Flow Shop Scheduling Research Articles

Reentrant hybrid flow shop scheduling with stockers in automated material handling systems using deep reinforcement learning

In smart factories, automated material handling system (AMHSs) replace manual material handling to increase production efficiency, in which stockers serve as the temporary storage for work-in-process inventories. Furthermore, costly machines and complex processes in advanced manufacturing lead to the need for multiple reentrant processes of the same workstation. However, previous works on scheduling problems rarely considered the function of stockers and reentrant processes, and their approaches were mostly based on metaheuristic algorithms. Recent advances in artificial intelligence enable the possibility of solving scheduling problems using deep reinforcement learning (DRL). Therefore, this work investigates the reentrant hybrid flow shop scheduling problem with stockers (RHFS2) inspired by AMHSs, and solves it by DRL. Firstly, the states, actions, and rewards of the Markov decision process for this problem are designed; and then, two deep Q network (DQN) approaches based on the actions for determining machines and jobs, respectively, are proposed. Simulation results demonstrate that our proposed DQN approaches outperform for finding better solutions of different-scale problems than classical metaheuristic algorithms.

Bi-objective carbon-efficient distributed flow-shop scheduling with multistep electricity pricing

A bi-objective distributed flow-shop scheduling problem with multistep electricity pricing and carbon emissions is studied. One objective is to minimise the completion time of production, and the other is to minimise the total cost of multistep electricity pricing and carbon emissions. A mixed integer programming model and a two-stage knowledge based cooperative algorithm with a local reinforcement strategy are proposed for the problem. The extensive numerical experiments show that the two-stage algorithm was effective statistical significantly in generating non-dominated solution sets and Pareto frontiers. Simulations on Electricity Prices are applied to examine different multistep electricity pricing schemes, and management implications were drawn for both government and companies.

Investigation on distributed scheduling with lot-streaming considering setup time based on NSGA-II in a furniture intelligent manufacturing

Distributed flexible flowshop scheduling is getting more important in the large-scale panel furniture industry. It is vital for a higher manufacturing efficiency and economic profit. The distributed scheduling problem with lot-streaming in a flexible flow shop environment is investigated in this work. Furthermore, the actual constraints of packaging collaborative and machine setup times are considered in the proposed approach. The average order waiting time for packaging and average order delay rate is used as objectives. Non-dominated sorting method is used to handle this bi-objective optimization problem. An improved encoding method was proposed to address the large-scale orders that need to be divided into sub-lots based on genetic algorithm. The proposed approach is firstly validated by benchmark with other multi-objectives evolutionary algorithms. The results found that the proposed approach had a good convergence and diversity. Besides, the influence of the proportion of large-scale orders priority level and sub-lot size was investigated in a panel furniture manufacturing scenario. The results can be concluded that the enterprise could obtain shorter order average waiting time and delay rate when the sub-lot sizes were set as two and the order priority level was allocated in the proportion of 1:2:3:4:5.

Heuristic approaches for scheduling of a two-machine flowshop with outsourcing lead-time

This article studies a scheduling problem of a two-machine flowshop , considering outsourcing lead-time, where outsourcing a job incurs outsourcing cost as well as outsourcing lead-time. Each job has an option of being outsourced, i.e. the first operation of the outsourced job is handled by an external subcontractor while the second operation must be processed in-house after its delivery. The objective is to find a schedule for minimizing the weighted sum of the outsourcing costs and the total completion time. For the problem, the subset of jobs to be outsourced and the processing order of jobs are interwoven, implying that decisions have to be made simultaneously. This study examines the properties of the optimal solution and proposes various heuristics based on iterative local search and the biased random-key genetic algorithm. Extensive computational experiments are carried out in various settings.

A regional biogeography-based optimization algorithm for the distributed assembly permutation flow-shop scheduling problem with fuzzy processing time

For solving the distributed assembly flow shop scheduling problem with fuzzy processing time (FDAPFSP), a regional biogeography-based optimization algorithm (RBBO) is proposed to minimize the maximum fuzzy completion time. The mathematical model is provided. In RBBO, all habitats are divided into regions based on the habitat suitability index, and the habitats of each region are subject to cross-regional migration and replacement procedures. A critical factory optimization strategy is developed to enhance local search capability. Taguchi method is used to determine the parameters of RBBO. In ten FDAPFSP instances, comparative testing of RBBO algorithm with various heuristic and swarm intelligence algorithms are conducted. The computation results show that in ten FDAPFSP cases, the proposed RBBO outperforms other algorithms in nine out of ten FDAPFSP cases.

An Adaptive Two-Class Teaching-Learning-Based Optimization for Energy-Efficient Hybrid Flow Shop Scheduling Problems with Additional Resources

Energy-efficient scheduling problems with additional resources are seldom studied in hybrid flow shops. In this study, an energy-efficient hybrid flow shop scheduling problem (EHFSP) with additional resources is studied in which there is asymmetry in the machine. An adaptive two-class teaching-learning-based optimization (ATLBO) which has multiple teachers is proposed to simultaneously minimize the makespan and the total energy consumption. After two classes are formed, a teacher phase is first executed, which consists of teacher self-learning and teacher training. Then, an adaptive learner phase is presented, in which the quality of two classes is used to adaptively decide the learner phase or the reinforcement search of the temporary solution set. An adaptive formation of classes is also given. Extensive experiments were conducted and the computational results show that the new strategies are effective and that ATLBO was able to provide better results than comparative algorithms reported in the literature in at least 54 of 68 instances.

A Q-learning memetic algorithm for energy-efficient heterogeneous distributed assembly permutation flowshop scheduling considering priorities

Most studies on distributed assembly permutation flowshop scheduling do not consider product priorities and factory heterogeneity. This causes delays in critical products and cannot reflect the real-world production situation. This paper focuses on the energy-efficient heterogeneous distributed assembly permutation flowshop scheduling considering priorities (EHDAPFS-P) to minimize total tardiness and total energy consumption simultaneously. Unlike traditional models, factory heterogeneity and product priorities are considered to better reflect the production environment and customer satisfaction in real-world situations. Then, a Q-learning memetic algorithm (QLMA) is proposed to solve this problem: (i) a high-quality initial population is obtained using a hybrid initialization strategy that combines four problem-specific heuristics; (ii) six efficient neighborhood structures are tailored to guide the population to converge to the promising areas; (iii) the most useful neighborhood structure is selected among the six structures using the Q-learning algorithm to accelerate the convergence, thus maximizing the cumulative and future improvements according to the population state; and (iv) an energy-saving strategy is developed to optimize the total energy consumption without deteriorating the total tardiness. The proposed QLMA is compared with seven state-of-the-art algorithms on 261 benchmark instances to demonstrate its superiority or at least competitiveness.

A Knowledge-Guided End-to-End Optimization Framework Based on Reinforcement Learning for Flow Shop Scheduling

Designing an effective and efficient end-to-end optimization framework with good generalization for shop scheduling is an emerging topic in the informational manufacturing system. Existing end-to-end frameworks have achieved satisfactory results for COPs such as traveling salesman problem and vehicle routing problem. However, the performances of these methods in solving complex COPs such as shop scheduling need to be improved. In this paper, a knowledge-guided end-to-end optimization framework based on reinforcement learning is proposed to solve the permutation flow shop scheduling problem (PFSP). Firstly, a new policy network is designed based on the problem characteristics to deal with different scales of PFSPs and achieve iterative end-to-end generation. Secondly, an improved policy-based reinforcement learning algorithm by using the knowledge accumulated during the training process is designed to enhance the training quality. Thirdly, a knowledge-guided improvement strategy is introduced through the cooperation of local search and supervised learning to improve the learning of the policy. Simulation results and comparisons show that the knowledge-guided end-to-end optimization framework can obtain better results than different kinds of commonly-used optimization methods in limited computation time for solving the PFSP.

A Reinforcement-Learning-Based 3-D Estimation of Distribution Algorithm for Fuzzy Distributed Hybrid Flow-Shop Scheduling Considering On-Time-Delivery.

With the increasing level of mass-customization and globalization of competition, environmentally friendly production scheduling for distributed manufacturing considering customer satisfaction has received growing attention. Meanwhile, uncertain scheduling is becoming a force to be considered within intelligent manufacturing industries. However, little research has been found that surveyed the uncertain distributed scheduling considering both energy consumption and customer satisfaction. In this article, the fuzzy distributed hybrid flow-shop scheduling problem considering on-time delivery (FDHFSP-OTD) is addressed, and a 3-D estimation of distribution algorithm (EDA) with reinforcement learning (RL) is proposed to minimize the makespan and total energy consumption while maximizing delivery accuracy. First, two heuristics and a random method are designed and used cooperatively for initialization. Next, an EDA with a 3-D probability matrix is innovated to generate offspring. Then, a biased decoding method based on Q -learning is proposed to adjust the direction of evolution self-adaptively. Moreover, a local intensification strategy is employed for further enhancement of elite solutions. The effect of major parameters is analyzed and the best combination of values is determined through extensive experiments. The numerical results prove the effectiveness of each specially designed strategy and method, and the comparisons with existing algorithms demonstrate the high-potential of the 3D-EDA/RL in solving the FDHFSP-OTD.

A hybridization of evolution strategies with iterated greedy algorithm for no-wait flow shop scheduling problems

This study investigates the no-wait flow shop scheduling problem and proposes a hybrid (HES-IG) algorithm that utilizes makespan as the objective function. To address the complexity of this NP-hard problem, the HES-IG algorithm combines evolution strategies (ES) and iterated greedy (IG) algorithm, as hybridizing algorithms helps different algorithms mitigate their weaknesses and leverage their respective strengths. The ES algorithm begins with a random initial solution and uses an insertion mutation to optimize the solution. Reproduction is carried out using (1 + 5)-ES, generating five offspring from one parent randomly. The selection process employs (µ + λ)-ES, allowing excellent parent solutions to survive multiple generations until a better offspring surpasses them. The IG algorithm’s straightforward search mechanism aids in further improving the solution and avoiding local minima. The destruction operator randomly removes d-jobs, which are then inserted one by one using a construction operator. The local search operator employs a single insertion approach, while the acceptance–rejection criteria are based on a constant temperature. Parameters of both ES and IG algorithms are calibrated using the Multifactor analysis of variance technique. The performance of the HES-IG algorithm is calibrated with other algorithms using the Wilcoxon signed test. The HES-IG algorithm is tested on 21 Nos. Reeves and 30 Nos. Taillard benchmark problems. The HES-IG algorithm has found 15 lower bound values for Reeves benchmark problems. Similarly, the HES-IG algorithm has found 30 lower bound values for the Taillard benchmark problems. Computational results indicate that the HES-IG algorithm outperforms other available techniques in the literature for all problem sizes.

A feedback-based artificial bee colony algorithm for energy-efficient flexible flow shop scheduling problem with batch processing machines

Energy-efficient flexible flow shop scheduling problem (EFFSP) and parallel batch processing machines (BPM) scheduling problem have been extensively studied; however, as the integration of EFFSP and parallel BPM scheduling problem, EFFSP with BPM is seldom investigated even though it often exists in many energy-intensive manufacturing processes such as casting and steelmaking. In this study, EFFSP with BPM at a middle stage in hot & cold casting process is considered, and a feedback-based artificial bee colony (FABC) algorithm is proposed to simultaneously minimize makespan, total tardiness, and total energy consumption. A new cooperation between two employed bee swarms and three search cases are implemented, which are employed bee phase and onlooker bee phase or employed bee phase and cooperation or employed bee phase. Feedback mechanism is established by evolution quality of employed bee swarms and adaptive threshold and used to dynamically determine which search case is executed on each generation. New scout phase and recombination operator are also applied. Extensive experiments are conducted and the computational results demonstrated that new strategies such as cooperation are effective and FABC has promising advantages in the considered EFFSP.

Modeling and Scheduling a Constrained Flowshop in Distributed Manufacturing Environments

This paper addresses a constrained distributed flowshop scheduling problem (CDFSP) that widely exists in modern manufacturing industry but has not been investigated before. Different from the distributed flowshop scheduling problem (DFSP) in the literature, CDFSP considers that all jobs are grouped for processing efficiently, and part of the groups subject to production requirements have a common deadline while the others do not have such a constraint. This constraint not only increases the complexity of the problem but also makes many solutions generated by the existing algorithms infeasible. Therefore, in this paper, a mathematical model is first established for the CDFSP with makespan criterion. After that, we explore the problem-specific knowledge to exclude infeasible solutions, and provide an acceleration method to evaluate feasible solutions in the insertion neighborhood. By automatically selecting parameters to match different search stages, a self-adaptive cooperative iterated greedy algorithm is designed where re-insertion and re-destruction mechanisms are integrated to address the infeasible solutions caused by a paradox and greedy mechanism. A cooperative mechanism is proposed to strengthen the coordination between family scheduling and job scheduling. Finally, the comprehensive experiments verify the effectiveness of the proposed algorithmic components and self-adaptive mechanism, and demonstrate the significant superiority of the proposed algorithm over five state-of-the-art metaheuristics.

A feedback learning-based selection hyper-heuristic for distributed heterogeneous hybrid blocking flow-shop scheduling problem with flexible assembly and setup time

Distributed manufacturing is increasingly common due to economic globalization. It has important practical significance to optimize global supply chains by considering cooperative scheduling of distributed production and flexible assembly. This paper studies a distributed heterogeneous hybrid blocking flow-shop scheduling problem with flexible assembly and setup time (DHHBFSP-FAST). The objective is to minimize makespan of all products. To tackle such problem, a mixed-integer linear programming model (MILP) is presented to formulate it. Then, a feedback learning-based selection hyper-heuristic (FLS-HH) is proposed, which contains high-level control strategies and low-level heuristics. For the high-level control strategies, the transition information between each pair of low-level heuristics is collected, then a feedback learning-based selection method is presented based on such transition information, which can automatically select the appropriate low-level heuristics. For the low-level heuristics, to assign jobs/products to machines, a composite dispatch rule is proposed. To generate an initial domain solution with high quality, a constructive heuristic based on double evaluation indexes is developed. The critical jobs and products are analyzed to avoid invalid searching. Based on such analysis, several low-level heuristics are presented to search the domain solution space, which combine six problem-specific perturbation heuristics and two local searches to balances exploration and exploitation. Comprehensive numerical experiments are carried out. The effectiveness of the proposed MILP and the special designs of FLS-HH are verified. To verify the effectiveness of FLS-HH, we compare it with 10 existing high-performing approaches. The comparison results show that FLS-HH significantly outperforms its competitors in solving DHHBFSP-FAST.

Research on sustainable collaborative scheduling problem of multi-stage mixed flow shop for crankshaft components

The crankshaft manufacturing process primarily comprises machining, single jacket, and double jacket stages. These stages collectively produce substantial carbon emissions, which significantly impact the environment. Low-carbon energy development and humanity's future are closely related. To promote the sustainable development of crankshaft manufacturing enterprises and improve the production efficiency of crankshafts, research on sustainable collaborative scheduling problems in multi-stage mixed flow shop for crankshaft components is conducted. In addition, the transportation process of related workpieces in the crankshaft manufacturing process, which generally have a large mass, also produces substantial carbon emissions. This paper constructs a multi-objective integer optimization model based on the manufacturing process characteristics of crankshaft components, with minimizing the maximum manufacturing time and carbon emissions as optimization objectives. Considering the complexity of the problem, a comprehensive algorithm integrating moth-flame optimization and NSGA-III is used to solve the mathematical model. Through case experiments, the integrated algorithm is compared and analysed with four classic multi-objective optimization algorithms: NSGA-III, NSGA-II, MOEA/D, and MOPSO. The experiments demonstrate that the algorithm presented in this paper offers significantly enhanced optimization efficiency in solving the problem under study compared to other algorithms. Moreover, this paper compares multi-stage collaborative scheduling and non-collaborative scheduling in the crankshaft manufacturing process, ultimately demonstrating that collaborative scheduling is more conducive to the sustainable development of manufacturing enterprises. The results indicate that the annual carbon emissions can reduce about 3.6 ton.

Application of genetic algorithm, GA, to solve a flow shop scheduling problem with changeover times in operations: a case study

Flow Shop Scheduling (FSS) Problems are examples of combinatorial optimization issues that are classified as NP-hard. Because of the NP-hard structure of FSS problems, it can be extremely challenging to find mathematical modeling methodologies that will result in an optimal solution for these problems. The Genetic Algorithm (GA), which is a metaheuristic approach, is one of the most important factors in the process of locating near-optimal answers to NP-hard optimization issues. In this research, a GA model for addressing an FSS problem was developed with the goal of lowering the overall weighted tardiness time and placing a constraint on the operation changeover time. When compared with the performance of the standard heuristics EDD, being used in the company under study, the GA model’s performance was shown to be superior. Based on the findings, it can be shown that the objective value was cut by 43%, going from 215.95 (h) to 123.07 (h). This demonstrates that the GA model is an effective strategy for addressing FSS problems

The Effectiveness of Genetic Algorithm, And the CDS Method In Solving Flowshop Scheduling Problems

Flow shop scheduling problem is considered NP-hard for m machines and n jobs. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we used Genetic Algorithm, and the CDS method for solving flow shop scheduling problem with makespan as the criteria. The objective of this model is to obtain a sequence of jobs and the minimization of the total completion time (makespan). To test the effectiveness of the method, a dataset of case studies is used to compare the makespan values obtained for each method.

Modeling and optimization of the hybrid flow shop scheduling problem with sequence-dependent setup times

The hybrid flow shop scheduling problem (HFSP) is an extension of the classic flow shop scheduling problem and widely exists in real industrial production systems. In real production, sequence-dependent setup times (SDST) are very important and cannot be neglected. Therefore, this study focuses HFSP with SDST (HFSP-SDST) to minimize the makespan. To solve this problem, a mixed-integer linear programming (MILP) model to obtain the optimal solutions for small-scale instances is proposed. Given the NP-hard characteristics of HFSP-SDST, an improved artificial bee colony (IABC) algorithm is developed to efficiently solve large-sized instances. In IABC, permutation encoding is used and a hybrid representation that combines forward decoding and backward decoding methods is designed. To search for the solution space that is not included in the encoding and decoding, a problem-specific local search strategy is developed to enlarge the solution space. Experiments are conducted to evaluate the effectiveness of the MILP model and IABC. The results indicate that the proposed MILP model can find the optimal solutions for small-scale instances. The proposed IABC performs much better than the existing algorithms and improves 61 current best solutions of benchmark instances.

A heuristic approach to minimizing the waiting time of jobs in two-stage flow shop scheduling

The paper presents the influence of the waiting time of jobs in a 2 machine k- job Flow Shop Scheduling (FSS) problem. The main intention of the study is to find a sequence of jobs that delivers the least sum of the time of waiting for jobs. A heuristic approach has been adopted to achieve the desired objective. The experiments are conducted for more than 2000 problems of various sizes for the problems with special structures and problems with random times of processing. The weighted mean absolute error (WMAE) for the average of the sum of the waiting times of jobs is computed for both kind of problems after comparing with the optimal solutions. WMAE has been obtained less than 0.0075 for problems with special structures and less than 0.087 for problems with random times of processing. The WMAE is also reducing significantly with the increase in job size. The results demonstrate that the presented step-by-step procedure of the heuristic delivers significantly close to optimal solutions.

An improved iterated greedy algorithm for distributed mixed no-wait permutation flowshop problems with makespan criterion

The distributed permutation flowshop scheduling is a critical issue in various industries, involving jobs allocation and scheduling among multiple flowshops. This paper extends the research to explore the Distributed Mixed No-Wait Permutation Flowshop Scheduling Problems (DMNWPFSP) with minimizing makespan. The innovation lies in an optimized mathematical model, hybrid heuristic algorithms, an improved iterated greedy algorithm (IIG), and high-quality solutions. Extensive experimental results demonstrate the effectiveness and superiority of the proposed IIG in terms of scheduling quality, computational efficiency, and robustness compared to existing approaches. The outcomes of this work contribute to the field of distributed flowshop scheduling, providing valuable insights for practitioners seeking to enhance production efficiency and competitiveness.

Machine Learning prediction model for Dynamic Scheduling of Hybrid Flow-Shop based on Metaheuristic

Optimizing scheduling and allocation strategies in dynamic production environments, notably in Hybrid Flow-Shops, presents significant challenges. This study focuses on resource assignment within dynamic contexts. It proposes an approach that use Genetic Algorithm (GA) to generate data and train machine Learning (ML) to predict near optimal allocations. Through experiments across various scenarios, the accuracy of prediction of different ML models for resource allocation is evaluated. Our findings highlight the potential of ML techniques to improve decision-making in dynamic and flexible manufacturing systems (FMS), contributing to efforts to enhance reactive scheduling strategies. Future work will assess the impact of these decisions on mean completion time, providing deeper insights into on-line scheduling efficiency.