A Branch and Bound Algorithm for Scheduling of Flexible Manufacturing Systems

Flexible manufacturing systems (FMSs), which can easily adapt to changes in job types, have been widely used in manufacturing areas. Scheduling of FMSs is a variant of a flexible job shop with transport robots and no buffer, and it is extremely hard as it involves determining the job processing sequence on machines and the sequence of robot tasks, with various jobs with different processing flows and the risk of deadlocks. Due to these characteristics, many existing studies have focused on developing heuristic algorithms. However, an optimal solution is still crucial to minimize FMSs makespan. Therefore, we propose a mixed integer programming (MIP) and a branch and bound (B&B) algorithm with a timed Petri net (TPN) to achieve optimal scheduling of FMSs. FMSs are first modeled with a TPN, and tight lower bounds are proposed based on bottleneck machines and sophisticated ready times. In addition, the search space is effectively reduced by the transition index marking (TIM)-based dominance rule and various deadlock prevention conditions based on the TPN. The experimental results show that our proposed B&B algorithm outperforms mathematical formulation and previous algorithms in various FMS instances. Note to Practitioners—Flexible manufacturing systems (FMSs) can often be found in various manufacturing areas composed of machines, material-handling robots, and controlling computers. With the increase in customer demand for diverse products manufactured in small quantities, the importance of FMSs has grown even more prominent in the manufacturing sector. In this paper, we develop a mixed integer programming (MIP) and a branch and bound (B&B) algorithm for optimal scheduling of FMSs with a timed Petri net (TPN). The proposed B&B can handle various FMS layouts by modeling with a TPN, regardless of the number of product routes, machines, and robots. Three lower bounds and dominance rules are proposed, and they have the great advantage of reduced computational time and search spaces. Our proposed method can also be implemented as a rolling horizon approach when jobs arrive in batches. Additionally, the algorithm can be adapted for use in other types of manufacturing systems, such as cluster tools, robotic cells, and track systems, which can be modeled using TPNs.