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For single and multi-machine scheduling problems with the criterion of minimizationmaximum lateness the metrics \rho has been used for the first time. A theorem of estimating theabsolute error has been proved. The idea of the offered approach consists in construction by aninitial instance of a problem of other instance for which it is possible to find the optimum orapproximated solution, with the minimal distance up to an initial instance in entered metric.