## 3 Related Work: Literature Review  
Scheduling theory is a widely discussed research topic in operations research and industrial engineering [5; 6; 7; 20; 21; 22]. However, since HTS is a relatively new technology, its scheduling problems have not yet been extensively studied. There is presently not much literature on HTS scheduling algorithms, despite the fact that they are clearly interesting from a theoretical point of view and applicable in practice. It was in the 1970s and early 1980s that the components that make HPS technologies possible came together. These were robots and small-scale servo-powered robotic devices, microplates, and apparently, most importantly, personal computers. In 1974, this technology was first used for enzyme-linked immunosorbent assay (ELISA) in London and at the Centers for Disease Control (USA) [23]. In early studies, heuristic and approximation methods such as genetic algorithms were proposed to solve the HTS scheduling problem [1; 24; 25]; however, they could not guarantee an optimal solution. Thus, the applicability of these methods is limited. In one of the first papers on the topic that we are aware of [4], the authors presented a computer-integrated model incorporating characteristics of HTS scheduling problems for different assays. They observed that, as with most hard scheduling problems, there are no efficient algorithms for finding optimal solutions in HTS; hence, they proposed the use of heuristic procedures and genetic algorithms, which had become known for their applicability in flowshop and jobshop problems in scheduling theory several decades earlier. In [24; 26], the authors focused on creating an optimal HTS schedule exploiting cyclic Petri net models. When defining the variables in their model, they used the starting and ending events of activities. This way of defining discrete time nodes was easy to implement in the scheduling model. Another study [27] was a continuation of previous work [26], and was also based upon Petri net concepts with the aim of determining a globally optimal schedule for HTS systems. In addition, these authors extended their model to include the hierarchical nesting of cycles. In paper [16], the authors modeled the HTS system using a dioid algebraic approach and applied max-plus algebra to the cyclic HTS. In max-plus algebra, the addition and multiplication operations of classical arithmetic are replaced by the max and addition operators, respectively. The scheduling problem was then transformed into the problem of calculating a feedback controller that could function correctly in the presence of variations, disturbances, and delays. In [3], the author studied timed event graphs with constraints, and modeled systems with nested schedules. To apply his findings, he used the proposed method to analyze a real HTS system, and found an optimal schedule. Extending the dioid and Petri net approaches, the authors of the mentioned works [24; 25; 26; 27] used mixed integer programming formulations to schedule real HTS systems. An important step forward in the analysis and practical use of the considered HTS scheduling problem was made in recent studies [11; 12; 13; 14] that significantly developed the mixed-integer programming (MIP) and resource-oriented Petri nets approaches, respectively, to model, analyze and solve the considered problem. The study in [11; 13] was motivated by the practical problem of automated testing for viruses and new drugs using HTS. The authors examined in detail how scheduling screening activities in a real-world HTS system affects its efficiency, throughput, operating costs, and screening quality. The purpose of that work was to minimize the total screening time and to study the features of the screening process that guarantee the optimal schedule.