Designing customized orthodontic treatments presents a significant challenge due to the diverse and heterogeneous requirements that must be met to correct misaligned teeth and malocclusions. These requirements include specific directives from orthodontists, individual patient considerations, physiological constraints, and technological limitations. The current approach mainly involves collaboration between technicians and orthodontists utilizing specialized CAD software and implementing manual methodologies. This paper outlines the formalization of an algorithm developed to facilitate the design of these medical treatments. A mathematical model based on existing knowledge is proposed to automate the generation of a patient's final dental configuration, which serves as the foundation for producing all necessary devices for the treatment plan. The mathematical model has been validated through collaboration with orthodontists and a manufacturer specialized in orthodontic devices. Feedback obtained from these collaborations demonstrates the effectiveness of the developed solution and its utility as a valuable resource during discussions with orthodontic professionals.