Mathematical model and software for project team formation based on intra-collective relationships

In modern conditions, the success of project activities is determined not only by the professional competencies of participants but also by their socio-psychological compatibility. Existing mathematical models of team formation, based on the classical assignment problem, are focused exclusively on the resource-based approach and do not take into account interpersonal relationships, which also affect the efficiency of joint activities. The aim of the work is to develop a mathematical model and software for forming project teams that combines the professional competencies of candidates and the sociometric characteristics of their relationships to achieve a synergistic effect. A model is proposed that extends the generalized assignment problem by incorporating sociometric indices of cohesion and conflict, and also excludes teams with mutual antipathies. To solve the NP-hard optimization problem, a genetic algorithm implemented in Python using the DEAP framework was applied. An individual is represented by a fixed-length chromosome, where the position corresponds to the role and the value to the candidate's index. The operation of the algorithm is demonstrated on a test example. The model and algorithm can be used by project managers, HR specialists, and educators for the informed formation of student and professional teams with a favorable socio-psychological climate.

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