New metrics for different classes of scheduling problems are introduced. We show how approximate solutions of NP-hard problems can be obtained using these metrics. To do this, we solve the optimization problem in which the introduced metric is used as the objective function, and a system of linear inequalities of (pseudo-)polynomial solvable instances of the initial problem represents the constraints. As a result, we find a projection of the considered sub-instance onto the set of solvable cases of the problem in the introduced metric.