Job Shop Scheduling Research Articles

Production costs and total completion time minimization for three-stage mixed-model assembly job shop scheduling with lot streaming and batch transfer

Assembly scheduling problems have broad applications in discrete manufacturing enterprises and hence gained extensive attention in academics. However, some important and actual factors including lot streaming, batch transfer of components and mixed-model assembly are yet not well studied. To adapt to actual production and enhance competitiveness, a three-stage mixed-model assembly job shop scheduling with lot streaming and batch transfer is investigated in this work. To tackle this problem, spatial-temporal links among three stages with differentiated production lot size are established and a novel mathematical model is formulated to minimize total completion time and production costs including setup costs, transport costs, and inventory costs. Besides, an improved multi-objective coevolutionary simulated annealing algorithm is developed. To promote the coevolution of processing, transfer, and assembly sub-problems, the multi-attribute combination rule, similarity rule, and consistency rule are respectively designed for each sub-problem. An adaptive execution strategy of sub-problems is trained by Q-learning to maximize the overall benefits. Experimental results show that both the discovered rule and the adaptive strategy are effective, and the proposed algorithm significantly outperforms seven competitive multi-objective algorithms in fixing the studied problem. More importantly, the developed production mode of “processing with lot streaming-batch transfer-mixed-model assembly considering pull production” has a better comprehensive performance than the other three actual production modes.

Multi-Agent Reinforcement Learning for Extended Flexible Job Shop Scheduling

An extended flexible job scheduling problem is presented with characteristics of technology and path flexibility (dual flexibility), varied transportation time, and an uncertain environment. The scheduling can greatly increase efficiency and security in complex scenarios, e.g., distributed vehicle manufacturing, and multiple aircraft maintenance. However, optimizing the scheduling puts forward higher requirements on accuracy, real time, and generalization, while subject to the curse of dimension and usually incomplete information. Various coupling relations among operations, stations, and resources aggravate the problem. To deal with the above challenges, we propose a multi-agent reinforcement learning algorithm where the scheduling environment is modeled as a decentralized partially observable Markov decision process. Each job is regarded as an agent that decides the next triplet, i.e., operation, station, and employed resource. This paper is novel in addressing the flexible job shop scheduling problem with dual flexibility and varied transportation time in consideration and proposing a double Q-value mixing (DQMIX) optimization algorithm under a multi-agent reinforcement learning framework. The experiments of our case study show that the DQMIX algorithm outperforms existing multi-agent reinforcement learning algorithms in terms of solution accuracy, stability, and generalization. In addition, it achieves better solution quality for larger-scale cases than traditional intelligent optimization algorithms.

Robust job shop scheduling with machine unavailability due to random breakdowns and condition-based maintenance

This paper presents a novel solution approach for a variant of the job shop scheduling problem with machine unavailability due to both condition-based preventive maintenance and corrective maintenance following random breakdowns. We first provide an exact mathematical formulation of the problem under simplifying assumptions, namely that the number of breakdowns for each job position on each machine is known, the degradation rates are fixed, and the preventive and corrective maintenance durations are deterministic parameters. Moreover, to handle the more realistic case of stochastic machine degradation, random breakdowns, and uncertain maintenance durations, a simulation-optimisation algorithm is proposed. The real makespan function is first approximated using multiple surrogate measures, which are optimised through independent genetic algorithms. Then, the fittest solutions obtained from these surrogate measures are simulated, and the best among them is added to an elite list, which is included in the genetic algorithms' populations for the next iteration. Schedule robustness is ensured by using an objective function that consists of the weighted average of the expected makespan and its 90th percentile. Furthermore, to reduce the likelihood of falling into a local optimum, a stopping criterion based on simulated annealing is implemented. Numerical experimentation on extended benchmark instances confirmed the validity of the mathematical formulation and the favourable performance of the proposed simulation-optimisation algorithm in terms of computational time and solution quality.

Optimizing flexible job shop scheduling with automated guided vehicles using a multi-strategy-driven genetic algorithm

The flexible job scheduling problem with automated guided vehicles (FJSP-AGVs) is a simplified model of some real manufacturing industries. It contains three strongly coupled subproblems: operation sequences assignment, machine selection, and automatic guided vehicle selection, leading to a huge solution space. Its several unresolved challenges, i.e., problem model and algorithmic designing, persist. Therefore, we first adopt the sequence-based modeling method to establish a mixed-integer linear programming model with makespan, and its correctness is verified by using the Gurobi solver. Subsequently, a multi-strategy-driven genetic algorithm (Mult_stra_GA) is proposed based on the implicit features of FJSP-AGVs. In Mult_stra_GA, for the operation sequence (OS) and the machine assignment (MS) subproblems, we design three targeted strategies, i.e., two layer-based encoding and decoding strategy, a multiple heuristics-based initialization strategy, double crossover, and dual mutation operators. Meanwhile, the problem-specific diversity checking and restart strategies are introduced to avoid Mult_stra_GA falling into local optima. Finally, we conduct experiments on four well-known benchmarks. Through the statistical analysis, the outcomes demonstrate that the Mult_stra_GA algorithm exhibits efficacy when contrasted with other advanced algorithms.

Dynamic Job-Shop Scheduling Based on Transformer and Deep Reinforcement Learning

The dynamic job-shop scheduling problem is a complex and uncertain task that involves optimizing production planning and resource allocation in a dynamic production environment. Traditional methods are limited in effectively handling dynamic events and quickly generating scheduling solutions; in order to solve this problem, this paper proposes a solution by transforming the dynamic job-shop scheduling problem into a Markov decision process and leveraging deep reinforcement learning techniques. The proposed framework introduces several innovative components, which make full use of human domain knowledge and machine computing power, to realize the goal of man–machine collaborative decision-making. Firstly, we utilize disjunctive graphs as the state representation, capturing the complex relationships between various elements of the scheduling problem. Secondly, we select a set of dispatching rules through data envelopment analysis to form the action space, allowing for flexible and efficient scheduling decisions. Thirdly, the transformer model is employed as the feature extraction module, enabling effective capturing of state relationships and improving the representation power. Moreover, the framework incorporates the dueling double deep Q-network with prioritized experience replay, mapping each state to the most appropriate dispatching rule. Additionally, a dynamic target strategy with an elite mechanism is proposed. Through extensive experiments conducted on multiple examples, our proposed framework consistently outperformed traditional dispatching rules, genetic algorithms, and other reinforcement learning methods, achieving improvements of 15.98%, 17.98%, and 13.84%, respectively. These results validate the effectiveness and superiority of our approach in addressing dynamic job-shop scheduling problems.

Computational-Intelligence-Based Scheduling with Edge Computing in Cyber-Physical Production Systems.

Real-time performance and reliability are two critical indicators in cyber-physical production systems (CPPS). To meet strict requirements in terms of these indicators, it is necessary to solve complex job-shop scheduling problems (JSPs) and reserve considerable redundant resources for unexpected jobs before production. However, traditional job-shop methods are difficult to apply under dynamic conditions due to the uncertain time cost of transmission and computation. Edge computing offers an efficient solution to this issue. By deploying edge servers around the equipment, smart factories can achieve localized decisions based on computational intelligence (CI) methods offloaded from the cloud. Most works on edge computing have studied task offloading and dispatching scheduling based on CI. However, few of the existing methods can be used for behavior-level control due to the corresponding requirements for ultralow latency (10 ms) and ultrahigh reliability (99.9999% in wireless transmission), especially when unexpected computing jobs arise. Therefore, this paper proposes a dynamic resource prediction scheduling (DRPS) method based on CI to achieve real-time localized behavior-level control. The proposed DRPS method primarily focuses on the schedulability of unexpected computing jobs, and its core ideas are (1) to predict job arrival times based on a backpropagation neural network and (2) to perform real-time migration in the form of human-computer interaction based on the results of resource analysis. An experimental comparison with existing schemes shows that our DRPS method improves the acceptance ratio by 25.9% compared to the earliest deadline first scheme.

Two-machine job-shop scheduling with one joint job

In this research, we consider a two-machine job-shop scheduling problem with one joint job where a joint job is defined as a job whose operations are to be processed by different machines. The machine repetition and transportation times between machines are also considered. This problem is associated with real-world applications in the fields of production planning and supply chains. We first demonstrate that this problem is NP-hard in the strong sense. We then propose polynomial-time algorithms based on dynamic programming for cases with a fixed number of jobs. We also propose lemmas to reduce the number of states in dynamic programming without loss of optimality, so that the time complexity is improved. Other methodologies, including preprocessing and the two-pointers method, are also embedded to improve the algorithms. The proposed algorithms have better time complexities than those of variants of a well-known algorithm when applied to the cases of our problem.

Two-machine job shop scheduling with optional job rejection

Two-machine job shop scheduling with optional job rejection

A hierarchical integration scheduling method for flexible job shop with green lot splitting

The integration of green scheduling and lot splitting scheduling is indispensable for ensuring the coordinated optimization of economic and environmental benefits in flexible job-shop scheduling (FJS). However, this integration involves not only the indicator of greenness and economy but also the process of production planning and scheduling, which is substantially complicated. To this end, a hierarchical integrated scheduling method is proposed by comprehensively considering the multilevel organizational structure and task configuration characteristics of flexible job-shop, as well as the differences in objectives on different scheduling levels: workshop level, process unit level, machine tool level. On the workshop level, a lot splitting model is presented to obtain the optimal processing task set for each production cycle with the minimum expected cost (startup cost, tardiness cost, and holding cost). On the process unit level, a task allocation model is given to allocate the optimal workload for each machine tool with the minimum processing energy consumption and maximum machine load. On the machine tool level, an operation sequencing model is established to obtain the optimal processing sequence for each machine tool with the minimum standby energy consumption and makespan. According to the solving characteristics of the hierarchical models, a multi-objective algorithm is applied. Finally, a case study is demonstrated to validate the proposed method.

Optimizing job shop scheduling with speed‐adjustable machines and peak power constraints: A mathematical model and heuristic solutions

AbstractThis paper addresses a job shop scheduling problem with peak power constraints, in which jobs can be processed once or multiple times on either all or a subset of the machines. The latter characteristic provides additional flexibility, nowadays present in many manufacturing systems. The problem is complicated by the need to determine both the operation sequence and starting time as well as the speed at which machines process each operation. Due to the adherence to renewable energy production and its intermittent nature, manufacturing companies need to adopt power‐flexible production schedules. The proposed power control strategies, that is, adjusting processing speed and timing to reduce peak power requirements may impact production time (makespan) and energy consumption. Therefore, we propose a bi‐objective approach that minimizes both objectives. A linear programming model is developed to provide a formal statement of the problem, which is solved to optimality for small‐sized instances. We also proposed a multi‐objective biased random key genetic algorithm framework that evolves several populations in parallel. Computational experiments provide decision and policymakers with insights into the implications of imposing or negotiating power consumption limits. Finally, the several trade‐off solutions obtained show that as the power limit is lowered, the makespan increases at an increasing rate and a similar trend is observed in energy consumption but only for very small makespan values. Furthermore, peak power demand reductions of about 25% have a limited impact on the minimum makespan value (4–6% increase), while at the same time allowing for a small reduction in energy consumption.

Multi-objective Quantum Annealing approach for solving flexible job shop scheduling in manufacturing

Flexible Job Shop Scheduling (FJSSP) is a challenging optimization problem with multiple conflicting objectives used to model and compute real-world process scheduling tasks. In order for a manufacturing system to remain competitive, it is necessary to compute such optimization problems quickly and efficiently. The limitations of conventional optimization methods frequently stem from a delicate balance between solution quality and computation time. Consequently, a pressing need for solution algorithms arises that can effectively transcend these limitations. This paper presents a novel Quantum Annealing-based solving algorithm (QASA) for computing FJSSP, leveraging the power of Quantum Annealing combined with classical techniques. The proposed approach aims to optimize a multi-criterial FJSSP considering makespan, total workload, and job priority simultaneously. QASA employs a Hamiltonian formulation with Lagrange parameters to integrate the problem's constraints and objectives. By assigning appropriate weights to the objectives, the method allows the prioritization of certain objectives over others. To handle the computational complexity of large FJSSP instances, the problem is decomposed into smaller subproblems, and a decision logic based on bottleneck factors is employed to select critical jobs for computation combined with variable pruning techniques. To evaluate the effectiveness of the proposed approach, experiments are conducted on benchmark problems, considering makespan, total workload, and priority objectives. Therefore, QASA combining tabu search, simulated annealing, and Quantum Annealing is used for efficient computation and is compared with a classical solving algorithm (CSA) combining tabu search and simulated annealing. The results demonstrate that QASA outperforms CSA in terms of solution quality, as measured by set coverage and hypervolume ratio metrics. Furthermore, computational efficiency analysis reveals that QASA achieves superior Pareto solutions compared to the classical approach, with a reasonable increase in computation time.

A Learning-Based Multipopulation Evolutionary Optimization for Flexible Job Shop Scheduling Problem With Finite Transportation Resources

In many practical manufacturing systems, transportation equipment such as automated guided vehicles is widely adopted to transfer jobs and realize the collaboration of different machines, but is often ignored in current researches. In this paper, we address the flexible job shop scheduling problem with finite transportation resources (FJSP-T). Considering the difficulties caused by the introduction of transportation and the NP-hard nature, the evolutionary algorithm is adopted as a solution approach. To this end, a learning-based multi-population evolutionary optimization (LMEO) is proposed to deal with the FJSP-T. First, the multi-population strategy is introduced and a cooperation-based initialization is designed by combining several heuristics to guarantee the quality and diversity of the initial population. Second, a reinforcement learning-based mating selection is proposed to realize the cooperation of different sub-populations by selecting appropriate individuals for evolutionary search. Then, a specific local search inspired by the problem properties is designed to enhance the exploitation capability of the LMEO. Moreover, a statistical learning-based replacement is designed to maintain the quality and diversity of the population. Extensive experiments are conducted to test the performances of the LMEO. The statistical comparison shows that the LMEO is superior to the state-of-the-art algorithms in solving the FJSP-T in terms of solution quality and robustness.

Surprisingly Popular-Based Adaptive Memetic Algorithm for Energy-Efficient Distributed Flexible Job Shop Scheduling.

With the development of the economy, distributed manufacturing has gradually become the mainstream production mode. This work aims to solve the energy-efficient distributed flexible job shop scheduling problem (EDFJSP) while simultaneously minimizing makespan and energy consumption. Some gaps are stated following: 1) the previous works usually adopt the memetic algorithm (MA) with variable neighborhood search. However, the local search (LS) operators are inefficient due to strong randomness; 2) the confidence-based adaptive operator selection model follows the experiences of the major crowds, which ignores the efficient operators with low weight, so it can not select the really efficient operator; 3) the previous works lack of efficient strategy to save energy; and 4) the mainstream memetic framework adopts LS to all solutions, which causes the population to converge too quickly and the diversity is extremely reduced. Thus, we propose a surprisingly popular-based adaptive MA (SPAMA) to overcome the above deficiencies. The contributions are as follows: 1) four problem-based LS operators are employed to improve the convergence; 2) a surprisingly popular degree (SPD) feedback-based self-modifying operators selection model is proposed to find the efficient operators with low weight and correct crowd decision making; 3) the full active scheduling decoding is presented to reduce the energy consumption; and 4) an elite strategy is designed to balance the resources between global and LS. In order to evaluate the effectiveness of SPAMA, it is compared with state-of-the-art algorithms on Mk and DP benchmarks. The results demonstrate the superiority of SPAMA to the state-of-art algorithms for solving EDFJSP.

Task Relatedness-Based Multitask Genetic Programming for Dynamic Flexible Job Shop Scheduling

Multitasking learning has been successfully used in handling multiple related tasks simultaneously. In reality, there are often many tasks to be solved together, and the relatedness between them is unknown in advance. In this paper, we focus on multitask genetic programming for the dynamic flexible job shop scheduling problems, and address two challenges. The first is how to measure the relatedness between tasks accurately. The second is how to select task pairs to transfer knowledge during the multitask learning process. To measure the relatedness between dynamic flexible job shop scheduling tasks, we propose a new relatedness metric based on the behaviour distributions of the variable-length genetic programming individuals. In addition, for more effective knowledge transfer, we develop an adaptive strategy to choose the most suitable assisted task for the target task based on the relatedness information between tasks. The findings show that in all of the multitask scenarios studied, the proposed algorithm can substantially increase the effectiveness of the learned scheduling heuristics for all the desired tasks. The effectiveness of the proposed algorithm has also been verified by the analyses of task relatedness and structures of the evolved scheduling heuristics, and the discussions of population diversity and knowledge transfer.

A Q-learning-based hyper-heuristic evolutionary algorithm for the distributed flexible job-shop scheduling problem with crane transportation

A Q-learning-based hyper-heuristic evolutionary algorithm for the distributed flexible job-shop scheduling problem with crane transportation

An effective memetic algorithm for distributed flexible job shop scheduling problem considering integrated sequencing flexibility

Thus far, the available works on sequencing flexibility in shop floor scheduling only consider the sequencing flexibility with serial operation constraint. However, the sequencing flexibility with discrete and hybrid operation constraints are also widely existed in the actual production and have significant impact on production efficiency. Therefore, this work proposes a distributed flexible job shop scheduling problem considering integrated sequencing flexibility (DFJSPS), in which the serial, discrete and hybrid operation constraints are considered simultaneously. A mixed integer linear programming model is proposed to solve the DFJSPS by using the CPLEX solver. Then, an efficient memetic algorithm (EMA) is designed with the objectives of minimizing makespan and total energy consumption. In the EMA, a five-layer coding method and an efficient initialization method are presented to obtain high quality initial solutions; and an efficient local search operator is designed to help the algorithm to improve its convergence speed. Comprehensive experiments show that the EMA outperforms other three well-known algorithms in most of the instances, demonstrating the superior performance of EMA for solving DFJSPS in terms of both computational efficiency and solution quality. In summary, the research fills the research gap on integrated sequencing flexibility in the field of shop floor scheduling; on the other hand, it can help production managers to obtain the efficient scheduling schemas in the decision-making systems about various types of sequencing flexibility.

Multi-strategy improved sparrow search algorithm for job shop scheduling problem

Multi-strategy improved sparrow search algorithm for job shop scheduling problem

MIP modeling of energy-conscious FJSP and its extended problems:From simplicity to complexity

Regarding four different energy-conscious scheduling problems, namely, flexible job shop scheduling problem (FJSP), FJSP with transportation time (FJSP-T), FJSP with sequence-dependent setup time (FJSP-SDST), and FJSP with both transportation time and sequence-dependent setup time (FJSP-SDST-T), thirteen mixed integer programming (MIP) models are developed to optimally solve the problems. These models include three nonlinear models and ten linear models, and they are designed from three different modeling ideas, namely, sequence-based modeling idea, adjacent sequence-based modeling idea and machine-position based modeling idea. For each modeling idea, the MIP models are formulated by following the principle: from the simplest FJSP to the most complex FJSP-SDST-T. Regarding nonlinear MIP models, different linearization techniques are used to obtain different linear models. Comparison experiments are conducted from both size and computational complexities to evaluate the models of different modeling ideas for the same problem, the models of the same modeling ideas for the same problem, the models of the same modeling idea for different problems and the models of different modeling ideas for different problems. Experimental results indicate the effectiveness and differences of the proposed MIP models. Specifically, in terms of the average percentage deviation of obtained solution (APE), for FJSP, the machine-position based model with APE being 0.30 outperforms the sequence and adjacent sequence-based models with APE being 0.34 and 3.0 respectively. For FJSP-T, the best sequence-based model with APE being 0.22 outperforms the best machine-position based model with APE being 0.79. For FJSP-SDST, the machine-position based model with APE being 0.06 outperforms adjacent sequence-based model with APE being 1.35.

A deep reinforcement learning based algorithm for a distributed precast concrete production scheduling

The environmental-friendly production demands higher manufacturing efficiency and lower energy cost; therefore, time-of-use electricity price constraint and distributed production have attracted more attention. For concrete precast architecture construction, the tardiness penalty and warehouse cost cannot be ignored, which should be optimized for lower cost. In this study, the concrete precast process is investigated as the group scheduling of a distributed flexible job shop problem. Each concrete precast is managed in a group, the setup time between different groups is considered. Two objectives, total weighted earliness and tardiness and total time-of-use electricity cost are minimized, simultaneously. To solve the integrated problem, three coordinated double deep Q-networks (DQN) are applied, which are organized as a learn-to-improve reinforcement learning approach. For distributed scheduling problem, operators in a single factory or in multiple factories differs in solution improvement; so selection DQN is designed to decide the type of the operators according to scheduling circumstances. Other two DQNs, i.e., local DQN and global DQN, are to select the optimization operators in one factory or in multiple factories, respectively. Furthermore, two solution refinement strategies are designed to decrease the objectives after reinforcement learning component. Numerical experiment and statistical analysis suggest that the proposed deep reinforcement learning based algorithm has superiority in solving the considered problem.

Improved Self-Learning Genetic Algorithm for Solving Flexible Job Shop Scheduling

The flexible job shop scheduling problem (FJSP), one of the core problems in the field of generative manufacturing process planning, has become a hotspot and a challenge in manufacturing production research. In this study, an improved self-learning genetic algorithm is proposed. The single mutation approach of the genetic algorithm was improved, while four mutation operators were designed on the basis of process coding and machine coding; their weights were updated and their selection mutation operators were adjusted according to the performance in the iterative process. Combined with the improved population initialization method and the optimized crossover strategy, the local search capability was enhanced, and the convergence speed was accelerated. The effectiveness and feasibility of the algorithm were verified by testing the benchmark arithmetic examples and numerical experiments.