Abstract
Graphs are powerful tools to model manufacturing systems and scheduling problems. The complexity of these systems and their scheduling problems has been substantially increased by the ongoing technological development. Thus, it is essential to generate sustainable graph-based modeling approaches to deal with these excessive complexities. Graphs employ nodes and edges to represent the relationships between jobs, machines, operations, etc. Despite the significant volume of publications applying graphs to shop scheduling problems, the literature lacks a comprehensive survey study. We proposed the first comprehensive review paper which (1) systematically studies the overview and the perspective of this field, (2) highlights the gaps and potential hotspots of the literature, and (3) suggests future research directions towards sustainable graphs modeling the new intelligent/complex systems. We carefully examined 143 peer-reviewed journal papers published from 2015 to 2020. About 70% of our dataset were published in top-ranked journals which confirms the validity of our data and can imply the importance of this field. After discussing our generic data collection methodology, we proposed categorizations over the properties of the scheduling problems and their solutions. Then, we discussed our novel categorization over the variety of graphs modeling scheduling problems. Finally, as the most important contribution, we generated a creative graph-based model from scratch to represent the gaps and hotspots of the literature accompanied with statistical analysis on our dataset. Our analysis showed a significant attention towards job shop systems (56%) and Un/Directed Graphs (52%) where edges can be either directed, or undirected, or both, Whereas 14% of our dataset applied only Undirected Graphs and 11% targeted hybrid systems, e.g., mixed shop, flexible, and cellular manufacturing systems, which shows potential future research directions.
Highlights
We proposed a novel categorization over the most common and efficient graph-based models being used in the shop scheduling problems
In our systematic search process, we used the combination of relevant keywords and selected papers which are pertinent to the modeling of manufacturing systems and shop scheduling problems using graph-based models and the application of graph theory in this context
Graph theory and graph-based models have been powerful tools to understand the functionality of different systems
Summary
Objectives of Scheduling ProblemsDifferent objective functions or performance measures are used in the scheduling problems. A route ( known as the sequence) refers to the order of machines that a job should passes through [34,38,39]. Manufacturing systems and their layouts may be distinguished by their uniformity, existence of fixed routes, the flexibility of machines, the number of machines, and existence of buffer, set up times, etc. These differences come from variations in demand and required levels of production flexibility [40].
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