Graph-Based Modeling in Shop Scheduling Problems: Review and Extensions

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.

Distributed job allocation using response threshold for heterogeneous robot team under deadline constraints

“…GNNs are widely used to solve various combinatorial optimization problems in recent years 33 . The nodes and edges in the graph depict the relationship between the jobs and the robots 39 . Gautier et al 32 proposed a deep Q‐learning based distributed job allocation with experience relay in a homogeneous robot team.…”

“…33 The nodes and edges in the graph depict the relationship between the jobs and the robots. 39 Gautier et al 32 proposed a deep Q-learning based distributed job allocation with experience relay in a homogeneous robot team. Wang and Gombolay 31 developed a graph attention network based RoboGNN scheduler for multi-robot job allocation with deadline constraints utilizing imitation learning for training.…”

Graph Coloring Implementation Using Welch Powell Algorithm In Lecture Scheduling Design For Mathmatics Department

“…. The following are characteristics of the minimal number of colors required for node coloring, or the chromatic number (Otala et al, 2021) and (Karin, 2021):…”