Optimization of corporate learning process management: a mathematical model and its application

This article considers the problem of optimization of the employee training process control at an enterprise, including the distribution of teachers, students, lessons and training rooms under multiple constraints. The relevance of the work is determined by the need for effective management of training processes in organizations, considering the qualifications of teachers, skills of employees, time constraints and the sequence of skill acquisition. To formalize the problem, a mathematical model was developed that allows for a linear description of the key aspects of training. The model includes multidimensional constraints such as training time, teacher employment, availability of training places and the sequence of skill acquisition. However, due to the combinatorial nature of the problem and discrete variables, its solution requires the use of specialized methods. To solve the problem, optimization approaches are used that include: formalization of the problem in a linear manner to identify subtasks that can be solved separately (for example, determining available classes for teachers); application of heuristic methods and dynamic programming for the final distribution of classes and resources. The proposed model demonstrates its effectiveness in personnel training management scenarios where both cost minimization and fulfillment of all specified constraints are important. Despite the limitations of the linear description, the model provides a simplification of the solution due to the structured approach to resource allocation. This makes it a universal tool applicable to the management of employee training in companies of various types. The materials of the article can be useful for the development of adaptive learning management systems, as well as for further research aimed at improving resource allocation algorithms.

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