In modern digital world, the amount of information is increasing dramatically. All this information requires immediate processing which can be done by automated systems. To accelerate processing in automated systems, new models, methods and efficient algorithms for their implementation are needed. The article considers the problem of distributing incoming messages to handlers in an automated system of an organization. The classical assignment problem and known methods of its solution are the mathematical basis for solving the problem. A generalization of the assignment problem with invalid combinations of assignments is considered as a model. A solution algorithm is developed and a software product for solving the described problem in the Python language is implemented. Moreover, numerical experiments are carried out to verify the quality of the developed algorithm and check its feasibility. The applied problem posed in this paper is relevant as in terms of its practical application and as the study of the mathematical model of the assignment problem and methods of its solution. The developed algorithm allows us to calculate the system load and regulate the number of handlers in operation. The obtained results can serve as input parameters for the simulation model of the incoming message processing system which will allow experimenting with the load of such a system.