Flexible Flow Shop Scheduling Problem Research Articles

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.

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.

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.

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.

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.

Energy-Efficient Flexible Flow Shop Scheduling With Due Date and Total Flow Time

One of the most significant optimization issues facing a manufacturing company is the flexible flow shop scheduling problem (FFSS). However, FFSS with uncertainty and energy-related elements has received little investigation. Additionally, in order to reduce overall waiting times and earliness/tardiness issues, the topic of flexible flow shop scheduling with shared due dates is researched. Using transmission line loadings and bus voltage magnitude variations, an unique severity function is formulated in this research. Optimize total energy consumption, total agreement index, and make span all at once. Many different meta-heuristics have been presented in the past to find near-optimal answers in an acceptable amount of computation time. To explore the potential for energy saving in shop floor management, a multi-level optimization technique for flexible flow shop scheduling and integrates power models for individual machines with cutting parameters optimisation into energy-efficient scheduling issues is proposed. However, it can be difficult and time-consuming to fine-tune algorithm-specific parameters for solving FFSP.

Effective upper and lower bounds for a two-stage reentrant flexible flow shop scheduling problem

Flow shop scheduling is important in modern industrial manufacturing to improve production efficiency. This paper studies a realistic two-stage reentrant flexible flow shop scheduling problem (TSRFFS) with broad applications in aircraft scheduling, manufacturing, and the medical industry, etc. Given a flow shop with a single machine in Stage 1, a set of parallel machines in Stage 2, and a set of jobs to be processed, the TSRFFS aims to determine the completion time of jobs in Stage 1 and then that in Stage 2, and finally returns to Stage 1, as well as determine the job-to-machine assignment in Stage 2 such that all jobs are served and the total processing time of jobs (makespan) is minimized. The optimal solution properties are investigated, based on which a mixed integer programming mathematical model and a greedy random constructive heuristic for near optimal solutions are proposed. By solving series of a revised parallel machine scheduling problem (Pm||Cmax), a lower bound method is developed. Extensive numerical experiments on 1560 random instances with up to 1000 jobs and 50 realistic airport simulation instances were conducted to demonstrate the effectiveness of the proposed algorithms. The average gap between the proposed upper bound and the best lower bounds is approximately 1.78%, and the average gap between the proposed lower bound and the best upper bounds is 0.91%, which far outperforms state-of-the-art approaches in terms of solution quality and computational time.

Optimising order picking efficiency in a warehouse and distribution centre: A flexible flow shop scheduling approach

The scheduling of order-picking problems is a critical aspect of warehouse and distribution centre operations. The efficient execution of order picking requires determining the sequence in which it is needed to pick items from storage locations, as well as the assignment of employees to different picking tasks. In this paper, we present an approach to optimise the process using the Flexible Flow Shop Scheduling Problem (FFSSP), which encompasses multiple order fulfilment stages performing a set of operations on various machines (groups of employees) assigned to the picking stages (e.g., order creating, product collection, quality control, packing, shipment). The aim of the study was to determine the sequence of operations on the machines to minimise the order completion time while taking into account the available resources. We used IBM'sCP Optimizer. The computational experiments showed, on the one hand, the advantages of solver usage for relatively small instances providing optimal solutions, while on the other hand, it demonstrated its disadvantages as for 11 large instances from 24, optimal solutions were not found. Moreover, in 6 cases from 24 ones, the solution which was found was 94% worse than the optimal one.

A hybrid meta-heuristic for the flexible flow shop scheduling with blocking

This paper investigates a multi-stage flexible flow shop scheduling problem with blocking on batch processing machines. The objective is to minimize the makespan and the total energy consumption of machines, simultaneously. We first describe the problem and formulate its mathematical model. Based on problem characteristics, we design a hybrid meta-heuristic algorithm based on ant colony optimization and genetic algorithms to solve the problem. In order to solve this problem efficiently, the proposed algorithm consists of two components, which are used to construct batch and overall scheduling, respectively. The search strategy based on ant colony optimization algorithm is designed to construct batches to improve the convergence of the algorithm. Based on this, a global scheduling strategy based on genetic algorithm is proposed to intensify the diversity. Finally, extensive simulation experiments are conducted to verify the effectiveness and efficiency of the proposed algorithm.

A multi-neighborhood-based multi-objective memetic algorithm for the energy-efficient distributed flexible flow shop scheduling problem

A multi-neighborhood-based multi-objective memetic algorithm for the energy-efficient distributed flexible flow shop scheduling problem

Modeling a Flexible Flow Shop Scheduling Problem without Unemployment by Considering Sequence-Dependent Preparation Times and Solving it with a Meta-Heuristic Algorithm

In this paper, the scheduling of the flexible flow shop scheduling problem without unemployment is considered by considering the sequence-dependent preparation times with parallel and identical machines in each workstation in order to minimize the maximum completion time that has been done so far. The assumption of the existence of sequence-dependent preparation times has not been observed in the literature on the issue of flexible workflow without unemployment. In this study, a mixed integer programming model for the problem is first developed. Since the problem under study is one of the NP-hard problems and the mathematical model solving software is not able to obtain the optimal solution of relatively large problems at a reasonable time, to provide a meta-heuristic method of genetic algorithm to obtain optimal solutions or close to optimal for the problem. The computational results show the relatively good performance of the genetic algorithm for solving problems in less time than the mathematical programming model.

Production Scheduling Methodology, Taking into Account the Influence of the Selection of Production Resources

The overwhelming majority of methodologies for the flexible flow shop scheduling problem proposed so far have a common feature, which is the assumption of constant time and cost for the execution of individual technological operations (ignoring an optimal selecting combination of individual employees and tools). Even if the existence of the influence of the selection of production resources on the course of operations is signaled in the available works, the research so far has not focused on the measurable effect of such a solution that takes into account this phenomenon in scheduling. The proposed production scheduling methodology, including the influence of employees and tools, turned out to be more effective in terms of minimizing the maximum completion time and the cost of the production process compared to existing solutions. The efficiency of the new proposed scheduling methodology was assessed using examples of four technological processes. The research was carried out on the basis of a dedicated adaptation of the Monte Carlo optimization algorithm in order to determine the actual effect of the new solution. The algorithm itself is not an integral part of the proposed solution, and the universal methodology developed will ensure significant profit for any optimization algorithm correctly implemented.

Bilevel learning for large-scale flexible flow shop scheduling

Many industrial practitioners are facing the challenge of solving large-scale scheduling problems within a limited time. In this paper, we propose a novel bilevel scheduler based on constraint Markov Decision Process to solve large-scale flexible flow shop scheduling problems (FFSP). There are many intelligent algorithms proposed to solve FFSP, but they take quite long time to execute or are even not working for large-scale problems. Our scheduler is able to decide the sequence of a large number of jobs in a limited time with the objective to minimize makespans. The upper level is designed to explore an initial global sequence, whereas the lower level aims to look for partial sequence refinements. In the implementation, Double Deep Q Network (DDQN) is used in the upper level and Graph Pointer Network (GPN) lies within the lower level. The two levels are connected by a sliding-window sampling mechanism. Based on datasets from public benchmarks and real-world industrial scenarios with over 5000 jobs, experiments show that our bilevel scheduler significantly outperforms seven baseline algorithms, including three state-of-the-art heuristics, three deep learning based algorithms, and another bilevel model, in terms of makespans and computational time. In particular, it only takes less than 200 s to get solutions of large-scale problems with up to 5000 jobs and matches the performance of the state-of-the-art heuristics.

Grid-Based Hybrid Genetic Approach to Relaxed Flexible Flow Shop with Sequence-Dependent Setup Times

In this paper, a hybrid genetic algorithm implemented in a grid environment to solve hard instances of the flexible flow shop scheduling problem with sequence-dependent setup times is introduced. The genetic algorithm takes advantage of the distributed computing power on the grid to apply a hybrid local search to each individual in the population and reach a near optimal solution in a reduced number of generations. Ant colony systems and simulated annealing are used to apply a combination of iterative and cooperative local searches, respectively. This algorithm is implemented using a master–slave scheme, where the master process distributes the population on the slave process and coordinates the communication on the computational grid elements. The experimental results point out that the proposed scheme obtains the upper bound in a broad set of test instances. Also, an efficiency analysis of the proposed algorithm indicates its competitive use of the computational resources of the grid.

Application of GATS, a hybrid mega-heuristic model,and DOE, to solve flexible flow shop scheduling problems:a case study

Flexible flow shop scheduling (FFSS) is an NP-hard combinatorial optimization problem. Solving this problem using mathematical modeling approaches is very difficult. Mega-heuristic algorithms, such as the genetic algorithm (GA) and tabu search (TS), are powerful tools for finding near-optimal solutions to problems of this type. This paper develops a GATS model by combining GA and TS for solving FFSS problems. In the model, GA is used as the platform for global search, and TS is used to support GA in local search. This paper also uses the design of experiments (DOE) to optimize the parameters of the GATS model. The performance of the models, GATS and GATS with DOE, is compared with traditional heuristics being used. The result indicates that the models are good approaches for FFSS problems.