Key Takeaways & Executive Findings
- •• First study to address the three-stage flexible job shop scheduling problem with assembly and AGV transportation (FJSP-T-A) with the objective of minimizing makespan. • Development of a mixed integer linear programming (MILP) model that provides optimal solutions for small-scale instances and serves as a benchmark for evaluating heuristic methods. • Proposal of a novel co-evolutionary algorithm (NCEA) incorporating a restart operation and multiple crossover strategies to effectively solve large-scale FJSP-T-A instances. • Statistical validation of the proposed algorithm's superiority over existing methods through RPI analysis and paired t-tests at the 95% confidence level.
Abstract
The flexible job shop scheduling problem (FJSP) is commonly encountered in practical manufacturing environments. A product is typically built by assembling multiple jobs during actual manufacturing. AGVs are normally used to transport the jobs from the processing shop to the assembly shop, where they are assembled. Therefore, studying the integrated scheduling problem with its processing, transportation, and assembly stages is extremely beneficial and significant. This research studies the three-stage flexible job shop scheduling problem with assembly and AGV transportation (FJSP-T-A), which includes processing jobs, transporting them via AGVs, and assembling them. A mixed integer linear programming (MILP) model is established to obtain optimal solutions. As the MILP model is challenging for solving large-scale problems, a novel co-evolutionary algorithm (NCEA) with two different decoding methods is proposed. In NCEA, a restart operation is developed to improve the diversity of the population, and a multiple crossover strategy is designed to improve the quality of individuals. The validity of the MILP model is proven by analyzing its complexity. The effectiveness of the restart operator, multiple crossovers, and the proposed algorithm is demonstrated by calculating and analyzing the RPI values of each algorithm's results within the time limit and performing a paired t-test on the average values of each algorithm at the 95% confidence level. This paper studies FJSP-T-A by minimizing the makespan for the first time, and presents a MILP model and an NCEA with two different decoding methods.
1. Introduction
Flexible production needs are becoming increasingly difficult for the conventional assembly line method to meet due to the diversification of market demand and the rise in product changes. The flexible job shop has become increasingly popular in modern manufacturing shops as a more adaptable and diverse style of production. Flexible job shops can handle many different types of products and operations in parallel, allowing each operation to be machined on any machine. Furthermore, it has been established that the flexible job shop problem (FJSP) is an NP-hard problem [1]. In actual production, the finished job often needs to be transported to another factory. A job is an integral part of the product and takes part in its assembly. The processing shop and assembly shop are separated by a specific amount of distance. From the processing shop to the assembly shop, the jobs need to be moved by AGVs. The quantity of AGVs is restricted because of their expensive price. Every task needs to be transported, which takes time as well.
This paper studies a three-stage assembly problem (FJSP-T-A). The first stage is the processing of FJSP. The second stage is the transportation of a multi-AGV and multi-load AGV transportation problem. The third stage is the assembly stage of a parallel machine assembly problem. FJSP-T-A needs to solve several sub-problems in three stages, namely, the processing machine selection sub-problem and operation sequencing sub-problem in the processing stage, the AGV selection sub-problem in the transportation stage, and the assembly machine selection sub-problem and operation sequencing sub-problem in the assembly stage. As a result, FJSP-T-A is a more intricate NP-hard problem than FJSP, the AGV scheduling problem, and the parallel machine scheduling problem.
This paper solves FJSP-T-A from both exact and approximation methods. The exact method is to resolve the problem by establishing a mixed integer linear programming (MILP) model specifically designed for FJSP-T-A. The MILP model serves as the foundation for research on the workshop scheduling problem, particularly when taking into account new goals or restrictions. The MILP model is crucial and capable of finding the best answer. We can extract the neighborhood structural characteristics, neighborhood relationships, neighbor...
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Shiming Yang, Leilei Meng, Saif Ullah, Chaoyong Zhang, Hongyan Sang, Biao Zhang (2025). MILP Modeling and Optimization of Three-Stage Flexible Job Shop Scheduling Problem with Assembly and AGV Transportation. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01281-z
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Frequently Asked Questions
What is the FJSP-T-A problem?
FJSP-T-A stands for the three-stage flexible job shop scheduling problem with assembly and AGV transportation. It integrates processing, transportation via AGVs, and assembly stages, aiming to minimize makespan.
What methods are proposed in this paper?
The paper proposes a mixed integer linear programming (MILP) model for exact solutions and a novel co-evolutionary algorithm (NCEA) with two decoding methods, a restart operation, and multiple crossover strategies for large-scale instances.
How is the effectiveness of the proposed algorithm validated?
The effectiveness is validated by comparing RPI values of algorithm results within time limits and performing paired t-tests at the 95% confidence level.
What is the significance of this study?
This is the first study to address FJSP-T-A with makespan minimization, providing a MILP model and an efficient co-evolutionary algorithm, which can improve scheduling efficiency in flexible manufacturing systems.
What are the key components of the NCEA?
The NCEA includes two different decoding methods, a restart operation to enhance population diversity, and a multiple crossover strategy to improve individual quality.
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