This scientific paper explores the increasingly widespread use of collaborative robots in the industrial environment, highlighting them as a solution to challenges related to the high costs of human labour and the associated management difficulties. The authors focus on the process of defining requirements for the implementation of collaborative robots, providing strategies based on mathematical management models. This approach translates into significant benefits for companies, such as cost reduction, quality improvement, and increased operational efficiency. Additionally, the paper proposes an innovative mathematical model for assessing total costs, budgeting, profitability, and electric power consumption associated with the operation of collaborative robots. This model allows for a comparison between the costs involved in using human labour and those associated with collaborative robots, providing critical information for technological investment decisions. The efficiency of this mathematical model is demonstrated through a practical application, where collaborative robots were integrated into a production environment, and costs and efficiency were evaluated compared to the use of human labour. This scientific paper provides a systematic and efficient approach to implementing collaborative robots in industrial processes, benefiting from strategies based on mathematical management models and an original mathematical model for evaluating performance and associated costs.