The following case of the classical NP-hard scheduling problem is considered. There is a set of jobs N with identical processing times p = const. All jobs have to be processed on a single machine. The objective function is minimization of maximum lateness. We analyze algorithms for the makespan problem, presented by Garey et al. (1981) and Simons (1978) and represent two polynomial algorithms to solve the problem and to construct the Pareto set with respect to criteria Lmax and Cmax. The complexity of presented algorithms equals O(Q n log n) and O(n2 log n), where 10^-Q is the accuracy of the input-output parameters.