Search Results (121)

Carbon cap-and-trade is a practical policy in guiding manufacturers to produce economic and environmental production plans. However, previous studies on carbon cap-and-trade are from a macro level to guide manufacturers to make production plans, rather than from a perspective of specific production scheduling, which leads to a lack of theoretical guidance for manufacturers to develop reasonable production scheduling schemes for specific production orders. This article investigates a specific scheduling problem in a flexible job-shop environment that considers the carbon cap-and-trade policy, aiming to provide guidance for specific production scheduling (i.e., resource allocation). In the proposed problem, carbon emissions have an upper limit. A penalty will be generated if the emissions overpass the predetermined cap. To satisfy the carbon emission cap, the manufacturer can trade carbon credits or adopt outsourcing strategy, that is, outsourcing partial orders to partners at the expense of outsourcing costs. To solve the proposed model, a novel and efficient memetic algorithm (NEMA) is proposed. An initialization method and four local search operators are developed to enhance the search ability. Numerous experiments are conducted and the results validate that NEMA is a superior algorithm in both solution quality and efficiency. Full article

The flexible job shop scheduling problem with job precedence constraints (FJSP-JPC) is highly relevant in industrial production scenarios involving assembly operations. Traditional methods, such as mathematical programming and meta-heuristics, often struggle with scalability and efficiency when solving large instances. We propose a deep reinforcement learning (DRL) approach to minimize makespan in FJSP-JPC. The proposed method employs a heterogeneous disjunctive graph to represent the system state and a multi-head graph attention network for feature extraction. An actor–critic framework, trained using proximal policy optimization (PPO), is adopted to make operation sequencing and machine assignment decisions. The effectiveness of the proposed method is validated through comparisons with several classic dispatching rules and a state-of-the-art DRL approach. Additionally, the contributions of key mechanisms, such as information diffusion, node features, and action space, are analyzed through a full factorial design of experiments. Full article

Dueto uncertainties in real-world production, dynamic factors have become increasingly critical in the research of distributed flexible job shop scheduling problems. Effectively responding to dynamic events can significantly enhance the adaptability and quality of scheduling solutions, thereby improving the resilience of manufacturing systems. This study addresses the dynamic distributed flexible job shop scheduling problem, which involves random job arrivals and machine breakdowns, and proposes an effective discrete improved gray wolf optimization (DIGWO) algorithm-based predictive–reactive method. The first contribution of our work lies in its dynamic scheduling strategy: a periodic- and event-driven approach is used to capture the dynamic nature of the problem, and a static scheduling window is constructed based on updated factory and workshop statuses to convert dynamic scheduling into static scheduling at each rescheduling point. Second, a mathematical model of multi-objective distributed flexible job shop scheduling (MODDFJSP) is established, optimizing makespan, tardiness, maximal factory load, and stability. The novelty of the model is that it is capable of optimizing both production efficiency and operational stability in the workshop. Third, by designing an efficacious initialization mechanism, prey search, and an external archive, the DIGWO algorithm is developed to solve conflicting objectives and search for a set of trade-off solutions. Experimental results in a simulated dynamic distributed flexible job shop demonstrate that DIGWO outperforms three well-known algorithms (NSGA-II, SPEA2, and MOEA/D). The proposed method also surpasses completely reactive scheduling approaches based on rule combinations. This study provides a reference for distributed manufacturing systems facing random job arrivals and machine breakdowns. Full article

With the advancement of logistics technology, Automated Guided Vehicles (AGVs) have been widely adopted in manufacturing enterprises due to their high flexibility and stability, particularly in flexible and discrete manufacturing domains such as tire production and electronic assembly. However, existing studies seldom systematically consider practical constraints such as limited AGV transport resources, AGV charging requirements, and charging station capacity limitations. To address this gap, this paper proposes a flexible job shop production-logistics collaborative scheduling model that incorporates transport and charging constraints, aiming to minimize the maximum makespan. To solve this problem, an improved PPO algorithm—CRGPPO-TKL—has been developed, which integrates candidate probability ratio calculations and a dynamic clipping mechanism based on target KL divergence to enhance the exploration capability and stability during policy updates. Experimental results demonstrate that the proposed method outperforms composite dispatching rules and mainstream DRL methods across multiple scheduling scenarios, achieving an average improvement of 8.2% and 10.5% in makespan, respectively. Finally, sensitivity analysis verifies the robustness of the proposed method with respect to parameter combinations. Full article

Dynamic scheduling in hybrid flexible job shops (HFJSs) presents a critical challenge in modern manufacturing systems, particularly under dynamic and uncertain conditions. These systems often exhibit inherent structural and behavioral symmetry, such as uniform machine–job relationships and repeatable event response patterns. To leverage this, we propose a time Petri nets (TPNs) model that integrates time and logic constraints, capturing symmetric processing and setup behaviors across machines as well as dynamic job and machine events. A transition select coding mechanism is introduced, where each transition node is assigned a normalized priority value in the range [0, 1], preserving scheduling consistency and symmetry during decision-making. Furthermore, we develop a symmetry-aware time Petri nets-based improved genetic algorithm (TPGA) to solve both static and dynamic scheduling problems in HFJSs. Experimental evaluations show that TPGA significantly outperforms classical dispatching rules such as Shortest Job First (SJF) and Highest Response Ratio Next (HRN), achieving makespan reductions of 23%, 10%, and 13% in process, discrete, and hybrid manufacturing scenarios, respectively. These results highlight the potential of exploiting symmetry in system modeling and optimization for enhanced scheduling performance. Full article

To address the multi-objective flexible job shop scheduling problem in rolling production mode (FJSP-RPM), this study proposes a Multi Objective Improved of Salp Swarm Algorithm (MISSA) that simultaneously optimizes equipment utilization and total tardiness. The MISSA generates initial population through various heuristic strategies to improve the initial population quality. The exploitation capability of the algorithm is enhanced through the global crossover strategy and variety of local search strategies. In terms of improvement strategies, the MISSA (using all three strategies) outperforms other incomplete variant algorithms (using only two strategies) in three metrics: Generational Distance (GD), Inverted Generational Distance (IGD), and diversity metric, achieving superior results in 9 test cases, 8 test cases, and 4 test cases respectively. When compared with NSGA2, NSGA3, and SPEA2 algorithms, the MISSA demonstrates advantages in 8 test cases for GD, 8 test cases for IGD, and 7 test cases for the diversity metric. Additionally, the distribution of the obtained solution sets is significantly better than that of the comparative algorithms, which validats the effectiveness of the MISSA in solving FJSP-RPM. Full article

In view of the Flexible Job-shop Scheduling Problem (FJSP) under multi-product and variable-batch production modes, this paper presents an intelligent scheduling approach based on a heterogeneity-enhanced graph neural network combined with deep reinforcement learning. By constructing a heterogeneity-enhanced incidence graph to dynamically represent the scheduling state, the proposed method effectively captures both the dependencies among operations and the interaction features between operations and machines. Moreover, the Proximal Policy Optimization (PPO) algorithm is leveraged to achieve end-to-end optimization of scheduling decisions. Specifically, the FJSP is formulated as a Markov Decision Process. A heterogeneous enhanced graph neural network architecture is designed to extract deep features from operation nodes, machine nodes, and their heterogeneous relationships. Then, a policy network generates joint actions for operation assignment and machine selection, while the PPO algorithm iteratively refines the scheduling policy. Finally, the method is validated in an aerospace component machining workshop scenario and the benchmark dataset. Experimental results demonstrate that, compared with traditional dispatching rules and existing deep reinforcement learning techniques, the proposed approach not only achieves superior scheduling performance but also maintains an excellent balance between response efficiency and scheduling quality. Full article

With increasing labor costs and rapidly dynamic changes in the market demand, as well as realizing the refined management of production, more and more attention is being given to considering workers, not just machines, in the process of flexible job shop scheduling. Hence, a new dual-resource flexible job shop scheduling problem (DRFJSP) is put forward in this paper, considering workers with flexible working time arrangements and machines with versatile functions in scheduling production, as well as a multi-objective mathematical model for formalizing the DRFJSP and tackling the complexity of scheduling in human-centric manufacturing environments. In addition, a two-stage approach based on a forensic-based investigation (TSFBI) is proposed to solve the problem. In the first stage, an improved multi-objective FBI algorithm is used to obtain the Pareto front solutions of this model, in which a hybrid real and integer encoding–decoding method is used for exploring the solution space and a fast non-dominated sorting method for improving efficiency. In the second stage, a multi-criteria decision analysis method based on an analytic hierarchy process (AHP) is used to select the optimal solution from the Pareto front solutions. Finally, experiments validated the TSFBI algorithm, showing its potential for smart manufacturing. Full article

Dynamic scheduling for flexible job shops under machine breakdown is a complex and challenging problem due to its valuable application in real-life productions. However, prior studies have struggled to perform well in changeable scenarios. To address this challenge, this paper introduces a dual-objective deep reinforcement learning (DRL) to solve this problem. This algorithm is based on the Double Deep Q-network (DDQN) and incorporates the attention mechanism. It decouples action relationships in the action space to reduce problem dimensionality and introduces an adaptive weighting method in agent decision-making to obtain high-quality Pareto front solutions. The algorithm is evaluated on a set of benchmark instances and compared with state-of-the-art algorithms. The experimental results show that the proposed algorithm outperforms the state-of-the-art algorithms regarding machine offset and total tardiness, demonstrating more excellent stability and higher-quality solutions. At the same time, the actual use of the algorithm is verified using cases from real enterprises, and the results are still better than those of the multi-objective meta-heuristic algorithm. Full article

This article aims to review the industrial applications of AI-based intelligent system algorithms in the manufacturing sector to find the latest methods used for sustainability and optimisation. In contrast to previous review articles that broadly summarised existing methods, this paper specifically emphasises the most recent techniques, providing a systematic and structured evaluation of their practical applications within the sector. The primary objective of this study is to review the applications of intelligent system algorithms, including metaheuristics, evolutionary algorithms, and learning-based methods within the manufacturing sector, particularly through the lens of optimisation of workflow in the production lines, specifically Job Shop Scheduling Problems (JSSPs). It critically evaluates various algorithms for solving JSSPs, with a particular focus on Flexible Job Shop Scheduling Problems (FJSPs), a more advanced form of JSSPs. The manufacturing process consists of several intricate operations that must be meticulously planned and scheduled to be executed effectively. In this regard, Production scheduling aims to find the best possible schedule to maximise one or more performance parameters. An integral part of production scheduling is JSSP in both traditional and smart manufacturing; however, this research focuses on this concept in general, which pertains to industrial system scheduling and concerns the aim of maximising operational efficiency by reducing production time and costs. A common feature among research studies on optimisation is the lack of consistent and more effective solution algorithms that minimise time and energy consumption, thus accelerating optimisation with minimal resources. Full article

With the development of Industry 4.0, discrete manufacturing systems are accelerating their transformation toward flexibility and intelligence to meet the market demand for various products and small-batch production. The flexible flow shop (FFS) paradigm enhances production flexibility, but existing studies often address FFS scheduling and automated guided vehicle (AGV) path planning separately, resulting in resource competition conflicts, such as equipment idle time and AGV congestion, which prolong the manufacturing cycle time and reduce system energy efficiency. To solve this problem, this study proposes an integrated production–transportation scheduling framework (FFSP-AGV). By using the adjacent sequence modeling idea, a mixed-integer linear programming (MILP) model is established, which takes into account the constraints of the production process and AGV transportation task conflicts with the aim of minimizing the makespan and improving overall operational efficiency. Systematic evaluations are carried out on multiple test instances of different scales using the CPLEX solver. The results show that, for small-scale instances (job count ≤10), the MILP model can generate optimal scheduling solutions within a practical computation time (several minutes). Moreover, it is found that there is a significant marginal diminishing effect between AGV quantity and makespan reduction. Once the number of AGVs exceeds 60% of the parallel equipment capacity, their incremental contribution to cycle time reduction becomes much smaller. However, the computational complexity of the model increases exponentially with the number of jobs, making it slightly impractical for large-scale problems (job count > 20). This research highlights the importance of integrated production–transportation scheduling for reducing manufacturing cycle time and reveals a threshold effect in AGV resource allocation, providing a theoretical basis for collaborative optimization in smart factories. Full article

In order to address the impact of equipment fault diagnosis and repair delays on production schedule execution in the dynamic scheduling of flexible job shops, this paper proposes a multi-resource, multi-objective dynamic scheduling optimization model, which aims to minimize delay time and completion time. It integrates the scheduling of the workpieces, machines, and maintenance personnel to improve the response efficiency of emergency equipment maintenance. To this end, a self-learning Ant Colony Algorithm based on deep reinforcement learning (ACODDQN) is designed in this paper. The algorithm searches the solution space by using the ACO, prioritizes the solutions by combining the non-dominated sorting strategies, and achieves the adaptive optimization of scheduling decisions by utilizing the organic integration of the pheromone update mechanism and the DDQN framework. Further, the generated solutions are locally adjusted via the feasible solution optimization strategy to ensure that the solutions satisfy all the constraints and ultimately generate a Pareto optimal solution set with high quality. Simulation results based on standard examples and real cases show that the ACODDQN algorithm exhibits significant optimization effects in several tests, which verifies its superiority and practical application potential in dynamic scheduling problems. Full article

The flexible job shop scheduling problem is relevant in many different areas. However, the usual deterministic approach sees its usefulness limited, as uncertainty plays a paramount role in real-world processes. Considering processing times in the form of fuzzy numbers is a computationally affordable way to model uncertainty that enhances the applicability of obtained solutions. Unfortunately, fuzzy processing times add an extra layer of complexity to otherwise straightforward operations. For example, in energy-aware environments, measuring the idle times of resources is of the utmost importance, but it goes from a trivial calculation in the deterministic setting to a critical modelling decision in fuzzy scenarios, where different approaches are possible. In this paper, we analyse the drawbacks of the existing translation of the deterministic approach to a fuzzy context and propose two alternative ways of computing the idle times in a schedule. We show that, unlike in the deterministic setting, the different definitions are not equivalent when fuzzy processing times are considered, and results are directly affected, depending on which one is used. We conclude that the new ways of computing idle times under uncertainty provide more reliable values and, hence, better schedules. Full article

Uncertainty in processing times is a key issue in distributed production; it severely affects scheduling accuracy. In this study, we investigate a dynamic distributed flexible job shop scheduling problem with variable processing times (DDFJSP-VPT), in which the processing time follows a normal distribution. First, the mathematical model is established by simultaneously considering the makespan, tardiness, and total factory load. Second, a chance-constrained approach is employed to predict uncertain processing times to generate a robust initial schedule. Then, a heuristic scheduling method which involves a left-shift strategy, an insertion-based local adjustment strategy, and a DMOGWO-based global rescheduling strategy is developed to dynamically adjust the scheduling plan in response to the context of uncertainty. Moreover, a hybrid initialization scheme, discrete crossover, and mutation operations are designed to generate a high-quality initial population and update the wolf pack, enabling GWO to effectively solve the distributed flexible job shop scheduling problem. Based on the parameter sensitivity study and a comparison with four algorithms, the algorithm’s stability and effectiveness in both static and dynamic environments are demonstrated. Finally, the experimental results show that our method can achieve much better performance than other rules-based reactive scheduling methods and the hybrid-shift strategy. The utility of the prediction strategy is also validated. Full article

The agricultural equipment market has the characteristics of rapid demand changes and high demand for machine models, etc., so multi-variety, small-batch, and customized production methods have become the mainstream of agricultural machinery enterprises. The flexible job shop scheduling problem (FJSP) in the context of agricultural machinery and equipment manufacturing is addressed, which involves multiple resources including machines, workers, and automated guided vehicles (AGVs). The aim is to optimize two objectives: makespan and the maximum continuous working hours of all workers. To tackle this complex problem, a Multi-Objective Discrete Grey Wolf Optimization (MODGWO) algorithm is proposed. The MODGWO algorithm integrates a hybrid initialization strategy and a multi-neighborhood local search to effectively balance the exploration and exploitation capabilities. An encoding/decoding method and a method for initializing a mixed population are introduced, which includes an operation sequence vector, machine selection vector, worker selection vector, and AGV selection vector. The solution-updating mechanism is also designed to be discrete. The performance of the MODGWO algorithm is evaluated through comprehensive experiments using an extended version of the classic Brandimarte test case by randomly adding worker and AGV information. The experimental results demonstrate that MODGWO achieves better performance in identifying high-quality solutions compared to other competitive algorithms, especially for medium- and large-scale cases. The proposed algorithm contributes to the research on flexible job shop scheduling under multi-resource constraints, providing a novel solution approach that comprehensively considers both workers and AGVs. The research findings have practical implications for improving production efficiency and balancing multiple objectives in agricultural machinery and equipment manufacturing enterprises. Full article