In this article, the simplest dynamic synchronization model of a multi-storey production process is formalized and investigated, with which several quality functionals are associated. The method of idempotent analysis was used to study the model. The initial conditions for the production process are set, a production system with a specific number of employees and resources is set, taking into account time. To manage the production system, it is necessary to find a compromise solution. A numerical example is given in which a compromise point is found for the case of three quality functionals.