Job Shop Scheduling Problem Research Articles

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.

A cooperative coevolutionary hyper-heuristic approach to solve lot-sizing and job shop scheduling problems using genetic programming

Lot-sizing and scheduling in a job shop environment is a fundamental problem that appears in many industrial settings. The problem is very complex, and solutions are often needed fast. Although many solution methods have been proposed, with increasingly better results, their computational times are not suitable for decision-makers who want solutions instantly. Therefore, we propose a novel greedy heuristic to efficiently generate production plans and schedules of good quality. The main innovation of our approach represents the incorporation of a simulation-based technique, which directly generates schedules while simultaneously determining lot sizes. By utilising priority rules, this unique feature enables us to address the complexity of job shop scheduling environments and ensures the feasibility of the resulting schedules. Using a selection of well-known rules from the literature, experiments on a variety of shop configurations and complexities showed that the proposed heuristic is able to obtain solutions with an average gap to Cplex of 4.12%. To further improve the proposed heuristic, a cooperative coevolutionary genetic programming-based hyper-heuristic has been developed. The average gap to Cplex was reduced up to 1.92%. These solutions are generated in a small fraction of a second, regardless of the size of the instance.

A deep reinforcement learning model for dynamic job-shop scheduling problem with uncertain processing time

The dynamic job-shop scheduling problem (DJSP) is a type of scheduling tasks where rescheduling is performed when encountering the uncertainties such as the uncertain operation processing time. However, the current deep reinforcement learning (DRL) scheduling approaches are hard to train convergent scheduling policies as the problem scale increases, which is very important for rescheduling under uncertainty. In this paper, we propose a DRL scheduling method for DJSP based on the proximal policy optimization (PPO) with hybrid prioritized experience replay. The job shop scheduling problem is formulated as a sequential decision-making problem based on Markov Decision Process (MDP) where a novel state representation is designed based on the feasible solution matrix which depicts the scheduling order of a scheduling task, a set of paired priority dispatching rules (PDR) are used as the actions and a new intuitive reward function is established based on the machine idle time. Moreover, a new hybrid prioritized experience replay method for PPO is proposed to reduce the training time where samples with positive temporal-difference (TD) error are replayed. Static experiments on classic benchmark instances show that the make-span obtained by our scheduling agent has been reduced by 1.59% on average than the best known DRL methods. In addition, dynamic experiments demonstrate that the training time of the reused scheduling policy is reduced by 27% compared with the retrained policy when encountering uncertainties such as uncertain operation processing time.

Improvement of job shop scheduling method based on mathematical optimization and machine learning

This research is concerned with finding the optimal solution of a job shop scheduling problem (JSSP) in a shorter time. As a result of recent trends such as Industry 4.0, machine learning has received a lot of attention, and job shop scheduling methods using machine learning techniques have been developed. We have focused on hybridization of machine learning and mathematical optimization. A JSSP can be formulated as a 0-1 mixed integer programming, and it is expected that the optimal solution can be obtained in a shorter time by providing a good initial solution for the optimization algorithm by means of a learner constructed with data of scheduling performed previously. In our method based on this idea, the processing times of all operations are used as input features to predict a good value of each binary variable which represents the precedence relationship between two operations processed on the same machine. However, the information about the operations which are not related to the intended two operations may work as noise in learning and prediction. In this paper, two limitation methods of input features are proposed. In one of the methods, the processing times of only the operations processed on the same machine that the intended operations are processed are input to the learner. In the other methods, the processing times of those operations and their pre/post operations are input. Numerical experiments showed that these methods are effective at least from the point of view of efficient construction of a learner, because the number of nodes in the input and hidden layers can be reduced. From the aspect of better learning and prediction, both of the methods worked well, that is, they could find the optimal solution in a shorter time than the previous method in the cases where the previous method could not achieve good prediction and took a relatively long solution time. However, in the cases where the previous method could solve the problem in a relatively short time, the limitation methods could not predict a good initial solution and took a relatively long solution time. Between the results of the two limitation methods, there were no difference. These results imply that the processing times of the pre/post operations do not strongly affect performance on learning and prediction and that it is important to analyze what makes a difference between the two cases and utilize the proposed methods in the former case.

Bi-Objective Job-Shop Scheduling Considering Human Fatigue in Cobotic Order Picking Systems: A Case of an Online Grocer

Increasing online retail has resulted in increased automation in order picking systems, leading to new challenges and opportunities in task scheduling. The job-shop scheduling problem is an optimization problem essential in such systems, but existing JSP literature often overlooks workplace fatigue, which harms employees’ well-being and costs U.S. employers up to €127 billion annually. In this work, we propose fatigue consideration in the job-shop scheduling problem in a cobotic order picking system to mitigate its negative effects. We present a new bi-objective mixed integer nonlinear programming problem formulation that considers worker fatigue and productivity during schedule optimisation. To put the results of simulated optimisation in perspective, we experimentally validate the fatigue model and scheduling results in a real operation. The mathematical model finds solutions that conventional single-objective optimisation cannot, allowing fractional fatigue distribution improvements more than 4x larger than the decrease in productivity they require in 53% of the considered virtual cases. The experiments show that our predictive fatigue model has an average RMSE of 2.20 kcal/min in estimating energy expenditure rates compared to heart rate measurements. It also shows a low correlation, meaning it is unfit for application. On the other hand, fatigue-conscious schedules show no clear benefit regarding measured and perceived fatigue. However, the scheduling model could also use heart rate measurements that do not show these inaccuracies. Our study highlights the need to further develop and validate the mathematical formulation and fatigue model and extend to other human factors and indirect fatigue effects.

Optimization of transport constraints and quality of service for joint resolution of uncertain scheduling and the job-shop problem with routing (JSSPR) as opposed to the job-shop problem with transport (JSSPT)

To better meet the qualitative and quantitative requirements of customers or relevant sector managers, workshop environments are implementing increasingly complex task management systems. The job shop scheduling problem (JSSP) involves assigning each task to a single machine while scheduling many tasks on different machines. Finding the best scheduling for machines is one of the challenging optimizations of difficult non-deterministic polynomial (NP) time problems. The fundamental goal of optimization is to shorten the makespan (total execution time of all tasks). This paper is interested in the joint resolution of scheduling and transport problems and more particularly the Job-shop problem with Routing (JSSPR) as opposed to the Job-shop problem with Transport (JSSPT). These two problems are modeled in the form of a disjunctive graph. For the JSSPT, the solution to the transport problem is not linked to any quality of service (QoS) criterion and the solution is therefore often semi-active. The Job-shop with Routing explicitly considers transport operations and uses algorithms from the transport community to solve the transport problem. It is shown that the routing part of the JSSPR is a problem of the vehicle routing family and of the Pickup and Delivery Problem family. QoS in the JSSPR is defined by the duration of tours, the duration of transport of parts and the waiting time for them. A new evaluation function – named Time-Lag Insertion Heuristic (TLH) – is proposed to evaluate a disjunctive graph by simultaneously minimizing the makespan and maximizing the quality of service. Thus, the solution obtained is not semi-active, but a compromise between the different criteria. This evaluation function is included in a metaheuristic. Our numerical evaluations demonstrate that, on the one hand, the TLH evaluation can find almost optimal solutions regarding the QoS criterion; and on the other hand, the TLH evaluation is not very sensitive to the order of insertion of the maximum time-lags during the different minimization steps.

Optimizing Automated Manufacturing Processes Using a Hybrid BRKGA Algorithm: A Case Study on Flexible Job-Shop Scheduling

In the modern era, industrial automation ofers significant competitive advantages. Replacing human labor with robots allows processes to be carried out much faster and more efficiently, with lower waste rates and the possibility of scheduling production 24/7. However, this also presents new challenges and opportunities in optimizing these automated processes. This paper proposes a hybrid algorithm BRKGA (Biased Random Key Genetic Algorithm) to optimize fexible job shop scheduling (FJSSP) problems in automated manufacturing systems. The algorithm is applied to a real-world case study in the Cinvestav Intelligent Manufacturing Laboratory, seeking to optimize the production of a four-piece product. The results demonstrate that the proposed algorithm outperforms previous results in terms of both, solution quality and computational efficiency.

Rainbow Versus Deep Q-Network: A Reinforcement Learning Comparison on The Flexible Job-Shop Problem

This study compares two promising reinforcement learning (RL) algorithms, Deep Q-Network (DQN) and Rainbow, for solving the Flexible Job-Shop Scheduling (FJSP) problem. FJSP is critical in both production management and combinatorial optimization; however, due to high computational complexity, attaining reasonable solutions for large-scale problems within limited computational time is challenging with traditional optimization methods. Although Rainbow excels in arcade learning environments, its performance has not yet been compared with DQN for a highly combinatorial and constrained problem such as the FJSP. Our findings show that both methods learn high-quality dispatching policies, although DQN slightly outperforms in most cases. Examining both methods is vital for assessing their performance relative to traditional methods, aiding decision makers in determining whether to incorporate the extensions integrated in Rainbow, which may signify additional implementation efforts and computational demand.

On the Verification of Distributed Control for Multi Job Shop Assignment Problem in Smart Manufacturing System

The increasing need of product individualization and rapid demand fluctuation leads industrial manufacturers to leveraging new control solutions for production planning and control. Among these, distributed control approaches for the multi job shop scheduling problem could be a promising solution to make smart manufacturing systems more responsive to the market. In this context, this paper aims at investigating the effectiveness and the benefits of distributed control approaches for solving the multi job shop assignment problem on a real-world smart manufacturing process involving the production of high-vacuum solar panels. The validation is carried out by leveraging Cyber-Physical Systems modelling and a digital model-based procedure which, interacting with the physical plant, provides the proper job assignment in order to optimize the overall makespan and work-in-progress in a fully-distributed fashion.

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

Evaluate Flexible Job Scheduling Problem Using Elitist Ant

One significant approach that is frequently utilized in many applications, particularly in industry, is scheduling .An extension of job scheduling, the Flexible Job Shop Scheduling Problem (FJSP), has a number of real-world uses .This subject has received a lot of attention due to its significance and complexity .This research discusses the importance of scheduling in real-life operations, particularly in production scheduling. It presents a model using Elitist Ant (EAS) to compute the maximum value (makspane) of the flexible job shop scheduling problem(FJSP). The model programmed by Python ver. (3.) with two instance from Brandimarte dataset to optimize logistics costs and meet customer demand. The study deduce that there are two relations by using two new formula. Firstly, the relation between number of elitist ant and total ants . Also, the evaporate value is effected by the first relation directly.

A multi-objective fuzzy flexible job shop scheduling problem considering the maximization of processing quality

This paper analyzes practical production characteristics, including customer's stringent quality requirements and uncertain processing time in aircraft shaft parts manufacturing. Considering the above characteristics, we propose a multi-objective fuzzy aircraft shaft parts production scheduling problem considering the maximization of production quality. We define this problem as a multi-objective fuzzy flexible job shop scheduling problem (MO-fFJSP) with fuzzy processing time. To address this problem, we developed an improved multi-objective spider monkey optimization (IMOSMO) algorithm. IMOSMO integrates strategies such as genetic operators, variable neighborhood search and Pareto optimization theory on the framework of the conventional Spider Monkey Optimization (SMO) framework and discretize the continuous SMO algorithm to solve MO-fFJSP. To enhance the efficiency of the algorithm, we further adjust the sequence of the local leader learning phase and the global leader learning phase within the proposed IMOSMO framework. We conduct a comparative analysis between the performance of IMOSMO and NSGA-Ⅱ using 28 cases of varying scales. The computational results demonstrate the superiority of our algorithm over NSGA-Ⅱ in terms of both solution diversity and quality. Moreover, the performance of the proposed algorithm upgrades as the problem scale increases.

Modified ant colony algorithm for job shop scheduling problem

Modified ant colony algorithm for job shop scheduling problem

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.

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.

混合改进麻雀算法解决柔性车间调度问题

混合改进麻雀算法解决柔性车间调度问题

A decode-based chaotic adaptive differential evolution for fuzzy job-shop scheduling problem

A decode-based chaotic adaptive differential evolution for fuzzy job-shop scheduling problem

A Decode-based Chaotic Adaptive Differential Evolution for Fuzzy Job-shop Scheduling Problem

A Decode-based Chaotic Adaptive Differential Evolution for Fuzzy Job-shop Scheduling Problem

A Combination of Association Rules and Optimization Model to Solve Scheduling Problems in an Unstable Production Environment

Production problems have a significant impact on the on-time delivery of orders, resulting in deviations from planned scenarios. Therefore, it is crucial to predict interruptions during scheduling and to find optimal production sequencing solutions. This paper introduces a selflearning framework that integrates association rules and optimisation techniques to develop a scheduling algorithm capable of learning from past production experiences and anticipating future problems. Association rules identify factors that hinder the production process, while optimisation techniques use mathematical models to optimise the sequence of tasks and minimise execution time. In addition, association rules establish correlations between production parameters and success rates, allowing corrective factors for production quantity to be calculated based on confidence values and success rates. The proposed solution demonstrates robustness and flexibility, providing efficient solutions for Flow-Shop and Job-Shop scheduling problems with reduced calculation times. The article includes two Flow-Shop and Job-Shop examples where the framework is applied.