Job Shop Scheduling Problem Research Articles

Dynamic scheduling for flexible job shop with insufficient transportation resources via graph neural network and deep reinforcement learning

The smart workshop is a powerful tool for manufacturing companies to reduce waste and improve production efficiency through real-time data analysis for self-organized production. Automated Guided Vehicles (AGVs) have been widely used for material handling in smart workshop due to their high degree of autonomy, flexibility and powerful end-to-end capability to cope with logistics tasks in production modes such as multiple species and small batch, and mass customization. However, the highly dynamic, complex and uncertain nature of the smart job shop environment makes production scheduling with insufficient transportation resources in mind a challenge. To this end, this paper addresses the dynamic flexible job shop scheduling problem with insufficient transportation resources (DFJSP-ITR), and learn high-quality priority dispatching rule (PDR) end-to-end to minimize makespan by the proposed deep reinforcement learning (DRL) method. To achieve integrated decision making for operation, machine and AGV, an architecture based on heterogeneous graph neural network (GNN) and DRL is proposed. Considering the impact of different AGV distribution methods on the scheduling objective, this paper compares two different AGV distribution methods. Experiments show that the proposed method has superiority and good generalization ability compared with the current PDRs-based methods regardless of the AGV distribution strategy used.

Inverse model and adaptive neighborhood search based cooperative optimizer for energy-efficient distributed flexible job shop scheduling

Solving the energy-efficient distributed flexible job shop scheduling problem (EEDFJSP) obtains increased attention. However, most previous studies barely considered the large-scale nature of the decision variables of EEDFJSP. In this paper, the large-scale EEDFJSP with two minimized objectives of makespan and total energy consumption (TEC) is studied. To efficiently deal with this problem, an inverse model and adaptive neighborhood search based cooperative optimizer is proposed. First, the inverse model is applied to the job shop scheduling problem. Then, the inverse model and adaptive local search operators cooperate search is designed to obtain offspring. Furthermore, an adaptive strategy for local search operators is developed. Finally, it is compared with other multi-objective optimization algorithms to confirm the effectiveness of the proposed algorithm, including MOEA/D, NSGA-II, IM-MOEA/D, HMMA, HSLFA, and SPAMA. Experimental results demonstrate the superior performance in solving EEDFJSP compared to these six state-of-the-art multi-objective optimization algorithms.

A Study of Deep Learning Neural Network Algorithms and Genetic Algorithms for FJSP

Flexible job-shop scheduling problem (FJSP) is a new research hotspot in the field of production scheduling. To solve the multiobjective FJSP problem, the production of flexible job shop can run normally and quickly. This research takes into account various characteristics of FJSP problems, such as the need to ensure the continuity and stability of processing, the existence of multiple objectives in the whole process, and the constant complexity of changes. It starts with deep learning neural networks and genetic algorithms. Long short-term memory (LSTM) and convolutional neural networks (CNN) are combined in deep learning neural networks. The new improved algorithm is based on the combination of deep learning neural networks LSTM and CNN with genetic algorithm (GA), namely, CNN-LSTM-GA algorithm. Simulation results showed that the accuracy of the CNN-LSTM-GA algorithm was between 85.2% and 95.3% in the test set. In the verification set, the minimum accuracy of the CNN-LSTM-GA algorithm was 84.6%, both of which were higher than the maximum accuracy of the other two algorithms. In the FJSP simulation experiment, the AUC value of the CNN-LSTM-GA algorithm was 0.92. After 40 iterations, the F1 value of the CNN-LSTM-GA algorithm remained above 0.8, which was significantly higher than the other two algorithms. CNN-LSTM-GA is superior to the other two algorithms in terms of prediction accuracy and overall performance of FJSP. It is more suitable for solving the discrete manufacturing job scheduling problem with FJSP characteristics. This study significantly raises the utilisation rate of the assembly shop’s equipment, optimises the scheduling of FJSP, and fully utilises each processing device’s versatile characteristics, which are quite useful for the production processes of domestic vehicle manufacturing companies.

Job-shop scheduling with limited flexible workers considering ergonomic factors using an improved multi-objective discrete Jaya algorithm

Job-Shop Scheduling Problem (JSP) with worker flexibility has gained significant attention in recent years, offering cost reduction and improved efficiency by limiting the number of workers. However, consideration of ergonomic factors is generally ignored for such systems. The ergonomic consideration is important to prevent stress, fatigue, and lack of focus among the workers, particularly when recurring manual tasks are involved. To prioritize productivity and workforce relief simultaneously, this article addresses the JSP with limited flexible workers considering ergonomic factors (JSPLFW-ER). The study focuses on worker workload and human energy expenditure as the key ergonomic factors. The average human energy expenditure rate is also considered to ensure that its value does not exceed the critical limit. An improved multi-objective discrete Jaya algorithm (IMDJA) is proposed to solve JSPLFW-ER by minimizing the makespan, maximum worker workload, and maximum human energy expenditure of the assigned operations. IMDJA incorporates a Jaya random partial updating mechanism in which a certain number of elements of the individual are randomly selected for Jaya updating. The number of elements to be selected for Jaya updating is evaluated using the Taguchi analysis. The performance of IMDJA is investigated with comprehensive experiments, using the 40 newly constructed instances and found competitive to solve JSPLFW-ER. Furthermore, a real-world industrial problem is presented with multiple experiments, which demonstrates the applicability of the JSPLFW-ER and effectiveness of the proposed IMDJA for solving the industrial problem.

Research on distributed scheduling of mechanical job shop based on hybrid differential evolution

Abstract The scheduling of mechanical job shops may be optimized, which is a significant approach to boosting production effectiveness. Based on the description of the job shop scheduling problem in this paper, a mathematical model is built with the objective function of minimizing the maximum completion time. The vector evaluation genetic algorithm, which samples the edge region, and the adaptation function, which completes the sampling of the core region, are both offered as improvements for the differential evolutionary algorithm focused on job shop scheduling. After the sampling has been encoded, the best scheduling solution is sought using a sequential differential strategy. The modified HEA-SDDE algorithm’s maximum completion time for the actual scheduling scenario of K’s job shop is decreased by 12.4%, and the posting rate of the best solution to the ideal solution reaches 0.516.

The impact of incentive-based programmes on job-shop scheduling with variable machine speeds

Given the high demand for energy in the manufacturing industry and the increasing use of renewable but volatile energy sources, it becomes increasingly important to coordinate production and energy availability. With the help of incentive-based programmes, grid operators can incentivise consumers to adjust power demand in critical situations such that grid stability is not threatened. On the consumer side, energy-efficient scheduling models can be used to make energy consumption more flexible. This paper proposes a bi-objective job-shop scheduling problem with variable machine speeds that aims on minimising the total energy consumption and total weighted tardiness simultaneously. We use a genetic algorithm to solve the model and derive Pareto frontiers to analyse the trade-off between both conflicting objectives. We gain insights into how incentive-based programmes can be integrated into machine scheduling models and analyse the potential interdependencies and benefits that result from this integration.

A framework of cloud-edge collaborated digital twin for flexible job shop scheduling with conflict-free routing

Synchronous scheduling of transportation resources such as automated guided vehicles (AGVs) and production resources can effectively improve the production efficiency of an automated flexible job shop, however limited transportation resources and persistent abnormal disturbances compromise the accuracy, reliability and practicability of such scheduling. In order to address the flexible job shop scheduling problem with limited transportation resources (FJSP-T) under abnormal disturbances, here we propose a cloud-edge combined digital twin (DT) flexible job shop scheduling (CE-DTFJSS) framework to realize real-time scheduling. Firstly, a time-space network based zero-one programming (TSN-ZOP) model is established to optimize makespan and energy consumption of flexible job shop scheduling with conflict-free routing. Subsequently, to achieve real-time interaction between scheduling system and physical workshop, a cloud-edge architecture is introduced to allocate computing resources for scheduling-supporting tasks such as simulation, state monitoring and distributed control in the DT system. Additionally, we design a cloud edge collaboration rescheduling strategy based on a rolling window, to update the parameters’ values in the improved time window Dijkstra nested multi-layer coding genetic algorithm we proposed, thus real-time scheduling can be achieved. The effectiveness of CE-DTFJSS are verified by a numeric simulation based on a real-world case of a digitalized automobile welding workshop. The experimental results indicate that compared with the scheduling scheme without considering AGVs routing problem, the CE-DTFJSS framework can reduce makespan and energy consumption by 8.30% and 3.73%, respectively, and real-time responses to abnormal disturbances can be rendered within 0.1 s.

Batch scheduling in a multi-purpose system with machine downtime and a multi-skilled workforce

The paper presents a discrete-time mixed-integer linear programming (MILP) model for a generalised flexible job-shop scheduling problem as represented by a state-task network. The problem is characterised by reentrant flow, sequence-dependent changeover time, machine downtime, and skilled labour requirements. Two preprocessing procedures are proposed to reduce the size of the MILP model, and represent a major contribution of the research. The procedures reduce the number of assignment variables by exploiting job precedence and workforce qualifications. Machine availability for each task is determined as a function of possible start and end times, given duration, and maintenance schedule. The overall objective is to maximise the number of scheduled tasks while minimising their total finish time. Computational experiments are conducted with real and randomly generated instances. The results show that optimal solutions can be obtained for medium-size problems within a reasonable amount of time, primarily due to the use of the preprocessing procedures.

Optimization of job shop scheduling problem based on deep reinforcement learning

Optimization of job shop scheduling problem based on deep reinforcement learning

The Problem of Machine Part Operations Optimal Scheduling in the Production Industry Based on a Customer’s Order

This research focuses on small- and medium-sized businesses that provide machining or other process services but do not produce their own products. Their daily manufacturing schedule varies according to client needs. Small- and medium-sized businesses strive to operate in these circumstances by extending their customer base and creating adequate production planning targets. Their resources are limited, including the technical and technological components of their equipment, tools, people resources, time, and capacities. As a result, planning operations with the present resources of small- and medium-sized businesses in the midst of the global economic crisis is a widespread issue that must be addressed. This study seeks to offer a novel mathematical optimization model based on a genetic algorithm to address job shop scheduling and capacity planning difficulties in small- and medium-sized businesses, therefore improving performance management and production planning procedures. On the basis of the created optimization model, an appropriate software solution, and quantitative data concerning the job shop scheduling and capacity planning challenges of manufacturing operations in small- and medium-sized businesses, the study findings will be obtained. The practical implications include the establishment and development of a decision support system based on the genetic algorithm optimization method, which may improve the effectiveness of the flexible job shop scheduling problem and capacity planning in the production planning process. The given model and the application of the differential precedence preservative crossover operator within genetic algorithms are what constitute the novelty of this study.

Q-learning based multi-objective immune algorithm for fuzzy flexible job shop scheduling problem considering dynamic disruptions

Confronted with complex industrial environments, dynamic disruptions like new job arrival and machine breakdown bring significant challenges to the robustness and stability of the manufacturing process, making the static production depart from the original scheduling scheme. To address this problem, a flexible job shop scheduling problem with fuzzy processing time, dynamic disruptions, and variable processing speeds is considered simultaneously. As well as three objectives of maximum completion time, total energy consumption, and average agreement index are demonstrated in this study. Then, a predictive-reactive dynamic/static rescheduling model is developed, where the off-line based mixed integer linear programming model and the on-line based rescheduling heuristics are proposed. Next, a multi-objective immune algorithm combined with a Q-learning algorithm (Q-MOIA) is developed. In the proposed algorithm, an active decoding heuristic based on the interval insertion mechanism is used to optimize the initial solutions. After that, the clonal selection-based immune algorithm and the Q-learning algorithm are adopted to improve the exploration and exploitation capabilities, respectively, where four objective-driven neighborhood structures are designed. Eventually, extensive computational experiments were conducted on 27 instances under static and dynamic scenarios to demonstrate the superiority and stability of the proposed predictive-reactive dynamic/static rescheduling model and the Q-MOIA. Comparative analysis with four state-of-the-art approaches revealed that proposed Q-MOIA outperformed in approximately 51.9, 66.7, and 83.3 % of the instances for the three multi-objective metrics.

A generic enhanced search framework based on genetic algorithm: Case study on job shop scheduling problem

Optimal allocation of production resources is an urgent need for the development of industrialization. Reasonable production scheduling algorithm and excellent scheduling scheme can efficiently plan production resources, reduce production costs and shorten order completion time. Genetic algorithm has become one of the most popular algorithms for solving job shop scheduling problem because of its simplicity, versatility and good robustness. However, the genetic algorithm for solving NP-hard problems such as job shop scheduling has the problem of falling into local optimum, which leads to the decrease of solution accuracy. This study focused on the problem and proposed a generic enhanced search framework based on genetic algorithm, which named niche adaptive genetic algorithm. The niche selection mechanism and adaptive genetic operators were used to enrich the diversity of population, balance the genetic probability and enhance the global search performance of the algorithm. The working mechanism of this algorithm is analysed by testing data, and the proposed algorithm was tested on job-shop scheduling problem instances. The results show that the performance of the proposed method is 0.79 percentage points higher than that of the standard genetic algorithm, and it has the ability to search for the global optimum.

Minimizing non-processing energy consumption/total weighted tardiness & earliness, and makespan into typical production scheduling model-the job shop scheduling problem

This manuscript proposes a hybrid method to solve the job shop scheduling problem (JSP). Here, the machine consumes different amounts of energy for processing the tasks. The proposed method is the joint execution of Feedback Artificial Tree (FAT) and Atomic Orbital Search (AOS), hence it is called the FAT-AOS method. The aim of the proposed multi-objective method is to lessen the non-processing energy consumption (NEC), total weighted tardiness and earliness (TWET), and makespan (Cmax). Depending on the machine’s operating status, such as working, standby, off, or idle, the energy-consumption model of the machine is constructed. The NEC is the essential metric and the Cmax and TWET are the classical performance metrics used to predict the effects of energy effectiveness in JSP. The proposed AOS technique optimizes the objective of the system and FAT is used to predict the optimal outcome. The proposed method’s performance is implemented in MATLAB and is compared with various existing methods. From this simulation, under the 15x15_1 instance, the proposed method makes the span the best value of 1370, the median is 1720, and the worst value become 2268 is obtained.

A cooperative hierarchical deep reinforcement learning based multi-agent method for distributed job shop scheduling problem with random job arrivals

Distributed manufacturing can reduce the production cost through the cooperation among factories, and it has been an important trend in the industrial field. For the enterprises with daily delivered production tasks, the random job arrivals are regular. Thus, the Distributed Job-shop Scheduling Problem (DJSP) with random job arrivals is studied, and it is a typical case from the equipment manufacturing industry. The DJSP involves two coupled decision-making processes, job assigning and job sequencing, and the distributed and uncertain production environment requires the scheduling method to be more responsive and adaptive. Thus, a Deep Reinforcement Learning (DRL) based multi-agent method is explored, and it is composed of the assigning agent and the sequencing agent. Two Markov Decision Processes (MDPs) are formulated for the two agents respectively. In the MDP for the assigning agent, fourteen factory-and-job related features are extracted as the state features, seven composite assigning rules are designed as the candidate actions, and the reward depends on the total processing time of different factories. In the MDP of the sequencing agent, five machine-and-job related features are set as the state features, six sequencing rules make up the action space, and the change of the factory makespan is the reward. Besides, to enhance the learning ability of the agents, a Deep Q-Network (DQN) framework with variable threshold probability in the training stage is designed, which can balance the exploitation and exploration in the model training. The proposed multi-agent method’s effectiveness is proved by the independent utility test and the comparison test that are based on 1350 production instances, and its practical value in the actual production is implied by the case study from an automotive engine manufacturing company.

Minimizing the expected maximum lateness for a job shop subject to stochastic machine breakdowns

This paper addresses a stochastic job shop scheduling problem with sequence-dependent setup times, aiming to minimize the expected maximum lateness. The stochastic nature is modeled by considering uncertain times between failures (TBF) and uncertain times to repair (TTR). To tackle this problem, a simheuristic approach is proposed, which combines a tabu search (TS) algorithm with Monte Carlo simulation. A total of 320 instances were used to conduct multiple experiments. Instances were generated with two distributions to study the behavior of stochastic TTR and TBF under log-normal and exponential distributions. Firstly, the performance of the simheuristic was evaluated for small instances by comparing it with the simulation of optimal solutions obtained with a mixed-integer linear programming (MILP) model. The simheuristic approach demonstrated an average improvement of around 7% compared to the simulation of MILP model solutions. Secondly, the simheuristic performance was evaluated for medium and large-size instances by comparing it with the simulation of the solutions obtained by the earliest due date (EDD) and process time plus work in the next queue plus negative slack (PT + WINQ + SL) dispatching rules. The results showed an average improvement of around 11% compared to EDD and 14% compared to PT + WINQ + SL. Furthermore, the results highlight that even when the two distributions have the same expected value and coefficient of variation, they can yield different expected maximum lateness values. This emphasizes the importance of precise distribution fitting when solving real cases to achieve effective scheduling performance.

Novel model and solution method for flexible job shop scheduling problem with batch processing machines

This study investigates a novel flexible job shop scheduling problem, where the machines have batch-processing capacity (FJSPB). This problem is widely applied in semiconductor and other high-tech manufacturing and supply chains. In this study, a multi-commodity flow (MCF) model has been proposed which can be effectively solved to optimality by commercial solvers for small-scale problems. In addition, an improved adaptive large neighborhood search (ALNS) algorithmic framework with an optimal repair and tabu-based components (ALNSIT) is proposed, which can achieve high-quality solutions for large-scale FJSPB in a reasonable time. In the ALNSIT, a perturbation strategy and an optimal repair strategy are integrated to improve the exploitation and exploration ability of the algorithm. The proposed model and algorithms are tested on numerous existing benchmark instances. Experimental results indicate the effectiveness of the proposed model and methods, and the optimal repair strategy can significantly reduce the computational burden of the ALNS algorithm. Comparison results further verify that the proposed ALNSIT can achieve better results than existing methods for solving the FJSPB, especially for large-scale instances. Furthermore, the impacts of a wide range of features including batch capacities and instance scales on the performance of the ALNSIT and scheduling results are discussed.

A multi-agent double Deep-Q-network based on state machine and event stream for flexible job shop scheduling problem

With the industry's rapid shift to large-scale personalized development, the need for a ramose multi-agent system capable of flexible job shop scheduling problem (FJSP) is apparent. As such, this paper proposes a novel framework that transforms the combinatorial optimization problem into a multi-stage sequence decision problem and introduces a multi-agent double Deep-Q-network algorithm (MADDQN) for FJSP. The event-driven workshop environment model based on state machine and event stream mechanism is constructed to transform FJSP into a Markov Decision Process (MDP) with more robust general performance and decouple the workshop environment model from the decision analysis model. The developed multi-agent reinforcement learning consisting of job agents and machine agents applies dispatching rules to maximize the cumulative reward of all agents by Boltzmann exploitation to avoid the local optimum. Results of numerical experiments reflect that the proposed MADDQN performs better than the traditional approaches in large-scale instances, and the real-time performance of the scheduling decision is guaranteed.

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

A Novel Evolutionary Algorithm for Energy-Efficient Scheduling in Flexible Job Shops

Improving productivity at the expense of heavy energy consumption is often no longer possible in modern manufacturing industries. Through efficient scheduling technologies, however, we are able to still maintain high productivity while reducing energy costs. This paper addresses a flexible job shop scheduling problem under Time-Of-Use electricity tariffs with the objective of minimizing total energy consumption while considering a predefined makespan constraint. We propose a novel two-individual-based evolutionary (TIE) algorithm, which incorporates several distinguishing features such as a tabu search procedure, a topological order based recombination operator, a new neighborhood structure for this specific problem, and an approximate neighborhood evaluation method. Extensive experiments are conducted on widely used benchmark instances, which show that the proposed TIE outperforms traditional trajectory-based and population-based methods. We also analyze the key features of TIE to identify its critical success factors, and discuss the impact of varying key parameters of the problem to derive practical insights.

A multi-objective migrating birds optimization algorithm based on game theory for dynamic flexible job shop scheduling problem

A multi-objective migrating birds optimization algorithm based on game theory for dynamic flexible job shop scheduling problem