## 2 Description of the Problem
This cyclic schedule, with a period of 200.5 s, is shown in Figure 2.  
In the Gantt chart in Figure 2, the following notation is used: workstations 0, 1, 2, and 3 denote Cytomat2C, Multidrop-384, Envision, and Teleshake, respectively. The abscissa axis corresponds to time. The robot's movement is shown with a red dotted line. The numbers in the figure indicate the time the robot arrives at and leaves the corresponding workstations. The first robot's cycle begins at time \(t=0\), when the robot picks up a screen-ready microplate, labeled MP\({}_{0}\), from workstation 0 (Cytomat2C), then moves this microplate MP\({}_{0}\) to workstation 1 within 19 s. The robot then visits workstations in the following order: the void robot moves (without a microplate) to workstation 2 (next in the sequence **S**) \(\rightarrow\) the robot moves with microplate MP\({}_{-2}\) (which starts two cycles before microplate MP\({}_{0}\)) to workstation \(0\rightarrow\) the void robot moves to workstation \(1\rightarrow\) the robot moves, loaded with microplate MP\({}_{0}\), to workstation \(2\rightarrow\) the robot moves with microplate MP\({}_{0}\) to workstation \(3\rightarrow\) the robot moves with microplate MP\({}_{-1}\) to workstation \(2\rightarrow\) the void robot moves to workstation \(0\), where the robot waits for 35 s and completes its 1-cyclic route at \(t=200.5\) s. The total processing time for the microplate MP\({}_{0}\) is significantly longer and amounts to 506 s. It begins at time \(t=-32\) (not shown in Figure 2), when this microplate is delivered by the auxiliary device to workstation 0, and ends at time \(t=474\) s, when microplate MP\({}_{0}\) is returned by the auxiliary device to the storage center, which occurs during the third cycle of the robot. The processing life of microplate MP\({}_{0}\) is indicated by a bold blue line with small triangles. The symbol MP\({}_{-k}\) (\(k=1,2,\ldots\)) denotes a microplate that enters the screening system \(k\) periods (cycles) before MP\({}_{0}\). It can be seen that two adjacent instances of the corresponding operation in workstation 3 (Teleshake) for two adjacent microplates intersect in time. In order not to overload Figure 2, operations from \(S\) to \(C\) and from \(C\) to \(S\) visible in Figure 1 are not shown in Figure 2. We denote the sequence of operations performed on the workstations as **O** = (\(O_{0}\), \(O_{1}\), \(O_{2}\), \(O_{3}\), \(O_{4}\), \(O_{5}\)), which means that operations \(O_{0}\) and \(O_{5}\) are performed on workstation \(M_{0}\) (Cytomat2C), operation \(O_{1}\) is performed on workstation \(M_{1}\) (Multidrop-384), operations \(O_{2}\) and \(O_{4}\) are performed on workstation \(M_{2}\) (Envision), and operation \(O_{3}\) is performed on workstation \(M_{3}\) (Teleshake). In this notation, the symbols \(R=(O_{0}\), \(O_{4}\), \(O_{1}\), \(O_{2}\), \(O_{3}\)) denote a periodically repeating sequence of completed operations, which uniquely determines the cyclic route of movement of the loaded robot. The Gantt chart shows that four identical microplates are sequentially introduced into the system by the robot at times 0, 200.5, 401, and 601.5 s, respectively. The bold horizontal lines show the processing operations at the workstations, and the thin dotted line shows the route of the robot between the workstations. For the reader's convenience, to distinguish between operations on different microplates, their horizontal lines are depicted in different colors and use indicators represented by small triangles, squares, and diamonds, respectively. Figure 2 clearly shows that the Cytomat2C and Envision workstations perform two operations (on different microplates) during each cycle in the process sequence. Remark. We will study the scheduling problem under consideration from the point of view of PERT/CPM project management.