Industrial Scheduling Problems Research Articles

Solving Flexible Job-Shop Scheduling Problem with Heterogeneous Graph Neural Network Based on Relation and Deep Reinforcement Learning

Driven by the rise of intelligent manufacturing and Industry 4.0, the manufacturing industry faces significant challenges in adapting to flexible and efficient production methods. This study presents an innovative approach to solving the Flexible Job-Shop Scheduling Problem (FJSP) by integrating Heterogeneous Graph Neural Networks based on Relation (HGNNR) with Deep Reinforcement Learning (DRL). The proposed framework models the complex relationships in FJSP using heterogeneous graphs, where operations and machines are represented as nodes, with directed and undirected arcs indicating dependencies and compatibilities. The HGNNR framework comprises four key components: relation-specific subgraph decomposition, data preprocessing, feature extraction through graph convolution, and cross-relation feature fusion using a multi-head attention mechanism. For decision-making, we employ the Proximal Policy Optimization (PPO) algorithm, which iteratively updates policies to maximize cumulative rewards through continuous interaction with the environment. Experimental results on four public benchmark datasets demonstrate that our proposed method outperforms four state-of-the-art DRL-based techniques and three common rule-based heuristic algorithms, achieving superior scheduling efficiency and generalization capabilities. This framework offers a robust and scalable solution for complex industrial scheduling problems, enhancing production efficiency and adaptability.

Industrial multi-resource flexible job shop scheduling with partially necessary resources

This paper is dedicated to the study of industrial extensions of the flexible job shop scheduling problem with multiple resources in order to propose an alternative to expensive optimization software for small to medium-sized manufacturing companies. In this context, we propose a generic model able to tackle some constraints often found in industrial scheduling problems. This model tackles partially necessary resources by decomposing operations into stages. Instances are solved by a simulated annealing metaheuristic which is further improved using efficient conditions to filter non-interesting solutions. We compare our approach to a constraint programming model using a commercial solver. Extensive experiments and statistical analysis show that our method is competitive and of practical use in the industrial context.

Solving the flow-shop scheduling problem with human factors and two competing agents with deep reinforcement learning

With the development of globalized production, customer satisfaction has become a critical concern for companies. Multi-agent models have gained attention, aiming to meet customer demands while reducing costs. The bi-agent flow-shop scheduling problem (BAFSP) in the manufacturing industry is the main focus of this article, where agents represent different customers. The objective of BAFSP is to minimize the total weighted makespan for agents. The BAFSP introduces various position-dependent learning effects. Furthermore, each task has an independent release date, aligned with real production scenarios. A deep reinforcement learning (DRL) approach based on the transformer architecture is proposed to address the BAFSP with learning effects (BAFSP-LE). Experimental results demonstrate that the proposed method outperforms other commonly used heuristics. To explore the feasibility of combining DRL with metaheuristics, the proposed DRL method is used as an initial solution generator. The method improves the performance of these metaheuristics within the same computation time.

A web-based interactive decision support system for a multi-objective lot-sizing and production scheduling model

In the course of globalization and the corresponding steadily growing market dynamics, companies are faced with an increasing challenge to remain competitive. Therefore, the efficient use of the available resources, while maintaining a high level of service and customer satisfaction, is a key instrument for ensuring success. Within this framework, production scheduling can be seen as one of the most decisive operational activities of a manufacturing company, with the production orders being sequenced in a way that allows the achievement of an efficient allocation of the available resources. Furthermore, the correlated lot-sizing represents a crucial influencing factor in production scheduling. In this article, a novel methodology to solve multi-objective lot-sizing and production scheduling problems is proposed. Essentially, it provides an interactive three-phase framework that supports a procedure for simultaneous decision-making regarding lot-sizing and production scheduling. The main goal is not only to find an appropriate production schedule that best meets the decision-maker’s preferences but also to gain a deeper insight into the relationship among criteria and a better understanding of possible trade-offs between competing objectives. To guide the user through the whole decision-making process, a web-based interactive application was developed. The proposed methodology was applied to a case study regarding an automotive supplier company, revealing itself as a viable and practical technique able to solve real-world multi-objective lot-sizing and production scheduling problems in the manufacturing industry.

A novel implicit decision variable classification approach for high-dimensional robust multi-objective optimization in order scheduling

This paper efficiently addresses the high-dimensional robust order scheduling problem. A novel algorithm named dynamic cooperative coevolution based on an implicit decision variable classification approach (DCC/IDVCA) is developed to search for robust order schedules. To significantly reduce the computational resources required for solving the high-dimensional robust order scheduling problem, we propose decomposing the original decision variables through implicit classification methods. First, a novel estimation method is introduced to evaluate the weighted contribution of variables to robustness. This method utilizes historical information, including the variation of the overall mean effective fitness and the frequency of variables being classified into highly robustness-related subcomponents in previous cycles, for evaluating their weighted contribution to robustness. Then, based on the corresponding weighted robustness contributions, the original variables are classified into highly and weakly robustness-related variables. Finally, these two types of variables are decomposed into highly and weakly robustness-related subgroups within a dynamic cooperative coevolution framework and optimized separately. In the experimental section, the proposed algorithm is applied to two practical order scheduling problems in discrete manufacturing industry. The experimental results demonstrate that the proposed algorithm achieves competitive outcomes compared to state-of-the-art high-dimensional robust multi-objective optimization algorithms.

Long-sighted dispatching rules for manufacturing scheduling problem in Industry 4.0 hybrid approach

The introduction of Cyber–Physical Systems, the implementation of machine learning, and the proposal of other technologies are some of the main features of Industry 4.0, which aims to change the way of production by introducing more flexibility and more autonomous decision-making by machines. The presence of centralized and decentralized systems and the continuous change in the market scenario has led to a transition of production systems from highly centralized or decentralized processes to a hybrid architecture that incorporated advantages of the production control approaches. The analysis of the production performances of recent semi-heterarchical architectures encourage to assess these architectures by introducing new scheduling approach that overcome the risk to take a myopic perspective: the long-sighted approach. To this aim, two new dispatching rules are proposed, both evaluated with different variability. This is significant because it allows the measurement of the performance of the production system, as well as the definition of the reactive and proactive capacity of semi-heterarchical architectures in an increasingly competitive market.

Mathematical scheduling model of complex industrial process combining swarm intelligence algorithm and swarm dimension reduction technology

The swarm intelligence algorithm is widely used in scheduling problems due to its superior searchability and adaptability, but it faces high computational costs and low efficiency when dealing with high-dimensional complex data. To enhance the handling of large-scale and intricate data, as well as enhance the accuracy and efficiency of scheduling, this study develops a mathematical model for industrial scheduling. The model is based on swarm intelligence algorithms such as symbiotic evolution algorithms, grey wolf algorithms, cuckoo algorithms, population dimensionality reduction techniques, and resource optimal allocation calculation methods. The final test results showed that the accuracy of the model in calculating the objective function was about 80 % in cases of high complexity and about 90 % in cases of low complexity. Compared with other algorithms, its accuracy was improved by 7 %, error rate was reduced by 50 %, time cost was reduced by about 30 %, and conversion rate was fast and more stable on average after 200 generations. The experimental results indicate that the proposed mathematical scheduling model, which integrates multiple intelligent algorithms and population dimensionality reduction technologies, has certain practices and feasibility in large-scale and multi-dimensional production for enterprises. This study combines swarm intelligence algorithms with population dimensionality reduction techniques, which is an innovative attempt at complex industrial scheduling problems.

Innovative Optimization Algorithms for Large-Sized Industrial Scheduling Problems

Innovative Optimization Algorithms for Large-Sized Industrial Scheduling Problems

A Reinforcement Learning Driven Artificial Bee Colony Algorithm for Distributed Heterogeneous No-Wait Flowshop Scheduling Problem With Sequence-Dependent Setup Times

The distributed heterogeneous factory system is a typical scenario in the manufacturing industry. A distributed heterogeneous no-wait flowshop scheduling problem with sequence-dependent setup times (DHNWFSP-SDST) is studied in this paper. The differences in factory configuration and transportation time are considered in DHNWFSP-SDST. A mixed-integer linear programming (MILP) model is constructed and an artificial bee colony algorithm (ABC) with Q-learning (QABC) is proposed to address the DHNWFSP-SDST. Heuristic methods named NEH_H and DHHS are designed to construct potential initial candidates for the population. The neighborhood structures based on the job blocks are introduced in QABC to explore the solution space during the evolution processes. The Q-learning mechanism is employed to select neighborhood structures via empirical knowledge in the operation processes. The speed-up methods to accelerate the evaluation of the obtained neighborhood are designed to reduce the computation time of the QABC. The experimental results show that the QABC is a potential algorithm to address the DHNWFSP-SDST. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Distributed manufacturing under the heterogeneous environment generally exists in real manufacturing systems. The scheduling problem refers to the reasonable arrangement of production orders to optimize certain indicators under limited time, resources, and computing costs. Distributed heterogeneous no-wait flowshop scheduling problem with setup times is an important industrial scheduling problem in distributed heterogeneous manufacturing systems. The problem takes into account the differences in factory configuration and transportation time in distributed regions. The problem is a kind of NP-hard problem as the solution space is huge. A reinforcement learning driven artificial bee colony algorithm is designed to address the problem. Heuristic methods are utilized to construct potential initial solutions. Neighborhood structures are designed to further optimize the initial solution. The effective empirical guidance is provided by Q-learning for the selection of the neighborhood structure of the algorithm to avoid invalid search. The experimental results show that the QABC obtains a high-quality scheduling scheme in a reasonable time.

Food Production Scheduling: A Thorough Comparative Study between Optimization and Rule-Based Approaches

This work addresses the lot-sizing and production scheduling problem of multi-stage multi-product food industrial facilities. More specifically, the production scheduling problem of the semi-continuous yogurt production process, for two large-scale Greek dairy industries, is considered. Production scheduling decisions are made using two approaches: (i) an optimization approach and (ii) a rule-based approach, which are followed by a comparative study. An MILP model is applied for the optimization of short-term production scheduling of the two industries. Then, the same problems are solved using the commercial scheduling tool ScheduleProTM, which derives scheduling decisions using simulation-based techniques and empirical rules. It is concluded that both methods, despite having their advantages and disadvantages, are suitable for addressing complex food industrial scheduling problems. The optimization-based approach leads to better results in terms of operating cost reduction. On the other hand, the complexity of the problem and the experience of production engineers and plant operators can significantly impact the quality of the obtained solutions for the rule-based approach.

Scheduling and batching with evolutionary algorithms in simulation–optimization of an industrial formulation plant

Industrial scheduling problems are usually characterized by a high complexity and in many, if not all cases, a detailed representation of many specific features of the production process and of the constraints is necessary to ensure that the resulting schedules are feasible when they are executed. Such detailed representations are provided by commercial discrete-event simulation programs which are often employed in the planning phase to detect bottlenecks and to validate design decisions, but usually do not provide optimized schedules. In this paper, we combine a tailored Evolutionary Algorithm with a high-fidelity simulation model in a Simulation–Optimization approach in order to obtain optimized executable production schedules.The industrial production process considered here is a formulation plant that consists of a formulation stage and a filling stage with optional intermediate storage in a set of buffer tanks. The operational constraints include limited operator availability and shift constraints, sequence-dependent changeover times in both stages, product- and line-dependent processing rates, and the need for synchronization of operations. The objective is to minimize the tardiness of a set of orders some of which have long operation times and small slack between the earliest possible end times and the due dates.The orders consist of a certain number of batches, but if all the batches of an order are processed on the same equipment, meeting the due dates is not possible. Therefore the orders have to be decomposed into sub-orders (production orders) to realize parallel processing of urgent orders on several units with the goal to meet due dates. The decision to distribute the total demand of the individual customer orders to production orders is also called batching decision in the literature.A distinctive feature of our approach is that three independent encodings of the batching, allocation and sequencing decisions are used. The batching decisions lead to variable-length chromosomes for the allocation and sequencing encodings. For the treatment of variable-length chromosomes, new crossover and mutation operators, as well as repair algorithms are presented.The results for three test cases show that the introduction of the batching decisions significantly improves the tardiness of the production schedules. A thorough tuning of the categorical parameters of the Evolutionary Algorithm has been performed and it is shown that the resulting parameter setting yields reproducible results, while outperforming simpler approaches.

Hybrid Monte Carlo tree search based multi-objective scheduling

As markets demand targeted products for highly differentiated use cases, the number of variants in production increases, whilst the volume per variant decreases. Different product variants result in differences in work content on workstation level which cause takt time losses and result in a poor utilization. In this context, matrix-structured production systems with neither temporal nor spacial linkage emerged to reduce the effects of different work content on the entire production system. However, matrix-structured production systems require far more complex production control. To that end, this paper presents a scheduling approach. The proposed scheduling system considers variable process sequences and their allocation to different workstations in order to optimize scheduling objectives. This contribution presents a Monte Carlo tree search based optimizer combined with local search as post optimizer to derive schedules in a short time span to enabling reactive scheduling. The application of the scheduler to a benchmark problem and an industrial scheduling problem demonstrates the quality of the results and illustrates how the scheduler reassigns the work content dynamically.

Synergetic energy-conscious scheduling optimization of part feeding systems via a novel chaotic reference-guided policy

PurposeThis paper aims to investigate a multi-objective electric vehicle’s (EV’s) synergetic scheduling problem in the automotive industry, where a synergetic delivery mechanism to coordinate multiple EVs is proposed to fulfill part feeding tasks.Design/methodology/approachA chaotic reference-guided multi-objective evolutionary algorithm based on self-adaptive local search (CRMSL) is constructed to deal with the problem. The proposed CRMSL benefits from the combination of reference vectors guided evolutionary algorithm (RVEA) and chaotic search. A novel directional rank sorting procedure and a self-adaptive energy-efficient local search strategy are then incorporated into the framework of the CRMSL to obtain satisfactory computational performance.FindingsThe involvement of the chaotic search and self-adaptive energy-efficient local search strategy contributes to obtaining a stronger global and local search capability. The computational results demonstrate that the CRMSL achieves better performance than the other two well-known benchmark algorithms in terms of four performance metrics, which is inspiring for future researches on energy-efficient co-scheduling topics in manufacturing industries.Originality/valueThis research fully considers the cooperation and coordination of handling devices to reduce energy consumption, and an improved multi-objective evolutionary algorithm is creatively applied to solve the proposed engineering problem.

A MILP approach for detailed pipeline scheduling and storage management problem in the phosphate industry

Short-term detailed multiproduct pipeline scheduling is a complex problem with many industry-specific constraints. We are interested in solving an operational scheduling problem of a straight pipeline in the phosphate industry. In this article, we propose a mixed-integer linear programming model (MILP) with a discrete-time formulation to provide a detailed scheduling solution for a storage-sensitive problem. The objective is to determine the charging and discharging schedule of the slurry pipeline, to satisfy products demand while respecting all pipeline and storage constraints. The model was tested on different instances, proving to be able to minimize products sold-outs and the total water quantity scheduled.

An advanced model for solving industrial scheduling problems

This paper summarizes an advanced model and a practiceoriented approach to solve scheduling problems of discrete manufacturing systems. An advanced scheduling approach is presented which is able to adapt to the requirements of real-life situations by taking into consideration the specific characteristics of modern manufacturing and assembly systems. These detailed constraints and capabilities of the actual resource environment include the alternative technological routes, the limited available machines, the unrelated processing time, the sequence dependent setup time and the jobs with due dates. An extended flexible job shop scheduling model is defined to solve the resource allocation problems and to create the fine schedule of the execution of jobs, tasks and operations. The paper describes the most important characteristics of the analyzed problem class and shows the main approach of the developed heuristic solving method. Our approach combines a special searching technique based on fast execution-driven simulation with a multi-objective optimization model.

Hybrid Approach for Solving Multi-Objective Hybrid Flow Shop Scheduling Problems with Family Setup Times

Solving industrial scheduling problems remains challenging despite the heavy research efforts in the last decade due to the introduction of new technologies in the context of industry 4.0. Such problems must be solved with light execution time to support near-real-time decision-making processes. In addition, the majority of real industrial Hybrid Flow Shop (HFS) scheduling problems must be solved to minimize multi-objective values that are conflicting in nature. Such problems are proven to be NP-hard. Therefore, in this paper, a hybrid multi-objective approach is presented for solving HFS scheduling problems. The hybrid technique is based on the Non-Dominated Sorting Genetic Algorithms three (NSGA III). The design of the hybrid approach is based on the use of multi-populations that are used to control different allocation-, sequencing-algorithms, and decision points over time. The problems are solved to minimize the makespan, the total number of family major setup times, the total tardiness, and the total number of penalties. The computational results show that the presented approach marginally outperforms other techniques that are published in the related literature for solving two-stage and four-stage HFS scheduling problems. Both problems are derived from real use-cases with real problem instances.

A branch and bound algorithm for a parallel machine scheduling problem in green manufacturing industry considering time cost and power consumption

The concept that green manufacturing can create social value has emerged around the world to reduce the amount of carbon emissions and preserve the ecological environment. Among the optimization problems faced by manufacturing firms, the parallel machine scheduling problem (PMSP) plays an important role both in theory and practice and has been intensively studied in recent decades. The traditional PMSP mainly focuses on time efficiency, such as makespan minimization. However, in response to global warming and other negative environmental impacts, it is important to pay attention to green manufacturing while considering the trade-off between social value (e.g. energy savings) and time costs. This paper considers the PMSP in green manufacturing considering the time cost and social value. In our model, the energy cost is related to the working speed of the machines. To efficiently solve this model, some properties are provided and proven and are also incorporated into the proposed branch and bound (BB) algorithm to limit the number of nodes in the BB tree. The algorithm is tested using a set of computational experiments involving with data obtained from an auto parts manufacturing company.

Application of genetic algorithm to industrial scheduling and problems of parameters evaluation

Genetic algorithms are widely used in various mathematical and real world problems. They are approximate metaheuristic algorithms, commonly used for solving NP-hard problems in combinatorial optimisation. Industrial scheduling is one of the classical NP-hard problems. We analyze three classical industrial scheduling problems: job-shop, flow-shop and open-shop. Canonical genetic algorithm is applied for those problems varying its parameters. We analyze some aspects of parameters such as selecting optimal parameters of algorithm, influence on algorithm performance. Finally, three strategies of algorithm – combination of parameters and new conceptualmodel of genetic algorithm are proposed.

Constraint Logic Programming for Real-World Test Laboratory Scheduling

The Test Laboratory Scheduling Problem (TLSP) and its subproblem TLSP-S are real-world industrial scheduling problems that are extensions of the Resource-Constrained Project Scheduling Problem (RCPSP). Besides several additional constraints, TLSP includes a grouping phase where the jobs to be scheduled have to be assembled from smaller tasks and derive their properties from this grouping. For TLSP-S such a grouping is already part of the input. In this work, we show how TLSP-S can be solved by Answer-set Programming extended with ideas from other constraint solving paradigms. We propose a novel and efficient encoding and apply an answer-set solver for constraint logic programs called clingcon. Additionally, we utilize our encoding in a Very Large Neighborhood Search framework and compare our methods with the state of the art approaches. Our approach provides new upper bounds and optimality proofs for several existing benchmark instances in the literature.

Iterated Greedy Algorithms for Flow-Shop Scheduling Problems: A Tutorial

An iterated greedy algorithm (IGA) is a simple and powerful heuristic algorithm. It is widely used to solve flow-shop scheduling problems (FSPs), an important branch of production scheduling problems. IGA was first developed to solve an FSP in 2007. Since then, various FSPs have been tackled by using IGA-based methods, including basic IGA, its variants, and hybrid algorithms with IGA integrated. Up until now, over 100 articles related to this field have been published. However, to the best of our knowledge, there is no existing tutorial or review paper of IGA. Thus, we focus on FSPs and provide a tutorial and comprehensive literature review of IGA-based methods. First, we introduce a framework of basic IGA and give an example to clearly show its procedure. To help researchers and engineers learn and apply IGA to their FSPs, we provide an open platform to collect and share related materials. Then, we make classifications of the solved FSPs according to their scheduling scenarios, objective functions, and constraints. Next, we classify and introduce the specific methods and strategies used in each phase of IGA for FSPs. Besides, we summarize IGA variants and hybrid algorithms with IGA integrated, respectively. Finally, we discuss the current IGA-based methods and already-solved FSP instances, as well as some important future research directions according to their deficiency and open issues. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many practical scheduling problems can be transformed into flow-shop scheduling problems (FSPs), most of which are NP-hard. In order to solve them in an industrial system setting, designing effective heuristics is important and practically useful and has, thus, attracted much attention from both researchers and engineers. As an easy and high-performance heuristic, an iterated greedy algorithm (IGA) is widely used and adapted to solve numerous FSPs. Its simple framework makes it easy to be implemented by practitioners, and its high performance implies its great potential to solve industrial scheduling problems. In this work, we aim to give practitioners a comprehensive overview of IGA and help them apply IGA to solve their particular industrial scheduling problems. We review the papers that solve FSPs with IGA-based methods, including basic IGA, its variants, and hybrid algorithms with IGA integrated. First, we provide practitioners with a tutorial on IGA, where an example for solving an FSP is introduced and an open platform is constructed. The platform collects and shares the related materials, e.g., open-source code, benchmarks, and website links of important papers. Then, we introduce various FSPs and specific designs of IGA-based methods. Finally, we discuss the current research and point out future research issues.