The parallel machines scheduling problem (Pm) comprises the allocation of jobs on the system’s resources, i.e., a group of machines in parallel. The basic model consists of m identical machines and n jobs. The jobs are assigned according to resource availability following some allocation rule. In this work, we apply the Ant Colony Optimization (ACO) metaheuristic which includes in the construction solution process different specific heuristic to solve Pm for the minimization Maximum Tardiness (Tmax). We also present a comparison of previous results obtained by a simple genetic algorithm (GAs) and an evidence of an improved performance of the ACO metaheuristic on this particular scheduling problem.