3D printing is considered the future of production systems and one of the physical elements of the Fourth Industrial Revolution. 3D printing will significantly impact the product lifecycle, considering cost, energy consumption, and carbon dioxide emissions, leading to the creation of sustainable production systems. Given the importance of these production systems and their effects on the quality of life for future generations, it is expected that 3D printing will soon become one of the global industry's fundamental needs. Although three decades have passed since the emergence of 3D printers, there has not yet been much research on production planning and mass production using these devices. Therefore, we aimed to identify the existing gaps in the planning of 3D printers and to propose a model for planning and scheduling these devices. In this research, several parts with different heights, areas, and volumes have been considered for allocation on identical 3D printers for various tasks. To solve this problem, a multi-objective mixed integer linear programming model has been proposed to minimize the earliness and tardiness of parts production, considering their order delivery times, and maximizing machine utilization. Additionally, a method has been proposed for the placement of parts in 3D printers, leading to the selection of the best edge as the height. Using a numerical example, we have plotted the Pareto curve obtained from solving the model using the epsilon constraint method for several parts and analyzed the impact of the method for selecting the best edge as the height, with and without considering it. Additionally, a comprehensive sensitivity and scenario analysis has been conducted to validate the results.