Job Shop Scheduling Research Articles

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.

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.

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.

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.

Joint multi-objective dynamic scheduling of machine tools and vehicles in a workshop based on digital twin

Dynamic job-shop scheduling is vital for improving job-shop efficiency and reducing energy consumption. A workshop is a complex combination of multiple functions. Previous studies regarding workshop scheduling showed several problems, such as delayed rescheduling response, single influencing factors, and the separation of machine tools and vehicles. Therefore, to address these issues, this paper constructs a multi-factor scheduling service system with various factors, such as machine failure, tool wear, and product quality. Combined with the international background of rising energy prices, the scheduling scheme is evaluated while having two goals to achieve: minimizing the completion time and achieving energy consumption flexibly by controlling the different parameters’ values. Introducing digital twin theory, machine fault prediction, tool wear prediction, and product quality monitoring can achieve the timeliness and predictability of the workshop scheduling, the joint scheduling of machine tools, and the vehicle transport tasks. Finally, the superiority of this method is verified by processing some critical parts in a marine diesel engine workshop.

A decomposition-based memetic algorithm to solve the biobjective green flexible job shop scheduling problem with interval type-2 fuzzy processing time

With increasing environmental awareness, energy consumption of industries is becoming a popular research topic. In industrial manufacturing, processing time is highly uncertain. This study investigates a green flexible job shop scheduling problem with interval type-2 fuzzy processing time (IT2GFJSP) with the objectives of makespan and energy consumption. To solve this problem, a decomposition-based memetic algorithm (DBMA) is used. In the proposed approach, (1) five initial rules are presented to generate a high-quality population; (2) crossover and mutation operators are designed to increase the exploration capability; (3) three effective neighborhood structures are designed to increase the exploitation capability; and (4) a new Tchebycheff aggregation method based on a subproblem decomposition-based (SDB) strategy is proposed to select high-quality individuals and design acceptance criterion. The improved performance of this method is demonstrated by comparison with two other effective methods. To verify the effectiveness of DBMA, it is compared with five other famous algorithms on 30 benchmarks. Computational results show that the DBMA can obtain better solutions than other algorithms when solving the IT2GFJSP.

Correction to: Smart scheduling of dynamic job shop based on discrete event simulation and deep reinforcement learning

Correction to: Smart scheduling of dynamic job shop based on discrete event simulation and deep reinforcement learning

The robust cyclic job shop problem

This paper deals with the cyclic job shop problem where the task durations are uncertain and belong to a polyhedral uncertainty set. We formulate the cyclic job shop problem as a two-stage robust optimization model. The cycle time and the execution order of tasks executed on the same machines correspond to the here-and-now decisions and have to be decided before the realization of the uncertainty. The starting times of tasks corresponding to the wait-and-see decisions are delayed and can be adjusted after the uncertain parameters are known. In the last decades, different solution approaches have been developed for two-stage robust optimization problems. Among them, the use of affine policies, row and row-and-column generation algorithms are the most common. In this paper, we propose a branch-and-bound algorithm to tackle the robust cyclic job shop problem with cycle time minimization. The algorithm uses, at each node of the search tree, a robust version of the Howard’s algorithm to derive a lower bound on the optimal cycle time. Moreover, we design a row generation algorithm and a column-and-row generation algorithm and compare it to the branch-and-bound method. Finally, encouraging preliminary results on numerical experiments performed on randomly generated instances are presented.

Knowledge-Based Reinforcement Learning and Estimation of Distribution Algorithm for Flexible Job Shop Scheduling Problem

In this study, a flexible job shop scheduling problem with time-of-use electricity price constraint is considered. The problem includes machine processing speed, setup time, idle time, and the transportation time between machines. Both maximum completion time and total electricity price are optimized simultaneously. A hybrid multi-objective optimization algorithm of estimation of distribution algorithm and deep Q-network is proposed to solve this. The processing sequence, machine assignment, and processing speed assignment are all described using a three-dimensional solution representation. Two knowledge-based initialization strategies are designed for better performance. In the estimation of distribution algorithm component, three probability matrices corresponding to solution representation are provided. In the deep Q-network component, 34 state features are selected to describe the scheduling situation, while nine knowledge-based actions are defined to refine the scheduling solution, and the reward based on the two objectives is designed. As the knowledge for initialization and optimization strategies, five properties of the considered problem are proposed. The proposed mixed integer linear programming model of the problem is validated by exact solver CPLEX. The results of the numerical testing on wide-range scale instances show that the proposed hybrid algorithm is efficient and effective at solving the integrated flexible job shop scheduling problem.

A Pareto-based two-stage evolutionary algorithm for flexible job shop scheduling problem with worker cooperation flexibility

The previous studies on the flexible job shop scheduling problems (FJSP) with machine flexibility and worker flexibility normally assume that each machine is operated by one worker at any time. However, it is not accurate in many cases because many workers may be required for machines in processing complex operations. Hence, this paper studies a universal version, i.e., FJSP with worker cooperation flexibility (FJSPWC), which defines that each machine can be used only if their required workers are prepared. A mixed-integer linear programming model tuned by CPLEX is established for the problem aiming to collaboratively minimize the makespan, maximum workload of machines and maximum workload of workers. To solve the problem efficiently, a Pareto-based two-stage evolutionary algorithm (PTEA) is proposed. In the PTEA, a well-tailored initialization operator and the NSGA-II structure are designed for global exploration in the first stage, and a competitive objective-based local search operator is developed to improve its local search ability and accelerate the convergence in the second stage. Extensive experiments based on fifty-eight newly formulated benchmarks are carried out to validate the effectiveness of the well-designed initialization operator and two-stage architecture. Comprehensive experiments are performed to evaluate the proposed PTEA, and the results reveal that the PTEA is superior to four comparison algorithms concerning the distribution, convergence, and overall performance.

Fuzzy Target Job Shop Scheduling Based on Improved Multi-population Genetic Algorithm with Clustering

Owing to the traditional genetic algorithm is difficult to hit the optimal solution in the optimization problem of fuzzy target shop scheduling, this paper converts the weighting of the two goals of processing completion time and customer satisfaction into a single objective task, and adds fuzzy completion time constraints on the basis of traditional shop scheduling constraints A fuzzy objective shop scheduling model is constructed, some genetic operators using different strategies are designed and a multi-population genetic algorithm based on clustering is proposed according to the similarity of populations The algorithm first generates multiple initial populations by extending the integer encoding of the processing order and processing machines, and each population undergoes independent genetic operations and then forms importation, integration, and artistic selection to share the excellent genes of individuals The algorithm is verified through experimental simulations that it has strong stability and global search capability: The probability of finding the global optimal solution has increased to 61%.

A teaching-learning-based optimization with feedback for L-R fuzzy flexible assembly job shop scheduling problem with batch splitting

A teaching-learning-based optimization with feedback for L-R fuzzy flexible assembly job shop scheduling problem with batch splitting

Dynamic distributed flexible job-shop scheduling problem considering operation inspection

Dynamic distributed flexible job-shop scheduling problem considering operation inspection

An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents

In this work, we present a method that applies Deep Reinforcement Learning, an approximate dynamic programming procedure using deep neural networks, to the job shop scheduling problem (JSSP). The aim is to show that a greedy-like heuristic trained on a subset of problems, can effectively generalize to some extent to unseen instances, and be competitive compared to other methods. We model the JSSP as a Markov Decision Process and we exploit the efficacy of reinforcement learning to solve the problem. We adopt an actor-critic scheme based on policy gradients, specifically the Proximal Policy Gradient method, where the action taken by the agent is influenced by policy considerations on the state-value function. The procedures take into account the challenging nature of JSSP, where the state and the action space change for every instance and after each decision. To tackle this variability, we introduced a novel model based on two incident Long-Short Term Memory networks, followed by an encoding model, different in structure for both the actor and the critic. Experiments show the algorithm reaches good solutions in a short time, proving that is possible to generate new greedy heuristics just from learning-based methodologies. We compared our algorithms against several established heuristics, an adaptive method, a commercial solver based on branch and cut, and another approach based on Deep Reinforcement Learning, proving the validity of the proposed method in terms of time and makespan. The model can generalize, to some extent, to larger problems originating from a different distribution.

Dynamic scheduling of multi-memory process flexible job shop problem based on digital twin

Digital twin is one of the newly-emerged enabling technologies for achieving intelligent manufacturing. Based on the physical–digital convergence, digital twin provides manufacturing systems with a new model of collaboration between the workforce and industrial processes. With the characteristics of real-time communication and data-driven enablers, the digital twin scheduling strategy requires close cooperation between workers, systems and processes. However, in the process of digitization and intelligentization, industry will need to face the challenge of supporting new technologies and worker skills development. To this end, the paper considers workers’ multi-memory process (learning and forgetting) in the flexible job shop scheduling problem (MPFJSP). Meanwhile, the dynamic scheduling strategy of the digital twin-driven MPFJSP is proposed under machine breakdowns aiming at simultaneously minimizing the makespan, total carbon emissions, total production cost and product quality stability. A virtual workshop is adopted to simulate and optimize the dynamic scheduling scheme to realize intelligent workshop scheduling. Finally, a computational experiment is carried out to verify the effectiveness and advantages of the proposed intelligent scheduling strategy.

On Optimum Sequencing of Job Shop Scheduling in Manufacturing Shop

Joh shop scheduling problem (JSSP) is an NP Hard problem. The most obvious real-world application of the JSSP is within manufacturing and machining as the parameter description describes. Companies that are able to optimize their machining schedules are able to reduce production time and cost in order to maximize profits. The aim of the problem is to find the optimum schedule for allocating shared resources over time to complete all n jobs within the problem. In this research we employ probability sequencing and make of comparison of job-shop sequencing rule such as first-come, first-served (FCFS) rule, which can be accomplished only by used of digital simulation. The result shown that using probability sequencing, when the machine is free, a job is selected in accordance with a sequencing rule and is allowed to occupy the machine for a time equal to its predetermined processing time. A job is complete when it has been processed through all centers on its route.

Quality-based scheduling for a flexible job shop

Recent developments in food consumption open up new challenges in production control in manufacturing systems with low levels of automation. The demand for fresh and healthy products, in combination with the demand for processed products, requires short throughput times and attribution of exposure to process-specific, time-sensitive negative quality influences on certain products. Therefore, this article presents a framework incorporating quality aspects into production planning and control by developing mixed-integer linear programming for scheduling and integrating it into simulation-based control for sequencing. The article applies this framework to a flexible job shop problem derived from a real-world use case. The resulting schedules are used in a simulation model using different order release schemes and priority rules to test how the scheduling approach could deal with dynamic manufacturing environments. The evaluation shows the satisfying integration of quality issues in a flexible job shop problem by minimizing the deterioration while not compromising on makespan and utilization.

Multi-criteria scheduling of realistic flexible job shop: a novel approach for integrating simulation modelling and multi-criteria decision making

Increased flexibility in job shops leads to more complexity in decision-making for shop floor engineers. Partial Flexible Job Shop Scheduling (PFJSS) is a subset of Job shop problems and has substantial application in the real world. Priority Dispatching Rules (PDRs) are simple and easy to implement for making quick decisions in real-time. The present study proposes a novel method of integrating Multi-Criteria Decision Making (MCDM) methods and the Discrete Event Simulation (DES) Model to define job priorities in large-scale problems involving multiple criteria. DES approach is employed to model the PFJSS to evaluate Makespan, Flow Time, and Tardiness-based measures considering static and dynamic job arrivals. The proposed approach is implemented in a benchmark problem and large-scale PFJSS. The integration of MCDM methods and simulation models offers the flexibility to choose the parameters that need to govern the ranking of jobs. The solution given by the proposed methods is tested with the best-performing Composite Dispatching Rules (CDR), combining several PDR, which are available in the literature. Proposed MCDM approaches perform well for Makespan, Flow Time, and Tardiness-based measures for large-scale real-world problems. The proposed methodology integrated with the DES model is easy to implement in a real-time shop floor environment.

Flexible job-shop scheduling with transportation resources

This paper addresses an extension of the flexible job-shop scheduling problem where transportation resources are explicitly considered when moving jobs from one machine to another. Operations should be assigned to and scheduled on machines and vehicles and the routes of vehicles should be determined. We extend the classical disjunctive graph model to include transportation operations and exploit the graph in an integrated approach to solve the problem. We propose a metaheuristic using a neighborhood function that allows a large set of moves to be explored. As the exact computation of the makespan of every move is time-consuming, we present a move evaluation procedure that runs in constant time (which does not depend on the size of the instance) to choose a promising move in the neighborhood of a solution. This move evaluation procedure is used in a tabu search framework. Computational results show the efficiency of the proposed approach, the quality of the move evaluation procedure and the relevance of explicitly modeling transportation resources. New benchmark instances are also proposed.