Job Shop Scheduling Problem Research Articles

A Constraint Programming Formulation of the Multi-Mode Resource-Constrained Project Scheduling Problem for the Flexible Job Shop Scheduling Problem

A Constraint Programming Formulation of the Multi-Mode Resource-Constrained Project Scheduling Problem for the Flexible Job Shop Scheduling Problem

Responsiveness to sudden disturbances in manufacturing through dynamic job shop scheduling using Quantum Annealing

An efficient production planning and control is inevitable for the economic operation of a manufacturing system. As an essential part of production planning and control, process scheduling aims to assign processes to the available resources of a manufacturing system under consideration of its objectives. This forms an optimization problem also known as job shop scheduling which can be solved with computer aided techniques. Exact solution methods are only practical up to a certain number of functional units and processes, therefore, approximation methods are used in industry. However, as the problem size increases, the computational solving time increases significantly and the solution quality decreases in equal measure. In order to react to the current effects of global crises, such as disruptions in supply chains, approaches for fast and efficient rescheduling are needed. A dynamic shop job scheduling approach using Quantum Annealing bears the potential to close this research gap. Previous work has shown that Quantum Annealing is able to solve static job shop scheduling problems within seconds while finding good solutions. However, in a flexible environment such as a manufacturing system, the static approach is not suitable for process scheduling. Therefore, a dynamic Quantum Annealing based approach for job shop scheduling with consideration of machine breakdowns and new job arrivals is proposed. The approach monitors a manufacturing system and reacts to changes in the job pool or availabilities in functional units with rescheduling. The method is tested with several use cases involving small and large-scale problems and is compared with a simulated annealing approach. Thereby, the Quantum Annealing based computations show better results regarding solution quality and computing time. Moreover, the dynamic approach bears the potential for industrial application, especially as a supplement to a conventional advanced planning system.

A new algorithm of the scheduling of a flexible manufacturing system based on genetic algorithm

In the flexible manufacturing system, a reasonable production scheduling is crucial in shortening the processing completion time and improving the equipment utilization. Traditional manual scheduling cannot effectively solve the complex workshop scheduling problems and cannot provide a scheduling solution that meets the requirements in a short period of time, which can lead to a decrease in processing efficiency. Aiming at the complex job shop scheduling problem, the genetic algorithm is used to find the optimal scheduling solution in this study, taking the number of overdue jobs, the total overdue time, the job completion time, the comprehensive load rate and the maximum load rate of the machine tool as the performance indicators of the scheduling algorithm. The chromosomes are designed as process gene chain and equipment gene chain to improve the diversity and the robustness to scheduling problems of chromosome through crossover, variation, selection and other processes. The impact of different parameter settings on the performance indicators of each scheduling algorithm is researched by adjusting the four algorithm-related parameters, and there has been a certain improvement in the results of the scheduling problems. This study provides a reference for the design and optimization of production scheduling algorithm based on genetic algorithm.

An improved memetic algorithm to solve the energy-efficient distributed flexible job shop scheduling problem with transportation and start-stop constraints.

In the current global cooperative production environment, modern industries are confronted with intricate production plans, demanding the adoption of contemporary production scheduling strategies. Within this context, distributed manufacturing has emerged as a prominent trend. Manufacturing enterprises, especially those engaged in activities like automotive mold production and welding, are facing a significant challenge in managing a significant amount of small-scale tasks characterized by short processing times. In this situation, it becomes imperative to consider the transportation time of jobs between machines. This paper simultaneously considers the transportation time of jobs between machines and the start-stop operation of the machines, which is the first time to our knowledge. An improved memetic algorithm (IMA) is proposed to solve the multi-objective distributed flexible job shop scheduling problem (MODFJSP) with the goal of minimizing maximum completion time and energy consumption. Then, a new multi-start simulated annealing algorithm is proposed and integrated into the IMA to improve the exploration ability and diversity of the algorithm. Furthermore, a new multiple-initialization rule is designed to enhance the quality of the initial population. Additionally, four improved variable neighborhood search strategies and two energy-saving strategies are designed to enhance the search ability and reduce energy consumption. To verify the effectiveness of the IMA, we conducted extensive testing and comprehensive evaluation on 20 instances. The results indicate that, when faced with the MODFJSP, the IMA can achieve better solutions in almost all instances, which is of great significance for the improvement of production scheduling in intelligent manufacturing.

An actor-critic framework based on deep reinforcement learning for addressing flexible job shop scheduling problems.

With the rise of Industry 4.0, manufacturing is shifting towards customization and flexibility, presenting new challenges to meet rapidly evolving market and customer needs. To address these challenges, this paper suggests a novel approach to address flexible job shop scheduling problems (FJSPs) through reinforcement learning (RL). This method utilizes an actor-critic architecture that merges value-based and policy-based approaches. The actor generates deterministic policies, while the critic evaluates policies and guides the actor to achieve the most optimal policy. To construct the Markov decision process, a comprehensive feature set was utilized to accurately represent the system's state, and eight sets of actions were designed, inspired by traditional scheduling rules. The formulation of rewards indirectly measures the effectiveness of actions, promoting strategies that minimize job completion times and enhance adherence to scheduling constraints. The experimental evaluation conducted a thorough assessment of the proposed reinforcement learning framework through simulations on standard FJSP benchmarks, comparing the proposed method against several well-known heuristic scheduling rules, related RL algorithms and intelligent algorithms. The results indicate that the proposed method consistently outperforms traditional approaches and exhibits exceptional adaptability and efficiency, particularly in large-scale datasets.

Improved Multiverse Optimization Algorithm for Fuzzy Flexible Job-Shop Scheduling Problem

An improved multiverse optimization (IMVO) algorithm is proposed herein for the fuzzy flexible job-shop scheduling problem pertaining to the non-deterministic polynomial-time hard (NP-hard) problem. First, we designed a hybrid initialization method to improve the quality of the initial solution, and thereafter, introduced a self-crossing technique along with an insert-based heuristic algorithm to simulate the process of exchanging objects between black/white holes and wormholes, respectively. Second, a universe selection mechanism is proposed to reduce the possibility of the algorithm falling into a local optimum. Third, four kinds of neighborhood structures were designed to improve the local search ability of the algorithm. In the decoding operation, we adopted the shift-left strategy to completely utilize the idle time of the machine. Finally, numerous experiments were conducted on the three benchmark test sets of various types and sizes to investigate the performance of the proposed IMVO algorithm. The experimental results demonstrated the effectiveness of the algorithm, especially in large-scale instances, displaying a strong superiority with an average maximum enhancement efficiency of 50.44%.

An MILP Model for Energy-Conscious Flexible Job Shop Problem with Transportation and Sequence-Dependent Setup Times

As environmental awareness grows, energy-aware scheduling is attracting increasing attention. Compared with traditional flexible job shop scheduling problem (FJSP), FJSP, with considering sequence-dependent setup times and transportation times (FJSP-SDST-T), is closer to real production. In existing research, little research has focused on FJSP-SDST-T with the minimization energy consumption. In order to make up the gap, a mixed integer linear programming (MILP) model has been formulated to solve FJSP-SDST-T with minimizing energy. Firstly, the total energy consumption of the workshop included the processing energy consumption, setup energy consumption, idle energy consumption, transportation energy consumption and common energy consumption, which were analyzed and formulated by introducing related decision variables. Then, the MILP model was detailedly formulated from the formulation of the energy consumption composition, the objective function, the decision variables and the constraint sets and the linearization. Finally, experiments were carried out on extended benchmark cases and the results showed the effectiveness of the MILP model.

Improvement of Ant Colony Algorithm Performance for the Job-Shop Scheduling Problem Using Evolutionary Adaptation and Software Realization Heuristics

Planning tasks are important in construction, manufacturing, logistics, and education. At the same time, scheduling problems belong to the class of NP-hard optimization problems. Ant colony algorithm optimization is one of the most common swarm intelligence algorithms and is a leader in solving complex optimization problems in graphs. This paper discusses the solution to the job-shop scheduling problem using the ant colony optimization algorithm. An original way of representing the scheduling problem in the form of a graph, which increases the flexibility of the approach and allows for taking into account additional restrictions in the scheduling problems, is proposed. A dynamic evolutionary adaptation of the algorithm to the conditions of the problem is proposed based on the genetic algorithm. In addition, some heuristic techniques that make it possible to increase the performance of the software implementation of this evolutionary ant colony algorithm are presented. One of these techniques is parallelization; therefore, a study of the algorithm’s parallelization effectiveness was made. The obtained results are compared with the results of other authors on test problems of scheduling. It is shown that the best heuristics coefficients of the ant colony optimization algorithm differ even for similar job-shop scheduling problems.

Solving Job-Shop Scheduling Problem Using Genetic Algorithm Approach

An effective job shop scheduling (JSS) in the manufacturing industry is helpful to meet the production demand and reduce the production cost, and to improve the ability to compete in the ever increasing volatile market demanding multiple products.In so many combinatorial optimization problems, job shop scheduling problems have earned a reputation for being difficult to solve. Job-shop scheduling is essentially an ordering problem. A new encoding scheme for a classic job-shop scheduling problem is presented. The aim is to find an allocation for each job and to define the sequence of jobs on each machine so that the resulting schedule has a minimal completion time.Genetic algorithm that has demonstrated considerable success in providing efficient solutions to many non polynomial-hard optimization problems is used to solve job-shop scheduling problem. The schedules given by genetic algorithms are constructed using a priority rule and under several constraints. After a schedule is obtained a checking operation is applied to ensure that the solution is feasible. The approach is tested on a set of instances. The results validate the effectiveness of the algorithm.

An Improved African Vulture Optimization Algorithm for Dual-Resource Constrained Multi-Objective Flexible Job Shop Scheduling Problems

According to the characteristics of flexible job shop scheduling problems, a dual-resource constrained flexible job shop scheduling problem (DRCFJSP) model with machine and worker constraints is constructed such that the makespan and total delay are minimized. An improved African vulture optimization algorithm (IAVOA) is developed to solve the presented problem. A three-segment representation is proposed to code the problem, including the operation sequence, machine allocation, and worker selection. In addition, the African vulture optimization algorithm (AVOA) is improved in three aspects: First, in order to enhance the quality of the initial population, three types of rules are employed in population initialization. Second, a memory bank is constructed to retain the optimal individuals in each iteration to increase the calculation precision. Finally, a neighborhood search operation is designed for individuals with certain conditions such that the makespan and total delay are further optimized. The simulation results indicate that the qualities of the solutions obtained by the developed approach are superior to those of the existing approaches.

Ranking of sequencing rules in a job shop scheduling problem with preference selection index approach

Scheduling different jobs in an appropriate sequence are very important in manufacturing industries due to the influence of conflicting criteria. It becomes difficult to sequence the jobs as the job number increases due to numerous computations involved. In this article, six jobs are considered to be treated on a machine one by one. Seven different priority sequencing rules provide seven different sequencing options for the jobs which are assessed using a set of nine criteria. Preference selection index (PSI) approach, a multi-criterion decision-making (MCDM) technique is proposed to rank them from best to worst. The PSI approach, unlike other MCDM methods, does not require to find the relative significance of the criteria, which reduces work of finding weights of criteria hence is a very easy and effective tool for decision making. A benchmark problem from the previous literature is considered and solved using the PSI approach and the obtained results are found to be correct.

Hierarchical Reinforcement Learning for Multi-Objective Real-Time Flexible Scheduling in a Smart Shop Floor

With the development of intelligent manufacturing, machine tools are considered the “mothership” of the equipment manufacturing industry, and the associated processing workshops are becoming more high-end, flexible, intelligent, and green. As the core of manufacturing management in a smart shop floor, research into the multi-objective dynamic flexible job shop scheduling problem (MODFJSP) focuses on optimizing scheduling decisions in real time according to changes in the production environment. In this paper, hierarchical reinforcement learning (HRL) is proposed to solve the MODFJSP considering random job arrival, with a focus on achieving the two practical goals of minimizing penalties for earliness and tardiness and reducing total machine load. A two-layer hierarchical architecture is proposed, namely the combination of a double deep Q-network (DDQN) and a dueling DDQN (DDDQN), and state features, actions, and external and internal rewards are designed. Meanwhile, a personal computer-based interaction feature is designed to integrate subjective decision information into the real-time optimization of HRL to obtain a satisfactory compromise. In addition, the proposed HRL framework is applied to multi-objective real-time flexible scheduling in a smart gear production workshop, and the experimental results show that the proposed HRL algorithm outperforms other reinforcement learning (RL) algorithms, metaheuristics, and heuristics in terms of solution quality and generalization and has the added benefit of real-time characteristics.

Integrated lot-sizing and scheduling: Mitigation of uncertainty in demand and processing time by machine learning

Production rescheduling is one of the most challenging problems in production management, in which some parameters, such as customer demand and job processing time, are subject to uncertainty during the planning horizon. This paper develops a scheduling and rescheduling method for the simultaneous lot-sizing and job shop scheduling problem, considering sequence-dependent setup times and capacity constraints. The objective is to find a trade-off between safety levels and production costs focusing on schedulability and optimality as the two most important performance indicators in the face of uncertainty. Therefore, a new adjustable formulation based on satisfiability modulo theories has been developed to tackle the demand and processing time uncertainty. Then, a combination of neural networks and a K-means based heuristic was applied to calibrate the model by determining the profitable value of the safety levels as a strategy to increase the robustness of the schedule. We also developed a Monte Carlo simulation to assess the performance of the proposed algorithm and compare it with other approaches addressed in the literature. The computational results show that the proposed algorithm is efficient and promising in protecting the schedulability of the model, taking the optimality criterion into account.

A hybrid fluid master–apprentice evolutionary algorithm for large-scale multiplicity flexible job-shop scheduling with sequence-dependent set-up time

In this article, a large-scale multiplicity flexible job-shop scheduling problem (FJSP) with sequence-dependent set-up time is studied. In this problem, the large production demand for each type of job yields the large-scale multiplicity manufacturing feature. To address the problem, a hybrid fluid master–apprentice evolutionary algorithm (HFMAE) is presented to minimize the makespan. In the first step, a fluid relaxation initialization method (FRI) and an initialize procedure are proposed to obtain high-quality initial solutions. In the FRI, an online fluid tracking policy is presented to improve the assignment decision and the sequencing decision of operations. In the second step, an improved master–apprentice evolutionary method (IMAE) is presented based on the generated initial solutions. In the IMAE, two neighbourhood structures and three makespan estimation approaches are presented to accelerate the solution space search efficiency. Numerical results show that the proposed HFMAE outperforms the comparison algorithms in solving large-scale multiplicity FJSPs.

Application of hybrid artificial bee colony algorithm based on load balancing in aerospace composite material manufacturing

The manufacturing of composite materials for the aerospace industry represents a cornerstone of future development in this advanced field. In this study, a mathematical model of flexible job-shop scheduling problem (FJSP) was established by extracting the key manufacturing information from an aerospace composite manufacturing workshop. Intelligent algorithms can effectively solve FJSP. However, when applied to a multi-objective FJSP (MOFJSP), they suffer from drawbacks such as blind search and low efficiency. Therefore, this study proposes a new artificial bee colony algorithm and implements it as part of a hybrid method (referred to as the HMABC) to solve MOFJSP. The method involves three steps: (1) A multiple-rule initial population is constructed to minimize randomness and improve quality. (2) A greedy decoding method is used to decode each individual to further narrow the search range to replace the conventional decoding method. (3) By considering the machine load index (which has often been neglected), the concept of machine load rate is proposed, and three heuristic strategies are designed (with the influences ranging from small to high) to diverge the solution in all directions instead of just a direction. The performance of the proposed method is compared with those of existing algorithms using a classical FJSP test example, and the effectiveness and efficiency of HMABC is verified. Finally, the method is applied to an actual aerospace composite manufacturing system to realize the scheduling of actual production activities.

Many-Objective Genetic Programming for Job-Shop Scheduling

This article overviews a recent PhD dissertation representing the first effort at many-objective optimization in job shop scheduling (JSS). The thesis develops genetic programming hyperheuristic (GP-HH) approaches to evolve effective dispatching rules for many conflicting objectives in JSS problems. The aim is to develop GP-HH methods that alleviate issues related to many-objective optimization in JSS problems and evolve new effective dispatching rules capable of enhancing job shops' productivity.

Solving Multiobjective Fuzzy Job-Shop Scheduling Problem by a Hybrid Adaptive Differential Evolution Algorithm

The job-shop scheduling problem (JSP) is NP hard, which has very important practical significance. Because of many uncontrollable factors, such as machine delay or human factors, it is difficult to use a single real-number to express the processing and completion time of the jobs. JSP with fuzzy processing time and completion time (FJSP) can model the scheduling more comprehensively, which benefits from the developments of fuzzy sets. Fuzzy relative entropy leads to a method that can evaluate the quality of a feasible solution following the comparison between the actual value and the ideal value (the due date). Therefore, the multiobjective FJSP can be transformed into a single-objective optimization problem and solved by a hybrid adaptive differential evolution (HADE) algorithm. The maximum completion time, the total delay time, and the total energy consumption of jobs will be considered. HADE adopts a mutation strategy based on DE-current-to-best. Its parameters (CR and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> ) are all made adaptive and normally distributed. The new individuals are selected according to the fitness value (FRE) obtained from a population consisting of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> parents and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> children in HADE. The algorithm is analyzed from different viewpoints. As the experimental results demonstrate, the performance of the HADE algorithm is better than those of some other state-of-the-art algorithms (namely, ant colony optimization, artificial bee colony, and particle swarm optimization).

A two-stage memetic algorithm for energy-efficient flexible job shop scheduling by means of decreasing the total number of machine restarts

Machine on/off control is an effective way to achieve energy-efficient production scheduling. Turning off machines and restarting them frequently, however, would incur a considerable amount of additional energy and may even cause damage to the machines. In this paper, we propose a mathematical model based on the energy-efficient flexible job shop scheduling problem (EEFJSP), aiming to minimize not just the makespan and total energy consumption but also the total number of machine restarts. Our idea here is that shifting the start time of operations on different machines appropriately can effectively decrease the number of restarts required and the total energy consumption. We present a two-stage memetic algorithm (TMA) to solve the EEFJSP. A variable neighborhood search approach is designed to improve the convergence speed and fully exploit the solution space of the TMA. An operation-block moving operator is developed to further reduce the total energy consumption as well as the total number of machine restarts without affecting the makespan. Extensive computational experiments carried out to compare the TMA with some well-known algorithms confirm that the proposed TMA can easily obtain better Pareto solutions for the EEFJSP.

Integrated Scheduling of the Production and Maintenance of Parallel Machine Job-shop Considering Stochastic Machine Breakdowns

The integrated scheduling of production and maintenance can make equipment maintenance in line with the production pace, so as to effectively prevent anormal interruptions of the production process due to equipment failure, and ensure the smooth implementation of the production scheduling plan. Aiming at the parallel machine job-shop environment, and considering stochastic machine failures and different degradation speeds of parallel machines, this paper introduced the minimal maintenance and preventive maintenance strategies to establish an integrated scheduling model for production and maintenance, designed a genetic algorithm based on process coding and binary hybrid coding to solve the model, and verified the correctness of the proposed model and the effectiveness of the algorithm through an instance. This study provided an effective decision-making method for parallel machine job-shop scheduling problems.

Hybrid genetic algorithm with variable neighborhood search for flexible job shop scheduling problem in a machining system

This paper proposes an improved hybrid genetic algorithm with variable neighborhood search (HGA-VNS) for addressing the flexible job shop scheduling problem (FJSP) considering the machine work load balance in machining system, with the minimization of the makespan. In the HGA-VNS algorithm, each solution is represented by a chromosome consists of two parts, where the first part is the code of the machining machine number, and the second part chromosome is the code of the machining process number. Second, considering the slow convergence speed of the previous algorithms, a combined methods in crossover and mutation operators that considers the machine work load balance is proposed. Third, a local search approach that carry out for key processes on the critical path which reduces the number of invalid transformations is proposed. For the HGA-VNS, using the orthogonal experiment approach, the best combination of parameters is provided. Then, the proposed HGA-VNS is tested on sets of extended instances based on the well-known benchmarks. Experimental results show that the HGA-VNS is effective, and its performance is significantly better than other algorithms in solving flexible job shop problems in a machining system. Finally, the proposed HGA-VNS is applied to optimize practical FJSP in enterprise F. Compared with the original scheduling scheme, the makespan of the optimal scheduling scheme is reduced by 14.92%, and HGA-VNS can obtain more efficient and economic solutions.