There is a steadily increase in the size and complexity of projects. As a result, traditional project scheduling techniques, such as non-polynomial (NP) algorithms can no longer provide an optimal solution to minimum project duration under predecessors and resource constraints.. This paper presents for the first time a general new approach that allows utilizing such algorithms in heuristic manner. This approach could be efficiently applied for solving most project scheduling problems. The main advantage of this approach is its ability to dissect the original problem to small controllable size sub problems for which exact techniques can be applied. Thus, it neutralizes the complexity of the applied algorithms (and their nonpolynomial growth). We discuss our experience applying this approach and give some insight as to the choice of parameters of the sliding frame.