We consider the problem of minimization the number of late jobs on parallel machines in presence of alpha time windows (di = ri + pi + alpha for all jobs). We prove the NPcompleteness of this problem even when m = 2 and di = d for all jobs. We develop a lower bound by solving a minimum cost flow problem associated to a relaxation of the problem. A set of heuristics are presented to minimize the number of late jobs based on a job-focused and machine-focused approach. A simulation experiment is realized to test the effectiveness of heuristics regarding the lower bound. This simulation has been computed for 1; 2; 5; 10; 15 and 20 machines and it shows that the best heuristic has an average deviation to the bound of 4.88%, 6.35%, 7.38%, 7.5%, 7.87% and 7.64% respectively.