Assembly Flow Shop Scheduling Problem Research Articles

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.

Mathematical models for multi-stage hybrid assembly flow-shop scheduling with preventive maintenance and release times

Effective job scheduling is crucial in production to reduce costs, improve customer satisfaction, enhance efficiency, and boost competitiveness, leading to transformative impacts in production environments. This article presents a pioneering approach that addresses assembly and processing at multiple stages in the scheduling process. Specifically, we introduce the first formulation of mixed integer linear programs (MILP) for a Multi-stage Hybrid Assembly Flow-shop with identical parallel machines. The models incorporate considerations for job release times and service tasks to implement preventive maintenance and effectively captures the intricacies of a Multistage Assembly flow-shop. Existing literature in Assembly flow-shop scheduling primarily focuses on the two-stage assembly flow-shop scheduling problem (TSAFSP) and its extensions, such as the three-stage assembly flow-shop scheduling problem, the Distributed two-stage assembly flow-shop scheduling problem (DTSAFSP), the Distributed assembly permutation flow-shop Scheduling Problem (DAPFSP), and the multi-stage assembly flow shop (MSAF). Our work deals with a challenging NP-hard problem. Inspired by a real-life production site dedicated to manufacturing heavy machinery, we validate our proposed mathematical models by solving various instances of the problem using exact methods. The experimental results confirm the effectiveness and robustness of our approach in tackling multi-stage hybrid assembly flow shop scheduling challenges.

Minimizing fuzzy makespan in a distributed assembly flow shop by using an efficient artificial bee colony algorithm

Assembly flow shop scheduling problem (AFSP) in a single factory has attracted widespread attention over the past decades; however, the distributed AFSP with DPm → 1 layout considering uncertainty is seldom investigated. In this study, a distributed assembly flow shop scheduling problem with fuzzy makespan minimization (FDAFSP) is considered, and an efficient artificial bee colony algorithm (EABC) is proposed. In EABC, an adaptive population division method based on evolutionary quality of subpopulation is presented; a competitive employed bee phase and a novel onlooker bee phase are constructed, in which diversified combinations of global search and multiple neighborhood search are executed; the historical optimization data set and a new scout bee phase are adopted. The proposed EABC is verified on 50 instances from the literature and compared with some state-of-the-art algorithms. Computational results demonstrate that EABC performs better than the comparative algorithms on over 74% instances.

An imperialist competitive algorithm for distributed assembly flowshop scheduling with Pm → 1 layout and transportation

Distributed assembly flow shop scheduling problem (DAFSP) has been extensively considered; however, DAFSP with Pm → 1 layout, in which m parallel machines are at fabrication stage and one machine is at assembly stage, is seldom handled. In this study, DAFSP with the above layout and transportation time is studied and an imperialist competitive algorithm with cooperation and division (CDICA) is presented to minimize makespan. Feature of the problem is used and a heuristic is applied to produce initial solution. Adaptive assimilation and evolution are executed in the weakest empire and adaptive cooperation is implemented between the winning empire and the weakest empire in imperialist competition process. Empire division is performed when a given condition is met. Many experiments are conducted. The computational results demonstrate that new strategies are effective and CDICA is a very competitive in solving the considered DAFSP.

Q-learning driven multi-population memetic algorithm for distributed three-stage assembly hybrid flow shop scheduling with flexible preventive maintenance

The distributed assembly flow shop scheduling (DAFS) problem has received much attention in the last decade, and a variety of metaheuristic algorithms have been developed to achieve the high-quality solution. However, there are still some limitations. On the one hand, these studies usually ignore the machine deterioration, maintenance, transportation as well as the flexibility of flow shops. On the other hand, metaheuristic algorithms are prone to fall into local optimality and are unstable in solving complex combinatorial optimization problems. Therefore, a multi-population memetic algorithm (MPMA) with Q-learning (MPMA-QL) is developed to address a distributed assembly hybrid flow shop scheduling problem with flexible preventive maintenance (DAHFSP-FPM). Specifically, a mixed integer linear programming (MILP) model targeted at the minimal makespan is first established, followed by an effective flexible maintenance strategy to simplify the model. To efficiently solve the model, MPMA is developed and Q-learning is used to achieve an adaptive individual assignment for each subpopulation to improve the performance of MPMA. Finally, two state-of-the-art metaheuristics and their Q-learning-based improvements are selected as rivals of the developed MPMA and MPMA-QL. A series of numerical studies are carried out along with a real-life case of a furniture manufacturing company, to demonstrate that MPMA-QL can provide better solutions on the studied DAHFSP-FPM..

A Q-learning artificial bee colony for distributed assembly flow shop scheduling with factory eligibility, transportation capacity and setup time

Distributed assembly flow shop scheduling problem (DAFSP) has been considered; however, DAFSP with factory eligibility,transportation capacity and setup time is seldom studied even though these three constraints often exist simultaneously in real-life multi-factory assembly production processes. In this study, DAFSP with Pm→1 layout, factory eligibility, transportation capacity and setup time is proposed and a Q-learning artificial bee colony (Q-LABC) is presented to minimize both makespan and total tardiness. A heuristic is designed to produce initial solution. In employed bee phase, factory set based heuristic is developed, population is divided into two parts by non-dominated sorting and two global search operators are applied in two parts respectively. A Q-learning algorithm has a fixed Q-table when a given condition is met, and is used to dynamically decide the way of selecting food source and the number of the selected food source for onlooker bee. Extensive experiments on 90 instances are conducted to show the effectiveness of new strategies and compare Q-LABC with two comparative algorithms. The computational results demonstrate that the new strategies of Q-LABC are effective and Q-LABC performs better than its comparative algorithms on at least 83.33% and 94.44% instances, respectively.

A two-stage assembly flow-shop scheduling problem with bi-level products structure and machines’ availability constraints

ABSTRACT This paper incorporates the preventive maintenance activities into the two-stage assembly flow-shop scheduling problem, which has m machines at the production stage and an assembly machine at the second one. In this paper, three maintenance policies are employed based on the maximization of machine’s reliability and availability. This problem is NP-hard. So, two hybrid optimization methods, namely variable neighborhood search together with simulated annealing algorithm, and variable neighborhood search along with tabu search algorithm, are used to find the proper job sequencing. Statistical methods are conducted based on the hypothetical testing and analysis of variance to determine the better solution method and sensitivity analysis. Also, the performances of the presented algorithms on the problems of different sizes are analyzed. Results have shown that variable neighborhood search with simulated annealing outperforms another algorithm in the quality of solutions and computational time.

An optimal block knowledge driven backtracking search algorithm for distributed assembly No-wait flow shop scheduling problem

The distributed assembly flow shop scheduling problem (DAFSP) is an important scenario in manufacturing system. In this paper, an optimal block knowledge driven backtracking search algorithm (BKBSA) is proposed to solve the distributed assembly No-wait flow shop scheduling problem (DANWFSP) with the objective of minimizing the completion time of assembly process. In BKBSA, three constructive heuristics are proposed to generate a competitive initial solution. Block-shifting based on block knowledge is embedded in the mutation strategy of BKBSA. The proposed block-shifting ensures that the optimal subsequence of a candidate solution is not destroyed in the mutation operation. The similarity between candidate solutions is utilized as feedback indicator to control the utilization of block-shifting. In addition, the VND algorithm based on factory-to-factory is proposed to further improve the optimal solution. Finally, the BKBSA and the other three state-of-the-art algorithms for DANWFSP are tested on 810 large-scale instances and 900 small-scale instances. The statistical analysis results show that BKBSA is an effective algorithm to solve DANWFSP.

Assembly flow shop scheduling problem considering machine eligibility restrictions and auxiliary resource constraints

This paper investigates a two-stage production system consists of a fabrication stage followed by an assembly stage. There are some unrelated parallel machines in the first stage to process the parts and then, the parts are assembled into the final product at an assembly workstation. To close the problem to real-world condition, machine eligibility, sequence-dependent setup times, and different release times are considered for the received parts. In addition, most of the researchers deal with machines as the only resource in conducting the scheduling problems. However, other additional resources such as specialised labours, tools, and industrial robots are usually not only required for processing jobs but also are often restricted to use. First, the problem is described and a new mixed-integer linear programming model is proposed that can solve the problem in small-sized scales. Since this problem is well known as a strong NP-hard problem, a new heuristic algorithm is proposed based on the basic idea of Johnson’s rule. Moreover, two proper lower bounds are introduced as references to evaluate the performance of the proposed heuristic algorithm. Numerical experiments show high quality of the final solutions provided by the proposed algorithm and also indicate effectiveness of two developed lower bounds.

Cooperated teaching-learning-based optimisation for distributed two-stage assembly flow shop scheduling

ABSTRACT Two-stage assembly flow shop scheduling problem with layout has been extensively considered in single factory; however, distributed two-stage assembly flow shop scheduling problem (DTAFSP) with layout in each factory is not studied fully; moreover, teaching-learning-based optimisation is seldom used to solve DTAFSP. In this paper, a cooperated teaching-learning-based optimisation (CTLBO) is proposed to minimise makespan. Multiple classes are constructed. The whole search procedure consists of two stages and each stage possesses two teacher's phases and a learner phase. Class cooperation between the best class and the worst one is implemented by exchanging search times and search ability at the second stage and seldom adopted in the existing works. Extensive experiments are conducted and CTLBO is compared with the existing methods to test its performances. Computational results demonstrate that CTLBO has very competitive performances on solving the considered DTAFSP.

Adaptive scheduling for assembly job shop with uncertain assembly times based on dual Q-learning

To address the uncertainty of production environment in assembly job shop, in combination of the real-time feature of reinforcement learning, a dual Q-learning (D-Q) method is proposed to enhance the adaptability to environmental changes by self-learning for assembly job shop scheduling problem. On the basis of the objective function of minimising the total weighted earliness penalty and completion time cost, the top level Q-learning is focused on localised targets in order to find the dispatching policy which can minimise machine idleness and balance machine loads, and the bottom level Q-learning is focused on global targets in order to learn the optimal scheduling policy which can minimise the overall earliness of all jobs. Some theoretical results and simulation experiments indicate that the proposed algorithm achieves generally better results than the single Q-learning (S-Q) and other scheduling rules, under the arrival frequency of product with different conditions, and show good adaptive performance. Abbreviations: AFSSP, assembly flow shop scheduling problem; AJSSP, assembly job shop scheduling problem; RL, reinforcement learning; TASP, two-stage assembly scheduling problem

An Improved Whale Optimization Algorithm for Distributed Assembly Flow Shop with Crane Transportation

In this study, we investigate a classical distributed assembly flow shop scheduling problem with crane transportation. The objectives are to minimise the weighted value of the makespan and the ener...

Robust scheduling for a two-stage assembly shop with scenario-dependent processing times

Recently, finding solutions to assembly flowshop scheduling problems is a topic of extensive discussion in research communities. While existing research assumes that job processing times are constant numbers, in several practical situations, due to several external factors like machine breakdowns, working environment changes, worker performance instabilities, and tool quality variations and unavailability, job processing times may vary. In this study, therefore, we address a two-stage assembly flowshop scheduling problem with two scenario-dependent jobs processing times to minimise the maximum makepsan among both scenarios (called robust makespan) In view of the NP-hard nature, we first derive a dominance property and a lower bound to propose a branch-and-bound algorithm to find a permutation schedule with minimum makespan. Following that, we use Johnson’s rule to propose eight polynomial heuristics for finding near-optimal solutions. Furthermore, we propose four cloud theory-based simulated annealing (CSA) hyper-heuristic algorithms incorporating seven low level heuristics to solve a robust two-stage assembly flowshop problem with scenario-dependent processing times. Finally, we empirically evaluate the effectiveness of all the proposed algorithms in minimising the robust makespan.

A novel imperialist competitive algorithm for fuzzy distributed assembly flow shop scheduling

Assembly flow shop scheduling problem with DPm → 1 layout has important applications in various manufacturing systems and has been extensively considered in single factory; however, this problem with fuzzy processing time is seldom studied in multiple factories. In this paper, fuzzy distributed assembly flow shop scheduling problem (FDAFSP) is considered, in which each factory has DPm → 1 layout, and an imperialist competitive algorithm with empire cooperation (ECICA) is developed to minimize fuzzy makespan. In ECICA, an adaptive empire cooperation between the strongest empire and the weakest empire is implemented by exchanging computing resources and search ability, historical evolution data are used and a new imperialist competition is adopted. Numerical experiments are conducted on various instances and ECICA is compared with the existing methods to test its performance. Computational results demonstrate that ECICA has promising advantages on solving FDAFSP.

An enhanced genetic algorithm for the distributed assembly permutation flowshop scheduling problem

The distributed assembly permutation flowshop scheduling problem (DAPFSP) is a new generalisation of the distributed permutation flowshop scheduling problem (DPFSP) and the assembly flowshop scheduling problem (AFSP), aiming to minimise makespan. This production mode is more complicated and competitive in the real production process and includes two phases: production and assembly. Firstly, the production is conducted in several identical factories, and the production in each factory can be considered to a permutation flowshop scheduling problem (PFSP) with multi-machines. Then, the jobs produced in the first stage are assembled into final products. An enhanced population-based meta-heuristic – genetic algorithm (GA) is proposed for this problem. A greedy mating pool is designed to select promising parents in the selection operation, and an effective crossover strategy is designed based on the local search for speeding up convergence. To enhance the exploitation capability, several different local search strategies are incorporated into the algorithm, which are based on two neighbourhood structures. The exhaustive experiment and statistical analysis show that the proposed algorithms outperform the existing algorithms.

An enhanced genetic algorithm for the distributed assembly permutation flowshop scheduling problem

The distributed assembly permutation flowshop scheduling problem (DAPFSP) is a new generalisation of the distributed permutation flowshop scheduling problem (DPFSP) and the assembly flowshop scheduling problem (AFSP), aiming to minimise makespan. This production mode is more complicated and competitive in the real production process and includes two phases: production and assembly. Firstly, the production is conducted in several identical factories, and the production in each factory can be considered to a permutation flowshop scheduling problem (PFSP) with multi-machines. Then, the jobs produced in the first stage are assembled into final products. An enhanced population-based meta-heuristic – genetic algorithm (GA) is proposed for this problem. A greedy mating pool is designed to select promising parents in the selection operation, and an effective crossover strategy is designed based on the local search for speeding up convergence. To enhance the exploitation capability, several different local search strategies are incorporated into the algorithm, which are based on two neighbourhood structures. The exhaustive experiment and statistical analysis show that the proposed algorithms outperform the existing algorithms.

A bi-objective model for the assembly flow shop scheduling problem with sequence dependent setup times and considering energy consumption

The two-stage assembly flowshop scheduling problem has been studied in this research. Suppose that a number of products of different kinds are needed to be produced. Each product is consists of several parts. There are m uniform machines in the first stage to manufacture the components (parts) of products and there is one assembly station in the second stage to assembled parts into products. Setup operation should be done when a machine starts processing a new part and setup times are treated as separate from processing times. Two objective functions are considered: (1) minimizing the completion time of all products (makespan) as a classic objective, and (2) minimizing the cost of energy consumption as a new objective. Processing speed of each machine is adjustable and the rate of energy consumption of each machine is dependent of its processing speed. At first, this problem is described with an example, and then needed parameters and decision variables are defined. After that, this problem is modeled as a mixed integer linear programming (MILP) and GAMS software is applied to solve small problems. To solve this bi-objective model, Epsilon Constraint algorithm is used on some test problems obtained standard references. Data of test problems were obtained from previous references and new parameters have been adjusted for considered problem. Conflicting of two considered objective functions has been valid through the result. In additional, result of solving test problems and sensitivity analysis show that how we can reduce energy consumption by adjusting completion times.

A branch-and-bound algorithm and four metaheuristics for minimizing total completion time for a two-stage assembly flow-shop scheduling problem with learning consideration

ABSTRACTThis article addresses a two-stage, three-machine assembly scheduling problem that considers the learning effect. All jobs are processed on two machines in the first stage and move on to be processed on an assembly machine in the second stage. The objective of the study is to minimize the total completion time of the given jobs. Because the problem is NP hard, the authors first established a lower bound and several adjacent propositions using a branch-and-bound algorithm to search for the optimal solution. Four metaheuristics are proposed to approximate the solutions: genetic algorithms, cloud theory-based simulated annealing, artificial bee colonies and iterated greedy algorithms. Four different heuristics are used as seeds in each metaheuristic to obtain high-quality approximate solutions. The performances of all 16 metaheuristics and the branch-and-bound algorithm are then examined and are reported herein.

A two-stage three-machine assembly scheduling flowshop problem with both two-agent and learning phenomenon

Two-stage three-machine assembly flow shop, multiple-agent scheduling problems, and scheduling models with time-dependent processing times have been separately receiving continuous attention on research community. All the three phenomena have been shown to exist in many real applications, but no study has so far integrated the two-stage assembly flow shop, two-agent, and time-dependent processing times simultaneously. In view of this lack of integrated study, we investigated a two-stage three-machine assembly flow shop scheduling problem with both two-agent and learning phenomenon. Our objective was minimizing the total completion time of the first agent’s jobs subject to a given upper bound imposed on the total completion time of the second agent’s jobs. To solve the problem, some dominant propositions and three lower bounds were first derived to be used in the branch-and-bound algorithm for the small-size jobs. Then, four versions of hybrid particle swarm optimization algorithms were proposed to find approximate solutions for small-size and big-size jobs, respectively.

Flow shop scheduling problems with assembly operations: a review and new trends

The past few years have witnessed a resurgence of interest in assembly flow shop scheduling as evidenced by increasing number of published articles in this field. A basic assembly flow shop consists of two types of stages: fabrication or machining stage and assembly stage. Machining and assembly stages are composed of either one or a set of machines that are working in parallel. Final products have hierarchical assembly structure with several components and assembly operation(s). The components need to be processed in the machining stage(s) and then assembled based on hierarchical assembly structure. The goal is to find the sequence of jobs that optimises certain objectives. Assembly flow shop scheduling problem has several interesting derivatives and applications in various manufacturing and service industries. This paper provides a consolidated survey of assembly flow shop models with their solution methodology. Finally, the paper concludes by presenting some problems receiving less attention and proposes several salient research opportunities.