Job Shop Scheduling Problem Research Articles

An improved deep reinforcement learning approach: A case study for optimisation of berth and yard scheduling for bulk cargo terminal

The cornerstone of port production operations is ship handling, necessitating judicious allocation of diverse production resources to enhance the efficiency of loading and unloading operations. This paper introduces an optimisation method based on deep reinforcement learning to schedule berths and yards at a bulk cargo terminal. A Markov Decision Process model is formulated by analysing scheduling processes and unloading operations in bulk port imports business. The study presents an enhanced reinforcement learning algorithm called PS-D3QN (Prioritised Experience Replay and Softmax strategy-based Dueling Double Deep Q-Network), amalgamating the strengths of the Double DQN and Dueling DQN algorithms. The proposed solution is evaluated using actual port data and benchmarked against the other two algorithms mentioned in this paper. The numerical experiments and comparative analysis substantiate that the PS-D3QN algorithm significantly enhances the efficiency of berth and yard scheduling in bulk terminals, reduces the cost of port operation, and eliminates errors associated with manual scheduling. The algorithm presented in this paper can be tailored to address scheduling issues in the fields of production and manufacturing with suitable adjustments, including problems like the job shop scheduling problem and its extensions.

An improved multi-objective Wild Horse optimization for the dual-resource-constrained flexible job shop scheduling problem: A comparative analysis with NSGA-II and a real case study

The equipment manufacturing industry needs skilled workers to operate a specific set of machines following process specifications. Optimizing machine and worker assignments to achieve maximum efficiency is a critical problem for workshop managers. This paper investigates a multi-objective dual-resource-constrained flexible job shop scheduling problem. An improved wild horse optimization (IWHO) algorithm is developed to simultaneously optimize three objectives: makespan, maximum machine workload, and total machine workload. To evaluate the quality of individuals in multi-objective optimization, the Pareto fast non-dominated sorting method is used, and the crowding distance is calculated. To update the algorithm's solution, the crossover and mutation operations are used. Further, a local neighborhood search strategy is employed to enhance searchability and avoid trapping into the local optima. The benchmark of the flexible job shop scheduling problem is extended to create test instances, and the performance of the suggested IWHO algorithm is evaluated compared with the NSGA-II. The computational results show that the IWHO algorithm provides a non-dominated efficient set within a reasonable running time. Furthermore, a buffers and chain coupler assembly process is designed to analyze the practical value of the IWHO algorithm. The proposed solutions can be used to generate daily schedules for managing machines, workers, and production cycles.

Deep reinforcement learning for dynamic flexible job shop scheduling problem considering variable processing times

In recent years, the uncertainties and complexity in the production process, due to the boosted customized requirements, has dramatically increased the difficulties of Dynamic Flexible Job Shop Scheduling (DFJSP). This paper investigates a new DFJSP model taking into account the minimum completion time under the condition of machine processing time uncertainty, e.t. VPT-FJSP problem. In the formulated VPT-FJSP process, each workpiece needs to be processed by required machine at a certain time slot where Markov decision process (MDP) and reinforcement learning methods are adopted to solve VPT-FJSP. The agent designed in this paper employs the Proximal Policy Optimization(PPO) algorithm in deep reinforcement learning, which includes the Actor-Critic network. The input of the network is to extract the processing information matrix and to embed some advanced states in the workshop by graph neural network, which enables the agent to learn the complete state of the environment. Finally, we train and test the proposed framework on the canonical FJSP benchmark, and the experimental results show that our framework can make agent better than genetic algorithm and ant colony optimization in most cases, 94.29% of static scheduling. It is also shown superiority compared to the scheduling rules in dynamic environment and has demonstrated strong robustness in solving VPT-FJSP. Furthermore, this study conducted tests to assess the generalization capability of the agent on VPT-FJSP at different scales. In terms of exploring Makespan minimization, the agent outperformed four priority scheduling rules. These results indicate that the proposed dynamic scheduling framework and PPO algorithm are more effective in achieving superior solutions.

Real-Time Selection System of Dispatching Rules for the Job Shop Scheduling Problem

Personalized market demands make the job shop scheduling problem (JSSP) increasingly complex, and the need for scheduling methods that can solve scheduling strategies quickly and easily has become very urgent. In this study, we utilized the variety and simplicity of dispatching rules (DRs) and constructed a DR real-time selection system with self-feedback characteristics by combining simulation techniques with decision tree algorithms using makespan and machine utilization as scheduling objectives, which are well adapted to the JSSP of different scales. The DR real-time selection system includes a simulation module, a learning module, and an application module. The function of the simulation module is to collect scheduling data in which is embedded a novel mathematical model describing the JSSP; the function of the learning module is to construct a DR assignment model to assign DR combinations to the job shop system, and the function of the application module is to apply the assigned DR combinations. Finally, a series of job shop systems are simulated to compare the DR assignment model with the NSGA-II and PSO algorithms. The aim is to verify the superiority of the DR assignment model and the rationality of the DR real-time selection system.

Agent-based hybrid tabu-search heuristic for dynamic scheduling

Dynamic scheduling has received widespread attention from academia and industry due to the increasing complexity in manufacturing systems. Highly dynamic and adaptable behaviours are necessary for an improved production efficiency in unstable and constantly changing environments. This paper proposes an agent-based hybrid tabu-search heuristic (AB-TSH) to solve dynamic flexible job-shop scheduling problems. The solution is fully implemented and tested in an industrial environment for seven distinct dynamic scenarios derived from a static scenario using the benchmark of AIP-PRIMECA Flexible Manufacturing System. The scheduling plan is obtained by exploitation using a greedy heuristic on tabu search solution points. The hybrid tabu-search heuristic is supported by a multi-agent system that react and re-optimize the scheduling plan in case of disturbances and unpredicted events. The proposed solution demonstrated superior performance in terms of makespan in the majority of dynamic scenarios tested when compared to previous studies in the literature. This improved performance is attributed to the solution’s ability to combine the scheduling plan both statically and dynamically.

Retracted: An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm

Retracted: An Effective Hybrid Multiobjective Flexible Job Shop Scheduling Problem Based on Improved Genetic Algorithm

Implementation of a Binary Kidney-Inspired Algorithm Based on a Parallel Method for Solving the Job Shop Scheduling Problem

Implementation of a Binary Kidney-Inspired Algorithm Based on a Parallel Method for Solving the Job Shop Scheduling Problem

Mathematical model and augmented simulated annealing algorithm for mixed-model assembly job shop scheduling problem with batch transfer

In the mixed-model assembly job-shops, all the components are transferred in batches from the processing stage to the assembly stage to reduce transportation costs and timely satisfy the assembly material requirements. However, batch transfer in such a workshop has not received due attention in the current literature. Thus, this work addresses the mixed-model assembly job-shop scheduling problem with batch transfer via a mathematical model and an augmented simulated annealing algorithm to minimize manufacturing and transportation costs. The mathematical model takes batch transfer constraints into account and constructs the temporal and spatial links among the processing, transfer, and assembly stages. Production sequencing knowledge and batch transfer knowledge are first extracted via gene expression programming algorithm and clustering method and then implanted into the algorithmic operators in the form of rules and strategies to directly identify the promising solution space. Besides, eleven neighborhood structures including the critical component-based and batch-based ones, are designed to enhance the exploitation ability. A restart mechanism considering crossover and tempering helps to get out of local optima. Experimental results indicate that by adopting the extracted knowledge, problem-specific neighborhood structures, and restart mechanism, the proposed algorithm significantly outperforms other comparison algorithms in fixing the studied problem.

A hybrid genetic tabu search algorithm for distributed flexible job shop scheduling problems

The distributed flexible job-shop scheduling problem (DFJSP) is an extension of the flexible job shop scheduling problem, which is a famous NP-complete combinatorial optimization problem. DFJSP consists of three sub-problems, assigning jobs to appropriate factories, scheduling operations to suitable machines, and determining the operation sequence on machines. Due to the complexity of DFJSP, there is only a little research on the problem. There are several benchmark sets proposed to test the performance of methods for solving DFJSP. However, many instances remain unresolved after a long time. This paper proposes a hybrid genetic tabu search algorithm (HGTSA) for DFJSP. The proposed HGTSA combines the global search ability of the genetic algorithm (GA) and the local search ability of the tabu search (TS) well. Two genetic operators are designed based on the critical factory to discrete the population. A new neighborhood structure is introduced into TS to search for more space of neighborhood solutions. To evaluate the performance of HGTSA, this paper compares it with four state-of-the-art algorithms on 69 benchmark instances. The experimental results demonstrate that HGTSA outperforms these comparison algorithms in terms of solution quality and computation efficiency. In particular, HGTSA has found 13 newly upper bounds of these benchmark instances.

A genetic algorithm-based approach for flexible job shop rescheduling problem with machine failure interference

Rescheduling is the guarantee to maintain the reliable operation of production system process. In production system, the original scheduling scheme cannot be carried out when machine breaks down. It is necessary to transfer the production tasks in the failure cycle and replan the production path to ensure that the production tasks are completed on time and maintain the stability of production system. To address this issue, in this paper, we studied the event-driven rescheduling policy in dynamic environment, and established the usage rules of right-shift rescheduling and complete rescheduling based on the type of interference events. And then, we proposed the rescheduling decision method based on genetic algorithm for solving flexible job shop scheduling problem with machine fault inter-ference. In addition, we extended the "mk" series of instances by introducing the machine fault interference information. The solution data show that the complete rescheduling method can respond effectively to the rescheduling of flexible job shop scheduling problem with machine failure interference.

Multiobjective Optimization for FJSP Under Immediate Predecessor Constraints Based OFA and Pythagorean Fuzzy Set

In the flexible job shop scheduling problem (FJSP), immediate predecessor operations have an explicit impact on the scheduling results, and are often ignored. To analyze the influence of immediate predecessor operations on machine tool manufacturing workshops, four forms of immediate predecessor operations with the consideration of uncertain transportation and preparation time are defined. Then, the four forms of immediate predecessor operations are integrated into the FJSP, and a multiobjective FJSP is constructed. An improved optimal foraging algorithm (OFA) and Pythagorean fuzzy set (PFS) are combined to establish a multiobjective optimization algorithm, named PFSOFA. This algorithm is then used to solve the multiobjective FJSP. In PFSOFA, the Pareto fronts are mapped into PFSs. The Pythagorean fuzzy numbers (PFNs) in a PFS are transformed into right triangles, and the distances between the PFNs and the reference PFNs are defined as the distances between their right triangle centroids. Then, all distances of a PFS are integrated by the distance prospect function to obtain a distance prospect value. This value is then used to lead the iteration of PFSOFA. Through extensive experiments, including a real factory application case, the performance of PFSOFA is verified to be better than four classical multiobjective optimization algorithms for solving the multiobjective FJSP constructed in this paper. And for the factory case, PFSOFA also obtained the better schemes.

Mathematical model and adaptive simulated annealing algorithm for mixed-model assembly job-shop scheduling with lot streaming

Mixed-model assembly and lot streaming are two key technologies to improve efficiency and reduce setups in a multi-variety and small-batch discrete manufacturing environment. Yet few studies consider the two technologies in assembly job-shop scheduling problems. Thus, this paper investigates the mixed-model assembly job-shop scheduling problem with lot streaming, which contains two closely coordinated stages with differentiated production lot size: the processing stage with lot streaming and the mixed-model assembly stage with single-piece flow. To tackle this problem, a mathematical model including new constraints i.e. production sequence constraints within/among sublots, sequence-dependent setup constraints between sublots and mixed-model assembly constraints, is developed to establish the temporal and spatial links between the processing and assembly stages. Besides, an adaptive simulated annealing algorithm is proposed. In this algorithm, a sublot sequence rule considering sublot and assembly features is discovered via gene expression programming to promote the performance of initial solutions; a Q-learning-based temperature control mechanism is designed to adaptively adjust the acceptance probability of inferior solutions and accordingly avoid local optima; an adaptive selection mechanism of neighborhood operators is designed to increase the chance of finding potential solutions; an adaptive adjustment mechanism of neighborhood size is put forward to balance computing resources and the coverage of neighborhood space. Experimental results show that both the discovered rule and the adaptive mechanisms are effective, and the developed algorithm is more adapt to fix the studied problem than other state-of-the-art algorithms.

An improved quantum particle swarm algorithm for solving multi-objective fuzzy flexible job shop scheduling problem

Due to the dynamic nature of work conditions in the manufacturing plant, it is difficult to obtain accurate information on process processing time and energy consumption, affecting the implementation of scheduling solutions. The fuzzy flexible job shop scheduling problem with uncertain production parameters has not yet been well studied. In this paper, a scheduling optimization model with the objectives of maximum completion time, production cost and delivery satisfaction loss is developed using fuzzy triangular numbers to characterize the time parameters, and an improved quantum particle swarm algorithm is proposed to solve it. The innovations of this paper lie in designing a neighborhood search strategy based on machine code variation for deep search; using cross-maintaining the diversity of elite individuals, and combining it with a simulated annealing strategy for local search. Based on giving full play to the global search capability of the quantum particle swarm algorithm, the comprehensive search capability of the algorithm is enhanced by improving the average optimal position of particles. In addition, a gray target decision model is introduced to make the optimal decision on the scheduling scheme by comprehensively considering the fuzzy production cost. Finally, simulation experiments are conducted for test and engineering cases and compared with various advanced algorithms. The experimental results show that the proposed algorithm significantly outperforms the compared ones regarding convergence speed and precision in optimal-searching. The method provides a more reliable solution to the problem and has some application value.

A spatial pyramid pooling-based deep reinforcement learning model for dynamic job-shop scheduling problem

The dynamic job-shop scheduling problem (DJSP) is a typical of scheduling tasks where rescheduling is performed when encountering unexpected events such as random job arrivals and rush order. However, the current rescheduling approaches cannot reuse the trained scheduling policies or the experiences due to the variant size of scheduling problems. In this paper, we propose a deep reinforcement learning (DRL) scheduling model for DJSP based on spatial pyramid pooling networks (SPP-Net). A new state representation is proposed based on the machine matrix and remaining time matrix which is decomposed from the scheduling instance matrix. And a new reward function is derived from the area of total scheduling time where the accumulated reward is negatively linearly dependent with the make-span of a scheduling task. Moreover, a size-agnostic scheduling policy is designed based on the SPP-Net and SoftMax function, which is trained by the proximal policy optimization (PPO). Besides, various paired priority dispatching rules (PDR) are used as available actions. Static experiments on classic benchmark instances show that our scheduling model achieves better results on average than existing DRL methods. In addition, dynamic scheduling experiments are tested and our model obtains better results than the PDR scheduling methods in reasonable time when encountering unexpected events such as random job arrivals and rush order.

An effective reformative memetic algorithm for distributed flexible job-shop scheduling problem with order cancellation

Order cancellation, due to such as customer plan adjustments or market changes, usually occurs in the real production environment of distributed flexible job shop scheduling problem (DFJSP). However, thus far, all exiting researches about DFJSP have not consider order cancellation, which normally leads to resource waste and makes the original scheme infeasible. Hence, in this work, we propose a DFJSP considering order cancellation (DFJSPC) for the first time; and design a reformative memetic algorithm (RMA) to solve the DFJSPC aiming at optimizing the makespan and total energy consumption. In the RMA, a five-layer encoding operator and a new load balancing initialization method are designed to improve the quality of the initial population. Some effective crossover, mutation and local search operators are designed, which can fully expand the solution space of the algorithm and improve its convergence speed. A total of 60 DFJSPC benchmark instances are constructed, and some comparative experiments are carried out among the proposed RMA and three well-known algorithms, namely NNIA, NSGA-II and NSGA-III. The final experimental results verified the outstanding performance of the RMA. This research will provide a theoretical basis for the order cancellation problem in distributed production settings, and help manufacturers to properly handle canceled orders to reduce resource waste and reschedule the infeasible schemes causing from order cancellation.

Knowledge-driven two-stage memetic algorithm for energy-efficient flexible job shop scheduling with machine breakdowns

This paper focuses on the multi-objective energy-efficient flexible job shop scheduling problem with machine breakdowns. To mitigate the impact of machine breakdowns, a rescheduling strategy is implemented in the scheduling process. In addition to sequencing the operations, the current problem is to determine the appropriate allocation of the machine and the proper speed of the machine to minimize both makespan and total energy consumption simultaneously. A mixed integer linear programming model is established to describe the considered problem. With the aim of effectively solving this problem, a knowledge-driven two-stage memetic algorithm (KTMA) is proposed. In the first stage, a hybrid initialization strategy that combines three problem-specific heuristics is applied to generate a high-quality initial population. Then, a knowledge-driven variable neighborhood search approach is designed for quickly converging and fully exploiting the solution space of the KTMA. In the second stage, two energy-saving strategies are designed to further reduce the total energy consumption. Extensive experiments carried out to compare the KTMA with some well-known algorithms confirm that the proposed KTMA can efficiently solve this problem.

Necessary and Sufficient Conditions for Feasible Neighbourhood Solutions in the Local Search of the Job-Shop Scheduling Problem

The meta-heuristic algorithm with local search is an excellent choice for the job-shop scheduling problem (JSP). However, due to the unique nature of the JSP, local search may generate infeasible neighbourhood solutions. In the existing literature, although some domain knowledge of the JSP can be used to avoid infeasible solutions, the constraint conditions in this domain knowledge are sufficient but not necessary. It may lose many feasible solutions and make the local search inadequate. By analysing the causes of infeasible neighbourhood solutions, this paper further explores the domain knowledge contained in the JSP and proposes the sufficient and necessary constraint conditions to find all feasible neighbourhood solutions, allowing the local search to be carried out thoroughly. With the proposed conditions, a new neighbourhood structure is designed in this paper. Then, a fast calculation method for all feasible neighbourhood solutions is provided, significantly reducing the calculation time compared with ordinary methods. A set of standard benchmark instances is used to evaluate the performance of the proposed neighbourhood structure and calculation method. The experimental results show that the calculation method is effective, and the new neighbourhood structure has more reliability and superiority than the other famous and influential neighbourhood structures, where 90% of the results are the best compared with three other well-known neighbourhood structures. Finally, the result from a tabu search algorithm with the new neighbourhood structure is compared with the current best results, demonstrating the superiority of the proposed neighbourhood structure.

Multi-objective green scheduling of integrated flexible job shop and automated guided vehicles

The traditional flexible job shop scheduling problem (FJSP) ignores transportation issues or merely introduces a time lag for transportation tasks while assuming an infinite number of transportation resources. With the development of intelligent manufacturing, automated guided vehicles (AGVs), which are the key transportation equipment for manufacturing enterprises, have been widely used for their high flexibility and stability. In addition, the increase in energy consumption and the trend of green manufacturing make it critical to take into account energy-related objectives in the decision-making of scheduling. Therefore, the multi-objective green scheduling problem of integrated flexible job shop and AGVs (MOGSP-IFJS&AGVs) is addressed in this paper. To solve this problem effectively, the multi-objective mixed-integer programming (MMIP) model is formulated to minimize total energy consumption and makespan simultaneously. An efficient heuristic algorithm (EHA) is designed to solve the MMIP model. In the EHA, one solution encoding scheme and corresponding greedy insertion decoding method considering the selection of AGVs are presented. To acquire a high-quality initial population, the population initialization method balancing the processing time and energy consumption is designed. Further, a local search strategy is presented to enhance the quality of solutions and accelerate the convergence speed of the EHA. Experiment results of 45 test instances indicate that the EHA can obtain better solutions than that of comparison algorithms, which confirms the effectiveness of the EHA for solving the MOGSP-IFJS&AGVs.

Integrated job-shop scheduling in an FMS with heterogeneous transporters: MILP formulation, constraint programming, and branch-and-bound

Current studies on scheduling of machines and transporters assume that either a single transporter or an infinite number of homogeneous transporters such as AGVs or mobile robots are available to transport semi-finished jobs, which seems very restrictive in practice. This paper addresses this gap by studying a job-shop scheduling problem that incorporates a limited number of heterogeneous transporters, where the objective is to minimize the makespan. The problem is modelled using mixed-integer linear programming and constraint programming. Different structure-based branch-and-bound algorithms with two lower-bounding strategies are also developed. A comprehensive numerical study evaluates the proposed models and algorithms. The research demonstrates that the adjustment of the proposed MILP model outperforms the existing formulation when applied to the homogeneous case. The study also uncovers interesting practical implications, including the analysis of the impact of different transporter types in the system. It shows that utilizing a fleet of heterogeneous transporters can improve the overall performance of the job shop compared to a relevant homogeneous case. The importance of the study is emphasized by highlighting the negative consequences of disregarding transporters' differences during the scheduling phase.

A data-driven simulation-optimization framework for generating priority dispatching rules in dynamic job shop scheduling with uncertainties

Modeling and optimizing dynamic job shop scheduling problems (DJSSP) without ample assumptions is inherently challenging due to the increasing complexity and uncertainty arising from various disruptive events. Moreover, establishing job due dates in dynamic job shop environments has become increasing difficult due to unforeseen events, while it remains a pivotal factor in determining tardiness-related objectives. A research gap exists in exploring the potential synergy between the two aforementioned aspects and its resulting implications. In this study, we propose a novel framework that combines data-driven simulation, machine learning, and evolutionary algorithm to generate new Priority Dispatching Rules (PDRs) for optimizing makespan and total tardiness. The framework incorporates a data-exchange mechanism for real-time updates of the simulation model based on the shop floor. Moreover, an online due date prediction model using XGBoost is developed, replacing the previous rough estimation of the Total Work Content (TWK) rule. Simulation experiments of various scales demonstrate that XGBoost-assisted due date prediction leads to an average reduction of 1.6% in makespan and 65.0% in total tardiness compared to the TWK rule. The proposed method outperforms existing well-known dispatching rules, yielding considerable improvements with average reductions of 90.8%, 40.3%, and 44.6% in total tardiness for vary-sized experiments. Finally, the approach is validated through a real industrial case study.