Flexible Job Shop Research Articles

Shared manufacturing-based distributed flexible job shop scheduling with supply-demand matching

Shared Manufacturing (sharedMfg) is a peer-to-peer (P2P) paradigm for sharing manufacturing resources, derived from the sharing economy. In sharedMfg, manufacturing service resources are integrated into a large set with defined service types. Based on its resource organization structure, we build a model for the shared manufacturing-based distributed flexible job shop scheduling problem (SM-DFJSP) with supply-demand matching. The goal is to minimize both the total cost and the makespan. The SM-DFJSP model enables the scheduling of jobs requiring different manufacturing services across distributed, heterogeneous, and flexible service resource units (SRUs) with diverse manufacturing functions. To solve the SM-DFJSP, we propose a hybrid estimation of distribution algorithm and Tabu search (EDA-TS), including EDA and TS components. Additionally, a multi-populations strategy and non-dominated solutions memory mechanism are designed to improve the exploration ability of the algorithm. Within the EDA component, three probability distribution models and some dispatching rules are designed to generate a new population. In the TS component, three neighborhood search structures are built that adopt hybrid short and long memory tabu strategy. Finally, comparison and ablation experiments on 25 instances demonstrate the superior performance of the EDA-TS algorithm in solving the SM-DFJSP, highlighting the effectiveness of the multi-population strategy and non-dominated solutions memory mechanism.

Flexible Job-shop Scheduling Optimization based on Improved Gray Wolf Algorithm

This article proposed an improved gray wolf optimizer to deal with the flexible job-shop scheduling problem. By using a random key for coding job positions and adopting a local search strategy, we achieve group reconstruction and updating with the help of three good fitness values of the population, hence continuously searching for the optimal solution. Simulation experiments were conducted on a standardized test case, demonstrating the effectiveness of this method.

Deep reinforcement learning-based memetic algorithm for energy-aware flexible job shop scheduling with multi-AGV

The integration of manufacturing and logistics scheduling issues in shop operations has garnered considerable attention. Concurrently, escalating concerns about global warming have propelled the emergence of green manufacturing as a critical challenge. Notably, extant research in this domain lacks an incorporation of green metrics within the framework of manufacturing and logistics-integrated scheduling. Furthermore, the determination of a critical block remains a challenging aspect, with an absence of consideration for a neighborhood structure founded on the critical block. Moreover, prior endeavors have predominantly relied on Q-learning to augment evolutionary algorithms, a strategy criticized for its limited learning capacity. Consequently, this study addresses these gaps by presenting an energy-efficient flexible job Shop scheduling with multi-autonomous guided vehicles (EFJS-AGV). The primary objectives are the simultaneous minimization of makespan and total energy consumption. To tackle this NP-hard problem, a deep Q-network-based memetic algorithm is proposed. The devised algorithm incorporates several distinctive features. Firstly, the strength Pareto evolutionary algorithm (SPEA2) is employed to swiftly explore the objective space, enhancing convergence and diversity. Secondly, four distinct local search operators based on critical paths and blocks are devised to efficiently reduce makespan. Thirdly, deep reinforcement learning is harnessed to understand the interplay between solutions and action selection. This understanding aids the evolutionary algorithm in selecting the most optimal operator. The efficacy of the proposed algorithm is rigorously evaluated through a comparative analysis with five state-of-the-art algorithms. The assessment is conducted on two benchmark datasets encompassing 20 instances. The numerical experimental results affirm the effectiveness of the proposed enhancements and algorithms. Furthermore, the superior performance of the proposed algorithm in addressing the EFJS-AGV substantiates its robustness and applicability.

Scheduling for the Flexible Job-Shop Problem with a Dynamic Number of Machines Using Deep Reinforcement Learning

The dynamic flexible job-shop problem (DFJSP) is a realistic and challenging problem that many production plants face. As the product line becomes more complex, the machines may suddenly break down or resume service, so we need a dynamic scheduling framework to cope with the changing number of machines over time. This issue has been rarely addressed in the literature. In this paper, we propose an improved learning-to-dispatch (L2D) model to generate a reasonable and good schedule to minimize the makespan. We formulate a DFJSP as a disjunctive graph and use graph neural networks (GINs) to embed the disjunctive graph into states for the agent to learn. The use of GINs enables the model to handle the dynamic number of machines and to effectively generalize to large-scale instances. The learning agent is a multi-layer feedforward network trained with a reinforcement learning algorithm, called proximal policy optimization. We trained the model on small-sized problems and tested it on various-sized problems. The experimental results show that our model outperforms the existing best priority dispatching rule algorithms, such as shortest processing time, most work remaining, flow due date per most work remaining, and most operations remaining. The results verify that the model has a good generalization capability and, thus, demonstrate its effectiveness.

Combination of genetic algorithm and shifting bottleneck heuristics to solve a job shop scheduling problem in wood processing company

The scheduling problem has always been the concern of most companies in the flexible Job shop or Job shop environments because of its complexity. It is really a challenge for researchers to solve or find out the optimum solution. The lead time production at Teak Woods line in a wood processing company, a case study, faced with about 80% of orders which could not be done on time, although its capacity meet requirements. Therefore, it is very useful and necessary to set up a production scheduling model in order to reduce production time and synchronize the product’s parts through efficient modulation in an optimum sequence of jobs on the shopfloor. A combination of Genetic Algorithm and Shifting Bottleneck Heuristics was used to find out high quality solutions. It shows that the productivity increased from 2.32 m3/day to 4.3 m3/day (up 98.27%); Processing time was reduced from 3248.6 minutes to 1352.1 minutes (down 58.38%); The sync time decreased from 7554.8 minutes to 350.8 minutes (down 95.36%).

Correction: A memetic NSGA‑II for the multi‑objective flexible job shop scheduling problem with real‑time energy tariffs

Correction: A memetic NSGA‑II for the multi‑objective flexible job shop scheduling problem with real‑time energy tariffs

Multi-objective optimization of dual resource integrated scheduling problem of production equipment and RGVs considering conflict-free routing.

In flexible job shop scheduling problem (FJSP), the collision of bidirectional rail guided vehicles (RGVs) directly affects RGVs scheduling, and it is closely coupled with the allocation of production equipment, which directly affects the production efficiency. In this problem, taking minimizing the maximum completion time of RGVs and minimizing the maximum completion time of products as multi-objectives a dual-resource integrated scheduling model of production equipment and RGVs considering conflict-free routing problem (CFRP) is proposed. To solve the model, a multi-objective improved discrete grey wolf optimizer (MOID-GWO) is designed. Further, the performance of popular multi-objective evolutionary algorithms (MOEAs) such as NSGA-Ⅱ, SPEA2 and MOPSO are selected for comparative test. The results show that, among 42 instances of different scales designed, 37, 34 and 28 instances in MOID-GWO are superior to the comparison algorithms in metrics of generational distance (GD), inverted GD (IGD) and Spread, respectively. Moreover, in metric of Convergence and Diversity (CD), the Pareto frontier (PF) obtained by MOID-GWO is closer to the optimal solution. Finally, taking the production process of a construction machinery equipment component as an example, the validity and feasibility of the model and algorithm are verified.

An improved MOEA/D for low-carbon many-objective flexible job shop scheduling problem

The low-carbon many-objective flexible job shop scheduling problem (LCMa-FJSP) has developed into a major topic of current research owing to global warming and energy crises. In this study on the LCMa-FJSP, a comprehensive scheduling model with four objectives, such as minimizing the completion time, total delay time, processing load rate of the bottleneck machine and total carbon emissions of the system is built. To solve this complex LCMa-FJSP, a novel multi-objective evolutionary algorithm (MOEA) with three modified strategies, named IMOEA/D-HS, is proposed. First, a novel hybrid initialization strategy combining five heuristic methods is used to obtain a reliable initial population. Second, a new restart strategy that considers limited restarts is applied to reduce carbon emissions while protecting the lifetime of the machine. Third, a local reinforcement strategy is proposed that can efficiently improve the convergence of a part of sub-problems identified by distance and angle-based evaluation indicator (APD). To impartially and comprehensively analyze and evaluate the performance of IMOEA/D-HS, it is compared with four state-of-the-art algorithms, i.e., MOEA/D-DRA, MOEA/DD, NSGA-III and RVEA on 15 numerical tests. The results demonstrate that IMOEA/D-HS outperforms these four algorithms in the terms of convergence and diversity, which proves its ability to solve complex LCMa-FJSPs.

Joint optimization of flexible job shop scheduling and preventive maintenance under high-frequency production switching

To secure a larger market share in the dynamically evolving personalized market demand, enterprises have to adopt a more flexible production mode. In this context, the implementation of parallel production with multiple product types necessitates frequent switching between different products, imposing elevated requirements on machine fault-free operation and stable production. There is a compelling motivation to investigate the joint optimization of the flexible job shop scheduling problem and preventive maintenance (FJSSP-PM). However, existing research has primarily focused on utilizing predetermined maintenance as inputs for optimizing production scheduling, while overlooking the uncertain maintenance requirements of machines during the production process. Therefore, this paper proposes a two-stage joint optimization model to simultaneously address three subproblems: machine assignment, operation sequencing, and maintenance arrangement. Specifically, the first stage involves constructing a mathematical model for the FJSSP to minimize penalties for tardiness and workload balancing. Subsequently, a comprehensive failure rate model is developed to determine maintenance requirements for machines with production-dependent failure behavior, particularly under high-frequency production switching scenarios. Furthermore, a feedback-updated strategy is proposed to achieve synchronous optimization of production and maintenance activities in an economically and operationally efficient manner. Given the complexity of the problem, a hybrid meta-heuristic algorithm is designed to effectively handle large-scale cases. The effectiveness of the proposed model in terms of cost-savings has been verified compared with existing relevant methods.

Multi-resource constrained flexible job shop scheduling problem with fixture-pallet combinatorial optimisation

There is a lack of research on the flexible job shop scheduling problem (FJSP) considering limited fixture-pallet resources in multi-product mixed manufacturing workshops. However, field research in a leading engine manufacturer in China has revealed that fixture-pallet resources are a key factor limiting capacity breakthroughs although they play an auxiliary role in the production process. Thus, in this paper, we propose a methodology for the multi-resource constrained flexible job shop scheduling problem with fixture-pallet combinatorial optimisation. First, a mixed integer programming model with machine-fixture-pallet constraints is constructed aiming to minimize makespan. Then, a novel genetic algorithm integrated with feasibility correction strategy and self-learning variable neighbourhood search (VNS) is proposed to address the complicated scheduling problem, where the feasibility correction strategy is designed to solve potential conflict between machine selection and fixture selection chromosomes and self-learning VNS is executed to further improve the optimisation capability. Moreover, the effectiveness and efficiency of proposed algorithm are demonstrated by computational experiments with real data from cooperated engine manufacturing plant, which would provide convincing support for real production scheduling under complex scenarios.

Bi-objective flexible job shop scheduling on machines considering condition-based maintenance activities

This paper investigates multi-objective flexible job shop scheduling considering maintenance activities. The condition-based maintenance strategy is used to reduce machines breakdown. After maintenance activities are completed, the machine degradation model’s parameters are updated using Bayesian inference to make it more realistic. A novel multi-objective evolutionary algorithm is designed to address the multi-criteria scheduling problem. An innovative insertion algorithm is proposed in this paper to balance production plan and maintenance activities. According to the experimental results, the designed evolutionary algorithm performs better than the other two traditional algorithms, and the insertion approach can reduce the impact of maintenance activities on production plan by up to 200%.

Large-Scale Dynamic Scheduling for Flexible Job-Shop With Random Arrivals of New Jobs by Hierarchical Reinforcement Learning

As the intelligent manufacturing paradigm evolves, it is urgent to design a near real-time decision-making framework for handling the uncertainty and complexity of production line control. The dynamic flexible job shop scheduling problem (DFJSP) is frequently encountered in the manufacturing industry. However, it is still challenging to obtain high-quality schedules for DFJSP with dynamic job arrivals in real-time, especially facing thousands of operations from a large-scale scene with complex contexts in an assembly plant. This paper aims to propose a novel end-to-end hierarchical reinforcement learning framework for solving the large-scale DFJSP in near real-time. In the DFJSP, the processing information of newly arrived jobs is unknown in advance. Besides, two optimization tasks, including job operation selection and job-to-machine assignment, have to be handled, which means multiple actions must be controlled simultaneously. In our framework, a higher-level layer is designed to automatically divide the DFJSP into sub-problems, i.e., static FJSPs with different scales. And two lower-level layers are constructed to solve the sub-problems. In particular, one layer based on a graph neural network is in charge of sequencing job operations, and another layer based on a multi-layer perceptron is used to assign a machine to process the job operations. Numerical experiments, including offline training and online testing, are conducted on several instances with different scales. The results verify the superior performance of the proposed framework compared with existing dynamic scheduling methods, such as well-known dispatching rules and meta-heuristics.

Energy-efficient scheduling for a flexible job shop problem considering rework processes and new job arrival

Sustainable production is not limited to environmental concerns only; It also provides economic benefits for businesses. Businesses that adopt sustainability principles can gain advantages in matters such as cost savings, competitive advantage, risk management, legal compliance and corporate reputation. Therefore, sustainability is no longer an option but a strategic imperative for businesses. For this reason, studies on energy-sensitive scheduling have started to increase recently. Another important factor in sustainable manufacturing is the reduction of scrap. Rework operations are required to reduce scrap. In this study, the multi-objective flexible job shop scheduling problem (MO-FJSP) that considers energy efficiency is discussed. The created model aims to minimize the energy consumption, total machine workload and makespan. In this study, new job arrivals are considered as dynamic events. Another dynamic event added to the model is the addition of rework processes between operations to reduce the scrap rate when a scrap decision is made during the production stages. The enhanced NSGA II algorithm was applied to solve this problem. The enhanced NSGA II algorithm was applied to test instances and its performance was compared using some of the multi-objective performance indicators. These experimental results prove the effectiveness of the proposed solution method.

Flexible Assembly Job Shop Scheduling Considering Assembly Sequence Variation Under Dual-resource Constraints Using Discrete Barnacles Mating Optimizer Algorithm

Flexible Assembly Job Shop Scheduling Considering Assembly Sequence Variation Under Dual-resource Constraints Using Discrete Barnacles Mating Optimizer Algorithm

Modeling the Integrated Flexible Job-Shop and Operator Scheduling in Flexible Manufacturing Systems

This paper addresses the integrated flexible job shop and operators scheduling problem, introducing shift-based constraints on operators. We investigate how the advanced modeling and solution techniques, specifically, Mixed-Integer Programming (MIP) and Constraint Programming (CP) perform on this intricate scheduling problem. We test the effectiveness of both the MIP and CP models on an illustrative example as well as on a set of larger instances and draw conclusions, which indicate the need to integrate these two models into some approximation scheme to tackle large-scale instances for this complex problem.

A Two-Stage Individual Feedback NSGA-III for Dynamic Many-Objective Flexible Job Shop Scheduling Problem

A Two-Stage Individual Feedback NSGA-III for Dynamic Many-Objective Flexible Job Shop Scheduling Problem

The Flexible Job Shop Scheduling Problem with Setups and Operator Skills: an application in the textile industry

The Flexible Job Shop Scheduling Problem (FJSSP) is one of the most studied problems in the literature thanks to its practical relevance. Many industrial production scheduling problems can be seen as a FJSSP with different constraints and objectives. The studied problem arises in a textile factory, precisely in the sewing process. Multiple real-world constraints are tackled. Individual skills of operators and different types of setup times are considered: machine-change setup time for operators, colour-change setup times and configuration-change setup times. The objective is to minimize the total tardiness. To the best of the authors’ knowledge, this is the first study that tackles this variant of the problem. This paper presents a preliminary study to validate the approach and evaluate the tractability of the industrial problem. A mixed-integer linear programming (MILP) model is proposed and solved using a commercial solver. Real-world data are used to generate more than 1000 problems that are clustered in 4 groups based on the number of jobs to be scheduled, the number of operators and flexibility of their skills. The results show that the proposed MILP model can reach optimality for the small size instances but it is intractable for most large-sized instances. Moreover, the results highlight how diversifying the operators’ skills can help find better solutions.

Integrated Genetic Algorithm with Dispatching Rules to solve the Flexible Job Shop Scheduling Problem under Multi-AMR Transportation Constraints

The Flexible Job Shop Scheduling Problem (FJSSP) is a challenging issue for industries and manufacturers. However, the transportation tasks in this problem should not be underestimated, as their impact is substantial, and they are frequently overlooked in the literature. In this paper, the FJSSP with multi-AMR (Autonomous mobile robot) transportation constraints is addressed. We developed a genetic algorithm with dispatching rules to solve the Flexible Job Shop Scheduling Problem with Multi-AMR Transportation Constraints by minimizing the total completion time. Two dispatching rules are used to assign transportation robots. The first rule is random assignment and the second rule is AMR per Job assignment. Our encoding and decoding process utilizes a three-layer sequence (machine sequence, operation sequence, and AMR sequence). Finally, we conducted comprehensive experiments on different benchmarks to assess the performance of the proposed algorithm with a variable number of AMR to transport the operations. The experimental results indicate that the proposed algorithm effectively and efficiently solve the problem.

Learning-Based Genetic Algorithm to Schedule an Extended Flexible Job Shop.

This work considers an extended flexible job-shop scheduling problem from a semiconductor manufacturing environment. To find its high-quality solution in a reasonable time, a learning-based genetic algorithm (LGA) that incorporates a parallel long short-term memory network-embedded autoencoder model is proposed. In it, genetic algorithm is selected as a main optimizer. A novel autoencoder model is trained offline via end-to-end unsupervised learning without relying on labeled data. This model captures the major linkages among decision variables and generates promising solutions in an informative low-dimensional space, striking a balance between computational efficiency and solution quality. To further improve its search ability, a co-evolving framework is designed, which includes both a network-embedded subpopulation and a regular one. The former focuses on its global search while the latter ensures LGA's convergence. An information exchange method between the two subpopulations balances global and local search, improving its overall optimization ability. This work conducts various numerical experiments to compare LGA with the CPLEX optimizer, several classical heuristics, and some popular methods. Results show that LGA outperforms its peers in finding high-quality solutions in a reasonable time.

A novel hybrid algorithm of genetic algorithm, variable neighborhood search and constraint programming for distributed flexible job shop scheduling problem

A novel hybrid algorithm of genetic algorithm, variable neighborhood search and constraint programming for distributed flexible job shop scheduling problem