MOEA/D is a generic decomposition-based multiobjective optimization framework which has been proved to be extremely effective in solving a broad range of optimization problems especially for continuous domains. In this paper, we consider applying MOEA/D to solve a bi-objective scheduling combinatorial problem in which task durations and due-dates are uncertain. Surprisingly, we find that the conventional MOEA/D implementation provides poor performance in our application setting. We show that this is because the replacement strategy underlying MOEA/D is suffering some shortcomes that lead to low population diversity, and thus to premature convergence. Consequently, we investigate existing variants of MOEA/D and we propose a novel and simple alternative replacement component at the aim of maintaining population diversity. Through extensive experiments, we then provide a comprehensive analysis on the relative performance and the behavior of the considered algorithms. Besides being able to outperform existing MOEA/D variants, as well as the standard NSGA-II algorithm, our investigations provide new insights into the search ability of MOEA/D and highlight new research opportunities for improving its design components.