Ant Colony Optimization algorithms are intrinsically distributed algorithms where independent agents are in charge of building solutions. Stigmergy or indirect communication is the way in which each agent learns from the experience of the whole colony. However, explicit communication and parallel models of ACO can be implemented directly on different parallel platforms. We do so, and apply the resulting algorithms to the Minimum Tardy Task Problem (MTTP), a scheduling problem that has been faced with other metaheuristics, e.g., evolutionary algorithms and canonical ant algorithms. The aim of this article is twofold. First, it shows a new instance generator for MTTP to deal with the concept of “problem class”; second, it reports some preliminary results of the implementation of two type of parallel ACO algorithms for solving novel and larger instances of MTTP.