# Graph-Based Modeling in Shop Scheduling Problems: Review and Extensions
## 6 Overview of the Full Dataset

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To have a better understanding of where the dataset stands within each category, this section presents simple visualizations to compare the frequency of subcategories in each macro category. Figure 23 compares the percentage of different graphs in the dataset. It is observed that undirected graphs have been utilized less than the other types, while some of these undirected graphs could have great potential applications in the field of shop scheduling. For instance, Markov Random Field (MRF) model and Bayesian Network (BN) are among a few probabilistic graph-based models which can potentially consider the uncertainty of the real-world shop environments. However, they barely appeared in the dataset, (i.e., one usage of MRF and no usage of BN was observed). On the other hand, the significant percentage of references using the disjunctive graphs stands out in this chart. Figure 24 shows that the majority of references reviewed in this study falls under the job shop macro category. This reveals an eye-opening gap in this literature, i.e., while job shop is not the most complicated and novel layout among shop manufacturing layouts, job shop and its relevant problems are still attracting so much attention. Whereas the intelligent systems including mixed systems have been practical in today's dynamic production environment, they have been relatively neglected (based on our dataset). This is also true about flexible manufacturing systems (FMS) and cellular manufacturing systems (CMS) which often incorporate newer technology such as IoT and robots. An interesting observation is that 57% of the top 10% most cited papers focus on flexible job shop (FJS) in comparison to the entire dataset where 28.9% of papers focus on FJS. Figure 23: Percentage of different types of graph-based models in the dataset. Figure 24: Percentage of different types of layouts in the dataset. We also observed that the proportion of the static (S) scheduling problems addressed in the dataset dramatically dominates the dynamic (D) ones, i.e., 87.4% of references addressed static scheduling comparing to 12.6% for dynamic scheduling problems. This dramatic difference can be noticed in Tables 6-8. Furthermore, an interesting point was observed by doing an additional analysis over the papers making up the top 10% of citations per year: of the top 10% of papers, 29% address dynamic scheduling which is notable in comparison to the entire dataset where only 12.6% address dynamic scheduling. Minimizing the makespan is by far the most frequently objective used in 67% of the references in our dataset. The second most popular objectives are performance measures related to tardiness including total tardiness, mean tardiness, and weighted tardiness. Finally, about 17% of collected references used other objectives such as workload, lateness, flow time, etc. Figure 25 simply shows these proportions. Considering the efficiency and practicality of approximate methods to solve the scheduling problems on one hand, and the time expensiveness of exact method on the other, a greater application of approximate solutions was expected. Our dataset has confirmed this expectation in Figure 26. To be more precise, overall, 201 different methods are found in 143 references in our dataset; out of which only 16% are exact methods. Moreover, about 94% of all papers in our dataset used at least one type of Approximate method. Linear programming (LP) and genetic algorithm (GA) are the most applied exact and approximate methods with 12.2% and 14.8% frequency among the data. Finally, Figure 27 shows the lack of usage of real case study among the reviewed papers in the dataset. Those 10% and 29% of references which used 'Real Case' and 'Numerical' (Num) case study, usually also applied their solution to a benchmark problem. Figure 26: Percentage of different types of solution methods in the dataset. Figure 27: Percentage of different types of case studies in the dataset.