Flexible Flow Shop Research Articles

Developing algorithm and dispatching rules for scheduling a realistic flexible flow shop with setups to minimize total weighted tardiness

Developing algorithm and dispatching rules for scheduling a realistic flexible flow shop with setups to minimize total weighted tardiness

Lower and upper bounds for scheduling a real-life assembly problem with precedences and resource constraints

In this work, we consider a real-life scheduling problem involving the production of off-road vehicles using a three-level assembly process, subject to precedence, machines, and resource constraints. This problem shares multiple characteristics with other scheduling problems such as the Parallel Machine Scheduling and Flexible Flow Shop Problems. However, it also comprises less investigated aspects such as a specific job precedence structure resulting in a directed rooted in-tree and a global resource constraint limiting the number of simultaneously active machines. We present a straightforward adaptation of a time-indexed mathematical formulation to the problem and introduce a new lower-bounding procedure. To solve the problem, we propose constructive heuristics based on classical priority rules and adaptations of job sequencing heuristics. We also propose CORE, a specialized approach tailored to leverage the problem structure. All the algorithms are extensively evaluated on two benchmark sets, various shop floor configurations, and eight real-life scenarios. Our results reveal the general effectiveness of job sequencing approaches and demonstrate the overall superiority of CORE.

A constraint programming approach for resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery

Production and distribution are both crucial components of supply chains. Integrated production and distribution scheduling (IPDS) in the context of flexible assembly flow shop scheduling and batch delivery problems is often overlooked. A realistic problem inspired by the production and distribution processes of a dishwasher factory can be modeled as a resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery (RCFAFSP-BDD). In this problem, order requirements are decomposed into several production tasks processed at different stages of the workshop, and are then delivered in batches via a third-party logistics provider to regional distributors at various locations. Auxiliary resource restrictions, hierarchical coupling constraints, machine eligibility restrictions and sequence-dependent setup times, are incorporated into the problem as operational constraints. To the best of our knowledge, this is the first attempt to solve this problem. This work formulates a mixed-integer linear programming (MIP) model to minimize total costs, including tardiness, inventory, and delivery costs. Given the problem’s strong NP-hard nature, the focus is on developing an efficient solution approach using constraint programming (CP). A CP model is proposed and enhanced with multiple redundant constraints. To reduce runtime, two branching strategies are designed for the CP model. Numerical experiments with varying instance scales reveal that the proposed CP model outperforms the MIP model in accuracy and efficiency within the given time limit. The redundant constraints and search strategy can reduce CP model runtime by up to 263.83%. Compared to manual scheduling at the studied factory, the CP model can cut costs by up to 26.59% for real data, offering viable alternatives for factory planners.

An adaptive shuffled frog-leaping algorithm for flexible flow shop scheduling problem with batch processing machines

Batch Processing Machines (BPM) and transportation are seldom studied simultaneously in Flexible Flow Shop. In this study, Flexible Flow Shop Scheduling Problem (FFSP) with BPM at the last stage and transportation is considered and an adaptive shuffled frog-leaping algorithm (ASFLA) is proposed to minimize makespan. To produce high-quality solutions, a heuristic is employed to produce initial solution, two groups are formed by using all memeplexes, then an adaptive memeplex search is implemented, in which the number of searches is dynamically determined by the quality of the memeplex, an adaptive group search is also conducted by exchanging memeplexes or supporting of the worse memeplex. A novel population shuffling and the worst memeplex elimination are proposed. A number of computational experiments are executed to test the new strategies and performances of ASFLA. Computational results demonstrate that new strategies are effective and ASFLA is a very competitive algorithm for FFSP with BPM and transportation.

The dual-resource-constrained re-entrant flexible flow shop a constraint programming approach and a hybrid genetic algorithm

ABSTRACT The dual-resource-constrained re-entrant flexible flow shop scheduling problem represents a specialised variant of the flow shop scheduling problem, inspired by real-world scenarios in screen printing industries. Besides the well-known flow shop structure, stages consist of identical parallel machines and operations may re-enter the same stage multiple times before completion. Moreover, each machine must be operated by a skilled worker, making it a dual-resource-constrained problem according to the existing literature. The objective is to minimise the total length of the production schedule. To address this problem, our study employs two methods: a constraint programming model and a hybrid genetic algorithm with a single-level solution representation and an efficient decoding heuristic. To evaluate the performance of our methods, we conducted a computational study using different problem instances. Our findings demonstrate that the proposed hybrid genetic algorithm consistently delivers high-quality solutions, particularly for large instances, while also maintaining a short computational time. Additionally, our methods improve existing benchmark results for instances from the literature for a subclass of the problem. Furthermore, we provide managerial insights into how dual-resource constraints affect the solution quality and the efficiency associated with different workforce configurations in the described production setting.

A multi-level action coupling reinforcement learning approach for online two-stage flexible assembly flow shop scheduling

Multi-product centralized delivery and kitting assembly present significant challenges to hierarchical co-processing in multi-stage manufacturing systems. The combinations of priority dispatching rules at each level are transiently adaptive, and the performance in online scheduling deteriorates rapidly with changing environment. This paper investigates the selection of rule combinations for sustained high-performance responsive scheduling in two-stage flexible assembly flow shop scheduling problem with asynchronous execution and complex decision correlation. A Multi-Level Action Coupling Deep Q-Network (MALC-DQN) approach is proposed for adaptive integrated scheduling in hybrid processing and assembly shops. Firstly, the problem is skillfully established as an event-triggered integrated decision markov decision process. The prioritized batch experience replay mechanism is employed to retain the complete correlation information of key decision sequences. Then, coupling and sequence feature extraction modules are developed to enhance the agent’s ability to perceive execution process and the environment. Furthermore, the multi-level wait-limit mechanism and efficient action filtering mechanism are designed to mitigate ineffective waiting waste and action space explosion during learning. Finally, a series of sophisticated experiments are conducted to validate the effectiveness of the proposed methodology. In 20 actual instances of different sizes, MLAC-DQN outperformed its closest competitor, with a 26.6% improvement in average tardiness. Moreover, extraordinary robustness is demonstrated in 16 sets of experiments involving different configurations of resources, orders, and arrival concentration levels.

A multiobjective optimizer with a K-means cluster algorithm for a distributed flexible flowshop rescheduling problem

A distributed flexible flowshop problem (DFFSP) has been extensively studied over recent years. It is assumed that all jobs to be processed are exactly known in advance, and machines are able to work continuously. In practice, however, new jobs often arrive suddenly. Machines sometimes break down unexpectedly. These lower the performance of the scheduling generated, even make it infeasible. To address this problem, this paper considers a rescheduling DFFSP (DFFRP) with new job arrivals and machine breakdowns. The objective is to minimize makespan and the robustness metrics at the same time. Firstly, we propose a multi-objective mixed-integer linear programming model and a non-dominated sorting genetic algorithm-II based on K-means clustering algorithm (KNSGA-II). Secondly, the problem-specific knowledge is explored and a speed-up strategy is designed to save the algorithmic computation. Thirdly, an initialization strategy based on K-means clustering algorithm is developed to generate high-quality initial solutions. And a novel crossover and mutation operator is employed to accelerate the convergence of the algorithm. Finally, by comparing with a number of advanced multi-objective algorithms in the literature in comprehensive experiments, the proposed algorithm has been demonstrated to be much more effective for solving the DFFRP under consideration.

A novel fuzzy finite-horizon economic lot and delivery scheduling model with sequence-dependent setups

This paper addresses the economic lot and delivery scheduling problem (ELDSP) within three-echelon supply chains, focusing on the complexities of demand uncertainty, limited shelf-life of products, and sequence-dependency of setups. We develop a novel mixed-integer non-linear programming (MINLP) model for a supply chain comprising one supplier, multiple manufacturers with flexible flow shop (FFS) production systems, and multiple retailers, all operating over a finite planning horizon. The common cycle (CC) strategy is adopted as the synchronization policy. Our model employs fuzzy set theory, particularly the “Me measure,” to effectively handle the retailers’ demand uncertainty. Our findings indicate that total supply chain costs escalate with an increase in demand, final components’ holding costs, and sequence-dependent setup costs, but decrease with increasing production rates. Furthermore, while total costs are significantly sensitive to changes in demand, they are relatively insensitive to fluctuations in sequence-dependent setup times. The models developed offer valuable managerial insights for optimizing costs in synchronized multi-stage supply chains, aiding managers in making informed decisions about production lot sizes and delivery schedules under both deterministic and fuzzy demand scenarios. Additionally, the proposed models bridge key research gaps and provide robust decision-making tools for cost optimization, enhancing supply chain synchronization in practical settings.

Metaheuristics for solving a flexible flow‐shop scheduling problem with s‐batching machines

AbstractA scheduling problem for a two‐stage flexible flow shop with s‐batching machines motivated by processes in additive manufacturing is considered. A batch is a group of jobs that are processed together on a single machine. Each job belongs to an incompatible family. Only jobs of the same family can be batched together. A maximum batch size is given. A setup time occurs between different batches. The jobs of a batch are processed in a serial manner, that is, the processing time of a batch is the sum of the processing times of the jobs forming the batch. Batch availability is assumed. A job has a weight, a due date, and a release date. The total weighted tardiness is considered as performance measure. We establish a mixed integer linear programming formulation for this scheduling problem. For large‐sized problem instances, an iterative decomposition approach (IDA) is proposed that uses a grouping genetic algorithm or an iterated local search (ILS) scheme to solve the single‐stage subproblems. Moreover, an alternative ILS scheme based on a disjunctive graph representation of the problem at hand is designed. Results of computational experiments based on randomly generated problem instances demonstrate that the IDA hybridized with ILS outperforms the two other schemes.

Real-time stochastic flexible flow shop scheduling in a credit factory with model-based reinforcement learning

There has been a significant increase in consumer credit worldwide in recent years. The scheduling of jobs in credit factories is essential for speeding up the loan application process, which can improve the efficiency of credit factories. In this study, we propose a reinforcement learning approach for addressing the scheduling problem in credit factories, which is a stochastic flexible flow shop scheduling problem (SFFSP). First, we propose a mathematical model for the credit factory stochastic flexible flow shop scheduling problem, which abstracts the decision-making process as a semi-Markov process. Then, a reinforcement learning reward mechanism is designed based on the proposed mathematical model. After that, a self-attention neural network is used to extract state information from global and local multidimensional data, enabling each decision to consider the state of the entire process and make a decision that aligns with the global goal. Meanwhile, Monte Carlo Tree Search (MCTS) is utilised to enhance the training effect and sample utilisation of reinforcement learning. Finally, we conduct extensive experiments and demonstrate that our method achieves better performance for SFFSP in credit factories compared to other approaches.

A discrete artificial bee colony algorithm and its application in flexible flow shop scheduling with assembly and machine deterioration effect

In real production, assembly and machine deterioration are extremely common phenomenon and flexible flow shop scheduling problem (FFSP) is also extensively investigated. However, assembly FFSP with machine deterioration effect (AFFSP-DE) is neglected. This paper addresses an AFFSP-DE with makespan criterion and proposes a discrete artificial bee colony (DABC) algorithm. In DABC, the number of employed (onlooker) bees is dynamically changeable according to evolutionary quality to adaptively allocate computing resources for two kinds of bees, and a new scout bee phase is designed to improve convergence speed. Finally, the relationships between makespan and different deterioration rates are analyzed systematically by extensive experiments, and the results demonstrate that DABC outperforms the existing algorithms over 82% test instances in solving the AFFSP-DE.

Scheduling optimization of flexible flow shop with buffer capacity limitation based on an improved discrete particle swarm optimization algorithm

To address the challenge of production scheduling in flexible flow shops with buffer capacity limitations, a mathematical model is established to minimize the maximum completion time and maximize equipment utilization. To efficiently solve the problem, an improved discrete particle swarm optimization algorithm with multi-population reduction (MPREDPSO) is developed. It integrates an elite retention strategy, which significantly contributes to its efficiency and robustness. The algorithm stands out for its ability to effectively navigate through potential local optima, a common pitfall in optimization problems, through a Euclid algorithm coupled with a sophisticated gene backtracking mechanism. The performance of MPREDPSO is rigorously tested and proven through comparative analyses. Its effectiveness is proven through comparisons with other algorithms, namely the discrete particle swarm algorithm, genetic algorithm, whale algorithm, grey wolf optimizer and whale swarm algorithm. In addition, MPREDPSO’s practical utility is demonstrated in a high-temperature ham sausage production workshop, showcasing its industrial application capabilities.

Bi-objective optimization of flexible flow shop scheduling problem with multi-skilled human resources

In this article, a Multi-skilled Resource-Constrained Flexible Flow Shop Scheduling Problem (MSRC-FFSSP) is introduced. To process each job at every machine within this problem category, it is imperative to possess at least one set of multi-skilled human resources. Each human resource can operate a minimum of 1 and a maximum of N jobs depending on their skills and each job requires a minimum set of different skills. For this problem, the model is formulated as a MILP model with two objectives: i) minimizing the total completion time and ii) minimizing the total idle time for human resources. Moreover, a case study in a preventive maintenance environment as a flow shop is performed to establish the applicability of the model in real-world problems. Given that the problem is NP-Hard, a Genetic Algorithm (GA) and a Simulated Annealing (SA) algorithm in which the related parameters are tuned by the Taguchi method are presented. Finally, numerical results have been presented to verify the model, in addition to the analysis of the idle time of human resources. Additionally, to solve this problem, it was shown that the GA has better efficiency and performance compared to the SA algorithm. However, the SA algorithm outperforms the GA in terms of running time.

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.

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.

Energy-Efficient Flexible Flow Shop Scheduling Under Time-Of-Use Rates with Renewable Energy Sources

In response to climate change, industries strive to curtail energy consumption while maintaining production efficiency. Focused on time-dependent electricity prices, this paper addresses the scheduling challenge in a flexible flow shop machine environment. The goal is to minimize both makespan and total electricity costs in a grid-connected manufacturing setup with battery storage, solar power, and a strategic turn on/turn of machine approach. A multi-objective mixed-integer linear programming model is developed, employing the ϵ-constraint method to reveal the trade-of between objectives and present Pareto-front solutions. The ensuing experimental study allows for the validation of the model and identification of its limits.

Multi-Objective Flexible Flow Shop Production Scheduling Problem Based on the Double Deep Q-Network Algorithm

In this paper, motivated by the production process of electronic control modules in the digital electronic detonators industry, we study a multi-objective flexible flow shop scheduling problem. The objective is to find a feasible schedule that minimizes both the makespan and the total tardiness. Considering the constraints imposed by the jobs and the machines throughout the manufacturing process, a mixed integer programming model is formulated. By transforming the scheduling problem into a Markov decision process, the agent state features and the actions are designed based on the processing status of the machines and the jobs, along with heuristic rules. Furthermore, a reward function based on the optimization objectives is designed. Based on the deep reinforcement learning algorithm, the Dueling Double Deep Q-Network (D3QN) algorithm is designed to solve the scheduling problem by incorporating the target network, the dueling network, and the experience replay buffer. The D3QN algorithm is compared with heuristic rules, the genetic algorithm (GA), and the optimal solutions generated by Gurobi. The ablation experiments are designed. The experimental results demonstrate the high performance of the D3QN algorithm with the target network and the dueling network proposed in this paper. The scheduling model and the algorithm proposed in this paper can provide theoretical support to make the production plan of electronic control modules reasonable and improve production efficiency.

Effective Two-Phase Heuristic and Lower Bounds for Multi-Stage Flexible Flow Shop Scheduling Problem with Unloading Times

This paper addresses the flexible flow shop scheduling problem with unloading operations, which commonly occurs in modern manufacturing processes like sand casting. Although only a few related works have been proposed in the literature, the significance of this problem motivates the need for efficient algorithms and the exploration of new properties. One interesting property established is the symmetry of the problem, where scheduling from the first stage to the last or vice versa yields the same optimal solution. This property enhances solution quality. Considering the problem’s theoretical complexity as strongly NP-Hard, approximate solutions are preferable, especially for medium and large-scale instances. To address this, a new two-phase heuristic is proposed, consisting of a constructive phase and an improvement phase. This heuristic builds upon an existing efficient heuristic for the parallel machine-scheduling problem and extends it to incorporate unloading times efficiently. The selection of the two-phase heuristic is justified by its ability to generate high-quality schedules at each stage. Moreover, new efficient lower bounds based on estimating minimum idle time in each stage are presented, utilizing the polynomial parallel machine-scheduling problem with flow time minimization in the previous stage. These lower bounds contribute to assessing the performance of the two-phase heuristic over the relative gap performance measure. Extensive experiments are conducted on benchmark test problems, demonstrating the effectiveness of the proposed algorithms. The results indicate an average computation time of 9.92 s and a mean relative gap of only 2.80% for several jobs up to 200 and several stages up to 10.

Multi-Objective Production and Scheduling Optimization of Offshore Wind Turbine Steel Pipe Piles Based on Improved Hesitant Fuzzy Method

This paper investigates the multi-objective optimization problem in the production of offshore wind turbine steel pipe piles (OWTSPP). Considering the particularity of the steel pipe pile production process, it is divided into a flexible flow shop scheduling (FFSS) stage and an open parallel shop scheduling (OPSS) stage, respectively. Mathematical models are established for each stage, and the critical path and production time information are obtained using a disjunctive graph model. Due to the inability of existing empirical scheduling methods to balance production goals, an improved Pythagorean hesitant fuzzy method (IPHFM) is proposed to solve the multi-objective optimization problem in steel pipe pile production. Specifically, the maximum completion time, machine total load, and total completion time are taken as optimization objectives. The improved Lagrange multiplier method with penalty terms is used to handle the constraints and objective functions, and a Lagrange objective function is generated. Then, the Lagrange objective function matrix is obtained by normalization and same-scale processing, and an algorithm is designed to obtain the Pareto front solution set. Finally, this paper compares the optimal scheduling plans under the empirical scheduling method and the improved method. The results show that the improved method can significantly improve production efficiency in both small-scale and large-scale production, with improvements of 15.7% and 22.16%, respectively.

New formulation for scheduling flexible flow shop problems

New formulation for scheduling flexible flow shop problems