In the article the models of management of the project team are considered, they are most difficult to formalize in the fields of knowledge in project management. The study presents economic and mathematical models for managing the project team for threshold collective behavior, for example, the crew of a sea vessel. When implementing specific projects, the experience of leadership and management of a small team often remains at the level of intuition, which leads to the individualization of knowledge and prevents the effective use of the management potential of the team. In the science of management, there are methods of managing personnel, are considered separately, without taking into account the mutual influence of psychological processes, does not allow to form a single, multifactor management concept for a small team in the project. And even more so in the development of project team management, the impact of project implementation conditions on the choice of management methods for the project team is rather poorly taken into account, requires the leader of the psychologist’s experience or significantly reduces the manageability of the project team. This method, unlike the existing ones, includes the team competence radial diagram analysis based on the «balance wheel» principle of a professional team coherence. Input data are professional testing and expert evaluation results (with the involvement of specialists and experts of appropriate qualification). Building and analysis of competence wheel diagrams allow to visualize the compatibility of professional knowledge and skills of all team members together to identify team and personal lack of knowledge and risks of project implementation. As a result, the decision-making person obtains knowledge deviation values, that can help him to make decisions for competence risks elimination. The complexity and multifactoriness of the choice of management methods for the project team, and sometimes the need for managers in direct recommendations for the management of the project team. The practical value of the obtained results lies in the enrichment of the methodology of the researched problems, which is useful for scientists, the possibility to use in business design of crewing companies.

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At present, in the global economic crisis and the COVID-19 pandemic, the development and operation of distance learning and student education are more relevant than ever. The COVID-19 crisis, in addition to the world pandemic, has dealt a devastating blow to the economy of the state and organisations. Insufficient level of research support, imperfection of organisational structure and organisation of management of scientific and technical activities in IT projects necessitate revision and improvement of the existing management system of such projects. The purpose of the study is to develop comprehensive models to increase the objectivity of the role assessment of the applicants' competences during the staffing of specialists for the IT company in conditions of uncertainty on the platform of fuzzy sets. The following theoretical methods of scientific cognition were used in the study: method of synthesis and analysis of information, statistical method, method of maximisation and method of Max-disjunction. The study considers the developed model for assessing the applicants' competences in the staffing of the role of specialists of the IT company using the platform of fuzzy sets. The study analyses the current problems of recruitment, human or labour resources in corporations whose activities are related to the development of software in various fields. The approximate composition of roles in modern IT companies with the recommended socionic types of information metabolism for each specific executor of the IT project is given. The incentive mechanism in the context of specific constraints enables the improvement of the system of rewarding IT staff and makes it possible to differentiate such staff using project management tools. The authors of the study have developed a fuzzy model for assessing the competences of a candidate for any position in an IT corporation. The study provides linguistic variables, the basis of the rules of fuzzy products, and the conclusion of the dependences of the output variable on the input data of the developed fuzzy model

Today, in the global world economic crisis and the Covid / SARS-19 pandemic, the development and functioning of business companies are more relevant than ever. In addition to the global pandemic, the Covid-19 crisis has dealt a devastating blow to the economy and business of the company, and enterprises have suffered severely financially. Development within the framework of proactive management of companies is based on following the required level of their competitiveness. This approach is adapted for business companies and connects together the dynamics of the external and internal business environment, the level of competitiveness of the organization, the level of innovative development, the system of goals of the business organization and the system of goals of business development programs. The conceptual model of content management of the business development program is analyzed, which establishes the compliance of the program objectives with the main factors of the competitiveness of companies and determines the value of projects as ensuring the achievement of these goals, takes into account the possibility of each project’s contribution to the achievement of several goals, as well as the influence of systemic effects in shaping the value of the program and justifying the necessary the amount of resources to provide it. Methods for assessing the values ​​of companies as the degree of compliance of their results with the set business goals. The method is based on the operations and properties of companies, allows to take into account the uncertainty of the conditions and results of the implementation of business companies, forming a two-parameter assessment of the value of the project - the business contribution to the achievement of each goal and the degree of this contribution. This approach, in contrast to the existing ones, makes it possible to take into account the achievement of goals to a greater extent in the following procedures for determining the content of the business. It has been established that synergy in business development programs is manifested in cost savings and an increase in the final value of projects by companies. Authors identified the main sources of the formation of the effect of business synergy associated with costs. Formalized the formation of the synergistic effect in terms of the theory of companies’ projects, arising from the joint implementation of projects within the program, allows with a greater degree of reliability to assess the achievement of the goals of business companies and the necessary resources in conditions of uncertainty.