Residual Scheduling: A New Reinforcement Learning Approach to Solving Job Shop Scheduling Problem

Job-shop scheduling problem (JSP) is a mathematical optimization problem widely used in industries like manufacturing, and flexible JSP (FJSP) is also a common variant. Since they are NP-hard, it is intractable to find the optimal solution for all cases within reasonable times. Thus, it becomes important to develop efficient heuristics to solve JSP/FJSP. A kind of method of solving scheduling problems is construction heuristics, which constructs scheduling solutions via heuristics. Recently, many methods for construction heuristics leverage deep reinforcement learning (DRL) with graph neural networks (GNN). In this paper, we propose a new approach, named residual scheduling, to solving JSP/FJSP. In this new approach, we remove irrelevant machines and jobs such as those finished, such that the states include the remaining (or relevant) machines and jobs only. Our experiments show that our approach reaches state-of-the-art (SOTA) among all known construction heuristics on most well-known open JSP and FJSP benchmarks. In addition, we also observe that even though our model is trained for scheduling problems of smaller sizes, our method still performs well for scheduling problems of large sizes in terms of makespan. Interestingly in our experiments, our approach even reaches zero makespan gap for 49 among 60 JSP instances whose job numbers are more than 100 on 15 machines.