In this paper, we consider a single machine scheduling problem where a breakdown period occurs in an online way. Two main objective functions are studied: the makespan and the maximum lateness. We propose two approximation algorithms for the makespan minimization for solving two variants of the problem: with different release dates or without release dates. We show that the competitive ratio of the two algorithms is 3/2 and that this bound is the best possible for the makespan minimization. For the maximum lateness minimization we propose a (1 + 2/2) = 1.70- approximation algorithm capable to solve the problem with delivery times but no release dates. This ratio is tight for the proposed algorithm and allows us to establish a precise window for the best possible ratio, which belongs to [3/2,1 + 2/2] = [1.50, 1.70]