## 8 Conclusions  
The hierarchical HPN model presented in this article can describe processes in a comprehensive class of flexible manufacturing systems. However, some structural and technical features of this model determine its most effective area of application. In the HPN model, the emphasis is on putting units into operation, their replacement, and the formation and use of a reserve of units. In this regard, the model is more suitable for the organization of maintenance and repair of mobile industrial equipment. It should be noted that the novelty of our approach also lies in the application of an optimization-simulation procedure. In modeling the maintenance of the autonomous robotic vehicle system, we managed to solve the problem of the rational placement of AAVs in a production area with the required number of reserve units. The simulation experiment results obtained via the Monte Carlo method were used to adjust the constraints of minimizing the maintenance cost, as shown in Equations (2) and (3). We can say that such an iterative procedure is, to some extent, analogous to machine learning; the difference is that, at this stage of our work, the decision to correct the optimization problem is made by the production system's analyst/manager. In our study of AAV systems, we obtained solutions close to optimal, in the performance of no more than 15-20 iterations. The HPN model contains a set of UNIT ID modules, which are individual multi-functional timers for each technology unit. This solution is new, and allows us to keep track of the time parameters of the unit's activity, the residual resource, and the remaining time before maintenance. The UNIT ID module performs these functions regardless of the production task or the place of the unit's use. This provides the ability to quickly move information about a unit to other hierarchical models, in order to transfer it to a new production system. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Maintenance** & **Time Before Scheduled** & **Operating Rate** & **Operating Rate** & **Operating Rate** & **Operating Rate** \\
**Time \(t_{M}\), h** & **Maintenance \(t_{MT}\), h** & \(E_{1}\) for AAV1, \%** & \(E_{2}\) for AAV2, \% & \(E_{3}\) for AAV3, \% & \(E_{4}\) for AAV4, \% \\ \hline \multirow{3}{*}{\(\mu=48\); \(\sigma=6\)} & A \({}^{1}\) & 100 & 62 & 63 & 66 & - \\  & B \({}^{2}\) & 100 & 51 & 59 & 58 & 40 \\ \cline{1-1}  & A \({}^{1}\) & 200 & 80 & 80 & 80 & - \\ \cline{1-1}  & B \({}^{2}\) & 200 & 37 & 86 & 64 & 62 \\ \hline \end{tabular} \({}^{1}\) Three autonomous vehicles; \({}^{2}\) three autonomous vehicles and reserve AAV4.  
\end{table} 
Table 9: AAV reserve efficiency assessment. It should be noted that the structure of the hierarchical model and its main modules can be adapted to a vast class of flexible production systems. The ZO module and the ZExec module structure allow the substitution of local models of various production tasks and technological equipment units. However, there are certain limitations to the application of the proposed hierarchical model. First, the desire to perform deeper detailing, in order to study the stochastic processes of the behavior of individual subsystems and elements of technological units, leads to congestion of the model's connections and an increase in the dimension of the PN model. As a result, the simulation time increases significantly, and the analysis of the obtained solutions becomes more complicated. Secondly, the tools that support PN modeling have limitations on the number of places and transitions in the model. Experiments with the AAV system have shown that it makes no sense to build a complete simulation model for an enterprise with 50-100 robotic vehicles. It is enough to divide the AAV fleet into groups that perform local production tasks, with the number of vehicles no more than 15. In this case, the simulation can be performed reasonably, and the obtained solution adequately describes the manufacturing system.