses a more economical problem representation and is computationally more efficient. The efficacy of the minimal flow algorithm and its use is illustrated for a production system but the applicability of the procedure is sufficiently broad for it to work in other problem situations just as well.