Purpose. The ongoing global changes have a significant impact on all areas of the world economy as a whole, including the domestic economy. Solving the problem of personnel shortages and the ever-increasing need of industry for qualified personnel can be achieved by improving the mechanisms of staffing management in project implementation across industries without involving intermediary firms. The purpose of the study is to increase the efficiency of decision-making in staffing management for the functioning of an organizational system by improving methodological tools. Methods. The study uses the parametric method of data analysis, the method of mathematical modeling, and also the method of structural and functional analysis. Findings. The article provides a description of the authors' model for staff selection management in the implementation of specific projects or work, while maintaining the current personnel in the organizational system. Production chains are considered and the need for localizing some parts of production chains on the territory of the Russian Federation is outlined. The possible causes and main consequences of personnel shortages in the Russian Federation are shown. The analysis of the main existing HR technologies allowed us to formulate an original approach to the rotation of existing human resources, which enables to rotate employees between projects, bypassing direct interaction with intermediaries and the labor market. The authors considered the specifics of forming a unified information base, which ensures unambiguous interpretation of the concepts used and the unity of means and methods for assessing the compliance of candidates with qualification requirements. It should be noted that the proposed management approach incorporates the redistribution practice successfully proven in the IT and consulting fields. Research application field. The developed model makes it possible to select candidates for project roles, taking into account the possibility of choosing candidates who do not strictly meet the initial requirements. Conclusions. A mathematical model for project staffing management in an organizational system is proposed. It differs from the known models by utilizing competencies and employee rotation in organizational systems. Competencies are represented as an original set of interchangeable elements (knowledge, skills, abilities), allowing for the selection of employees based on specified qualification requirements.