## 5 Conclusions  
The problem considered in this study is to find an optimal robust cyclic schedule of robot movements that ensures maximum performance of the HTS system for biochemical analysis. To address this problem, we propose a new efficient PERT/CPM project management method, which works in combination with a modified prohibited intervals algorithm. To demonstrate the validity and practical utility of this method, we focus on the theoretical and numerical analysis of a real HTS process for enzymatic assay. The main result obtained is that the new combined PERT/CPM method is strongly polynomial, in contrast to existing mixed integer programming methods. Another advantage of the new method is that it is able to simultaneously generate a whole set of different optimal solutions, which can be used in practice for controlling unexpected fluctuations of input data. A characteristic feature of these results is that they have theoretical significance and at the same time have a strong applied focus.  
While the present work focuses on HTS scheduling specifically for enzyme assays consisting of six workstations, the proposed mathematical model and project management techniques can be naturally extended to address and solve a variety of screening scheduling problems with a larger number of devices and more general formulations such as multi-degree cyclic scheduling, re-scheduling for unexpected disruptions, and the use of multiple robots to transport microplates. Since a wide variety of biochemical libraries are available today, each containing a huge number of compounds, it is essential to collect big data, compare results from different screens, schedule screening processes, and optimize them in an automated HTS system. These challenging problems can be addressed in future research by exploring new powerful and practice-oriented techniques from data science and artificial intelligence.  
Conceptualization, E.L. and V.K.; methodology, E.L., V.K. and P.Y.; validation, E.L., V.K., P.Y. and A.C.; formal analysis, E.L. and V.K.; investigation, E.L., V.K., P.Y. and A.C.; writing--original draft preparation, E.L., V.K., P.Y. and A.C.; writing--review and editing, E.L., V.K., P.Y. and A.C.; supervision, E.L. and V.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
All the data are available in the manuscript.  
The authors thank the anonymous reviewers for their helpful comments and suggestions.  
The authors declare no conflicts of interest.  
The list of main symbols and abbreviations used in this paper.  
\begin{tabular}{l l}
**Symbol** & **Meaning** \\ \(F\) & Set of prohibited intervals \\ \(U\) & Set of allowed intervals \\ \(S\) & Storage Center \\ \(\mathbf{S}\) & Technological sequence of workstations \\ \(\mathbf{O}\) & Technological sequence of operations on workstations \\ \(R\) & Robot’s route \\ \(T\) & 1-cyclic cycle time \\ (T\({}_{1}\), \(T_{2}\)) & 2-cyclic cycle time \\ CPM & Critical Path Method \\ HTS & High-Throughput Screening \\ MIP & Mixed Integer Programming \\ PERT & Project Evaluation Review Technique \\ PIM & Prohibited Intervals Method \\ \end{tabular}