Research on flexible job shop scheduling under finite transportation conditions for digital twin workshop

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Highlights

  • A flexible job shop scheduling model under finite transportation conditions is established.

  • An algorithm with redundant three-layer encoding and decoding of correction is designed to eliminate transportation constraint conflicts.

  • An entity-JSON transmission method between the scheduling result and the workshop Digital Twin (DT) system is proposed to apply scheduling result in DT system.

Abstract

Flexible job shop scheduling is one of the most effective methods for solving multiple varieties and small batch production problems in discrete manufacturing enterprises. However, limitations of actual transportation conditions in the flexible job shop scheduling problem (FJSP) are neglected, which limits its application in actual production. In this paper, the constraint influence imposed by finite transportation conditions in the FJSP is addressed. The coupling relationship between transportation and processing stages is analyzed, and a finite transportation conditions model is established. Then, a three-layer encoding with redundancy and decoding with correction is designed to improve the genetic algorithm and solve the FJSP model. Furthermore, an entity-JavaScript Object Notation (JSON) method is proposed for transmission between scheduling services and Digital Twin (DT) virtual equipment to apply the scheduling results to the DT system. The results confirm that the proposed finite transportation conditions have a significant impact on scheduling under different scales of scheduling problems and transportation times.

Introduction

The rapid development of intelligent manufacturing technology has contributed to upgrading the manufacturing process from a manual one to an intelligent one [1]. The order type has been transformed from a single-variety and large-volume to multi-variety and small-batch. Recently, to solve the problem of production scheduling under multi-variety and small-batch orders, flexible job shop scheduling (FJS) has become one of the research hotspots in the field of production scheduling [2,3]. However, most researchers have focused on the development of models and algorithms that are relatively complicated to verify and apply in practical engineering. With the application of Digital Twin (DT) technology in manufacturing, technical support for real-time production can be provided in practical manufacturing workshops [4,5]. Moreover, when production scheduling technology is applied to the DT system, job transportation between machines in the job-shop scheduling problem (FJSP) is not handled in accordance with the actual conditions. During actual production, strong coupling relationships and constraints exist between transportation and processing, which increases the difficulty of applying the real-time production process to the DT system [6]. Therefore, the application of FJS in the DT system under limited transportation conditions should be further investigated.

Flexible job shop scheduling was first proposed by Brucker and Schile [7] in 1990. Since then, many studies have focused on developing methods for solving this problem. In the early research, genetic algorithm (GA) [8,9], variable neighborhood search algorithm [10,11], and ant colony algorithm [12] were employed. However, these algorithms are prone to local optimization when solving complex combinatorial optimization problems. Other FJSP investigations have focused on hybrid algorithms. Xia et al. [13] mixed particle swarm optimization and simulated annealing to improve both global and local search capabilities. Yuan et al. [14] utilized hybrid differential evolution algorithms to solve FJSP. Lin et al. [15] improved the GA on the representation of chromosome coding to solve the scheduling problem and proved that it can outperform the prior GA. Defersha et al. [16] proposed an efficient two-stage GA for the FJSP. Therefore, it is effective to design improved algorithms with local and global search parameters according to the specific problem constraints.

With the continuation of the research, algorithms that achieve good results for FJSP solving have been developed. However, the originally proposed problem model was not like the actual demand. Therefore, researchers who were concerned about practical applications have begun to study FJSP under multiple factors and constraints. Deliktas et al. [17] and Kress et al. [18] considered the influence of sequence-dependent setup times in FJSP. Pei et al. [19] proposed a column generation-based approach for a two-stage FJSP with no wait time. Furthermore, other researchers [20], [21], [22], [23] have pointed out that sequence-related setup time and waiting time represent important factors in addition to the processing time. Moreover, in terms of transportation time, Zhang et al. [24] proposed an FJSP model accounting for transportation constraints and bounded processing times. Nouri et al. [25] simultaneously investigated the scheduling machine and transport robot in the FJSP. Dai et al. [26] proposed an energy-efficient FJSP with transportation constraints. Zhou et al. [27] studied the synchronous scheduling of logistics service and processing service in cloud manufacturing without considering logistics service with limited load capabilities. Rossi and Dini [28], Karimi et al. [29], and Zhang et al. [30] improved different algorithms to solve the FJSP with transportation time. Although many investigations have identified that transportation time is a very important factor in the FJSP, these studies define transportation time as a fixed value between different machines. However, in many cases during the actual transportation stage, the transportation machine is either in a waiting state or needs to return to the charging area. Pre- and post-transportation factors are bound to bring more complex constraints to the production schedule.

In DT workshop system research, Tao et al. [31] were the first to propose a five-dimensional model for smart manufacturing. Since then, researchers have studied workshop DT systems based on the proposed model. Liu et al. [32] proposed a DT-based super network workshop scheduling framework. Fang et al. [33] introduced a DT-based architecture and working principle of the new job shop scheduling model to arrange machines and workers. Negri et al. [34] proposed a DT framework for production schedules that accounts for the uncertainty parameters. Wang and Wu [35] established a planning and scheduling system DT model for management and control mechanisms. Lu et al. [36] reviewed the recent development of DT technologies in manufacturing systems and processes, and they summed up the research surge of DT in the field of engineering since 2016. Zhuang et al. [37] proposed five-dimensional modeling of shop-floor DT and pointed out that DT application has not yet been extended to the production stage. The application of DT technology is still a research difficulty in practical production. Although some studies have realized the importance of DT workshops in achieving production schedules, most of them have focused on the framework.

The application of FJS technology in the DT workshop system is one of the important intelligent manufacturing management technology research directions. However, due to a lack of transportation constraints, current FJS results cannot be applied to the DT workshops to manage actual production. Therefore, in this paper, coupling and scheduling of transportation and processing stages in the FJSP are investigated. The transportation and processing operations coupling model is established based on the limited transportation capacity constraint. As a result, the FJS model is improved. Moreover, the GA is enhanced and a three-layer encoding with redundancy and decoding with correction is designed to solve the scheduling problem. During the decoding process, the forward insertion operation of the transportation and processing stage is designed to improve the solution quality and algorithm convergence. At the genetic operator stage, relatively simple and effective crossover and mutation operators are designed based on three-layer coding. Finally, the scheduling data transmission structure is constructed and applied to the DT workshop system.

The remainder of this paper is organized as follows: In Section 2, the coupling relationship between transportation stage and processing is analyzed, and a scheduling model under limited transportation conditions is established. The improved genetic algorithm (IGA) is introduced in Section 3. Data experiments and applications are analyzed in Section 4. In Section 5, conclusions are drawn, and future work is discussed.

Section snippets

Problem description and notations

The conventional FJSP can be described as m machines in a machining system processing n types of jobs. Each job contains one or more predetermined operations. Each operation can be processed on several different machines, while the processing operation time varies according to the machine performance. An example of the FJSP processing time is shown in Table 1.

Based on the conventional FJSP model, during the processing stage, a time model with parameters, such as the setup time, waiting time,

Improved GA for FJSP under finite transportation conditions

In this section, a GA is selected to solve the problem. Genetic algorithm is one of the more effective methods for solving combinatorial optimization problems. However, it prematurely falls into local convergence. Therefore, in this section, an adaption improvement in GA's encoding, decoding, crossover, mutation, and other operations is proposed. Meanwhile, the population initialization method and forward insertion operations are designed to improve global searchability.

Experiment and verification

Two-aspect verification was conducted to confirm the effectiveness of the proposed model and the algorithm. Data experiments on different scales were conducted. Moreover, the transmission method between the scheduling result and the DT system was studied. In the DT virtual system, the scheduling results were input into the model to verify its effectiveness. All data experiments were tested in MATLAB on the same computer with an Intel i5-9400 CPU and 16 GB of RAM.

Conclusions

In this paper, an FJSP model under finite transportation conditions was established, GA was improved to solve the proposed problem, and an entity-JSON transmission method between the scheduling result and the DT was established to verify the proposed models. The coupling relationship between transportation and processing was analyzed, and the scheduling model was established. A three-layer encoding with redundancy and decoding with correction was designed within the algorithm to solve

Author Statement

Jun Yan: Methodology, Writing-Original draft preparation, Software. Zhifeng Liu: Conceptualization, Methodology, Supervision. Caixia Zhang: Visualization. Tao Zhang: Data curation. Yueze Zhang: Investigation. Congbin Yang: Writing- Reviewing and Editing, Project administration.

Declaration of Competing Interest

This manuscript has not been published or presented elsewhere in part or in entirety and is not under consideration by another journal. We have read and understood your journal's policies, and we believe that neither the manuscript nor the study violates any of these. There are no conflicts of interest to declare.

Acknowledgments

The authors are grateful for financial support from the National Natural Science Foundation of China (No. 51805012 and 51975019), the outstanding talent from Beijing University of Technology.

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