# Graph-Based Modeling in Shop Scheduling Problems: Review and Extensions
## 9 Conclusions and Future Research Directions  
Graph theory and graph-based models have been powerful tools to understand the functionality of different systems. Graphs particularly can simplify the analysis of complex systems. Graphs have major applications in a variety of fields including many sciences and engineering research areas. Manufacturing systems and their associated problems including shop scheduling problems extensively benefits from graph theory concepts since all elements of the systems including resources, materials, parts, processes, and their connections can be represented and analyzed by the connected network of nodes and edges called as graphs. Despite the tremendous number of publications applying graph concepts to shop scheduling problems, the literature lacks a comprehensive survey study in this area. To the best of our knowledge, our paper is the first review study in the literature to propose such a comprehensive review paper which systematically studies the overview and the perspective of this research field. First, we proposed our methodology (Figure 1) to collect and review relevant references utilizing graph theory to model and/or solve different variations of shop scheduling problems in the domain of manufacturing systems. This methodology can easily be generalized and extended to be used in other survey studies. Purely by the size of our collected data, we can conclude that this field of research is popular and of importance, even though neither shop scheduling nor graph theory are new concepts. This can be explained by the ever-evolving nature of manufacturing. As new technology is introduced, such as robots or IoT, the system can be altered and ideally optimized further, allowing researchers to revisit this space. Even in a shop floor without \"newer technology\", these systems are incredibly complex with many constraints and attributes that are not addressed in the classic versions of their scheduling problems, so generating sustainable modeling approaches and solutions addressing the complexity of systems with all constraints can help apply said solutions to a real manufacturing system. After finalizing out collected data, we used a novel procedure/measurement to analyze the distribution of the quality of journals publishing our collected references. This analysis is one of our critical contributions since it can confirm the validation of our dataset, and more importantly it can indicate the research trend and hotspot in the literature. Thereafter, considering the variety of problems addressed in our collected data, we proposed our own modified version of categorizations over system layouts, scheduling problem, and scheduling solutions methods. These categorizations are comprehensive and detailed enough to cover all aspects of problems' properties without over-subdividing or exhausting micro categories. Almost all papers in our dataset used at least one type of approximate method as scheduling solutions and some papers applied multiple methods, e.g., a slightly improved heuristics/meta-heuristics, to address classical scheduling problems. Considering the rich background of scheduling approximate solutions, insisting on improving the quality of solutions by proposing/improving an efficient method for well-studied shop scheduling problems seems unnecessary. Instead, future studies can focus on new problems and precisely embrace the complexity of the post-modern manufacturing environment and industry 4.0 by proposing sustainable and innovative modeling approaches incorporating different powerful graph-based techniques and concepts. Moreover, it was observed in our dataset that the integration of shop scheduling and process planning procedures has been relatively neglected. These two procedures should not be considered independent. It was shown that integrating the process planning and shop scheduling results into the strategic and sustainable development required in intelligent manufacturing systems. Thus, studying the integration problems is another essential future research area.