Abstract
This study provides a comprehensive scoping review with the aim of determining the mathematical methods applied to dairy cow replacements that will serve as a basis for future research in this field. In the WOS and Scopus databases, a search was carried out for peer-reviewed, English articles, where a process of discarding those that did not address the topic related to our objective was carried out, and where the titles, keywords, and full text were reviewed sequentially. We obtained a total of 40 selected articles. Dynamic programming is the most commonly used optimization technique, present in 58% of the studies, followed by stochastic simulation in 40%, and deterministic simulation in 8%. Machine learning methods or hybrid approaches are applied in only 5% of the cases. The review identifies milk production as the most frequently used response variable, appearing in at least 58% of the studies, and profit as the primary economic indicator, utilized in 78% of the cases. This research underscores the importance of these methods in improving the efficiency, profitability, and sustainability of dairy farming operations. Future research could address the inclusion in models of diseases and animal characteristics that have not yet been considered, as well as expand the scarce use of machine learning tools and the hybridization of such models with statistical ones.