The planning and scheduling of processes are the main foundations of modern manufacturing systems, and their efficient integration represents one of the principal interests in operations research. Most of the reported literature in operations research formulates the optimization process considering a single objective. However, real-world manufacturing systems are influenced by several variables that must be considered in a complete process planning task. To solve this gap, this paper presents a computational study where the main variables of process planning are integrated: production times, production costs, and the Makespan of the system. To incorporate such variables, the problem is reformulated as a multi-objective optimization system by employing an Adapted Non-dominated Sorting Genetic Algorithm ii (ANSGA-ii) methodology. Under such an approach, the ANSGA-ii codifies the process planning elements into its structure to execute the operators for determining the best tradeoff between objectives. In this work, different cases of study are considered and compared with some of the most employed multi-objective approaches in the literature to demonstrate the performance and robustness of the proposed method. Statistical analysis corroborates that the proposed ANSGA-ii can generate competitive results outperforming the techniques employed in the experimental study.