Assembly Flow Shop Research Articles

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.

Scheduling two-stage assembly flow shop with random machines breakdowns: integrated new self-adapted differential evolutionary and simulation approach

This paper takes random machines breakdowns and the two-stage assembly flow shop problem into consideration as a realistic assumption in industrial environments. In practical manufacturing environment, disruptions and unforeseen incidents occur, so a schedule being built based on deterministic information is not practical and may lead to poor performance. In this paper, machines in manufacturing and assembly stages are not always available due to random machines breakdowns which occur during processing of each operation. The goal is to minimize the expected the weighted sum of makespan and mean of completion time. Owning to its problem complexity and since the problem belongs to NP-hard class, use of meta-heuristic algorithms is justified to tackle the potential complexity of the problem considered, and hence, we proposed four meta-heuristics algorithms entitled: genetic algorithm, imperialist competitive algorithm, cloud theory-based simulated annealing and new self-adapted differential evolutionary (NSDE) to solve it. Machine breakdown and dynamic nature of the problem, the structural complexity increases markedly. In this regard, to overcome this form of complexity, simulation techniques are typically employed. Eventually, since the proposed problem has both types of complexities (algorithm complexity and structural complexity), simulation is integrated into the proposed meta-heuristic approaches to handle the complexities. We apply artificial neural network as a tuning tool for predicting the input parameters of each proposed meta-heuristics algorithms in uncertain condition. Also, we suggest Taguchi method as one the most important adjusting approaches for analyzing the effect of input parameters in each algorithm. The computational results show which proposed NSDE statistically is better than other proposed meta-heuristics algorithms according two important indicators: quality of solution and computational time.

Robust scheduling in two-stage assembly flow shop problem with random machine breakdowns: integrated meta-heuristic algorithms and simulation approach

PurposeIn real manufacturing systems, schedules are often disrupted with uncertainty factors such as random machine breakdown, random process time, random job arrivals or job cancellations. This paper aims to investigate robust scheduling for a two-stage assembly flow shop scheduling with random machine breakdowns and considers two objectives makespan and robustness simultaneously.Design/methodology/approachOwing to its structural and algorithmic complexity, the authors proposed imperialist competitive algorithm (ICA), genetic algorithm (GA) and hybridized with simulation techniques for handling these complexities. For better efficiency of the proposed algorithms, the authors used artificial neural network (ANN) to predict the parameters of the proposed algorithms in uncertain condition. Also Taguchi method is applied for analyzing the effect of the parameters of the problem on each other and quality of solutions.FindingsFinally, experimental study and analysis of variance (ANOVA) is done to investigate the effect of different proposed measures on the performance of the obtained results. ANOVA's results indicate the job and weight of makespan factors have a significant impact on the robustness of the proposed meta-heuristics algorithms. Also, it is obvious that the most effective parameter on the robustness for GA and ICA is job.Originality/valueRobustness is calculated by the expected value of the relative difference between the deterministic and actual makespan.

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.

A complete immunoglobulin-based artificial immune system algorithm for two-stage assembly flowshop scheduling problem with part splitting and distinct due windows

This paper considers a two-stage assembly flowshop scheduling problem with distinct due windows to minimise the sum of weighted earliness and tardiness. There are several identical parallel machines which produce parts in the first stage. When the required parts are available, a single assembly machine can group these parts into products in the second stage. It is assumed that a part can be split into sub-parts which can be processed independently on the parallel machines in the first stage. Setup is also considered. A mathematical model is established to describe and define the proposed problem. A new decoding method is developed by extending an existing decoding method. Two novel operators, named part splitting (PS) and optimal idle time insertion (ITI), are incorporated into the decoding procedure for improving the quality of the solution. A rule named Priority of Earliness and Tardiness (PET) and a Complete Immunoglobulin-based Artificial Immune System (C-IAIS) algorithm are proposed for solving the problem. To evaluate PET and C-IAIS algorithm, several existing algorithms are used in the experiments. Computational results show that C-IAIS algorithm performs better than other algorithms for solving the proposed problem.

Multi-Stage assembly flow shop with setup time and release time

This article addresses multi-stage assembly flow shop for the first time. We propose several industrial applications of this system in which the opening stage has m parallel machines and the following stages (e.g. assembly, transportation, painting, packaging, etc.) complete and prepare products for delivery. We develop a mixed binary linear optimization model and a constraint-free mathematical presentation for this problem. We explore performance measures of makespan and total completion time and derive polynomial optimal solutions for special cases that are likely to occur in industry. We also propose lower bounds as well as nine efficient heuristics for solving the problem with the objective of minimizing makespan. The results reveal that the proposed lower bounds is tight enough. Moreover, the optimization models and derived polynomial algorithms can be applied to assembly flow shops without setup or release time. Finally, we implement General Variable Neighborhood Search (GVNS) and Grey Wolf Optimizer to improve the heuristic solutions. Comparison of employed algorithms on randomly generated instances indicates that GVNS outperforms other heuristics. The performance of proposed heuristics and meta-heuristics are confirmed with detailed statistical analysis.

Scheduling the distributed assembly flowshop problem to minimize the makespan

In this paper, we studied the distributed assembly permutation flowshop scheduling problem (DAPFSP) with the makespan minimization as objective. We proposed iterated greedy-based approach that is labelled the bounded-search iterated greedy algorithm BSIG. In addition, four local search methods are designed to improve solution quality. The computational results show the effectiveness of BSIG in solving the DAPFSP specially with small instances where BSIG outperforms most of the existing algorithms.

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.

Bi-level genetic algorithms for a two-stage assembly flow-shop scheduling problem with batch delivery system

Abstract In this paper, an integrated production and distribution scheduling on a two-stage assembly flow-shop setting with a batch delivery system is addressed. The objective is to schedule the jobs in the two-stage assembly flow-shop and groups the completed products into a suitable number of batches for delivery with the minimum number of weighted tardy jobs and sum of delivery costs. After extending a mixed-integer linear programming (MILP) model, we proposed a bi-level genetic algorithm to solve the addressed problem that the first level of its chromosome is supposed to determine the sequence of the processing jobs, and the second level of it is responsible for allocating jobs to batches independently. To offer the more efficient algorithm, we change the structure of the proposed GA. Therefore, by applying the hierarchical decision-making approach, we present a bi-level improved genetic algorithm (IGA) in which according to the determined sequence in the first level, batches are determined. The proposed algorithms are evaluated based on computational experiments. The experiments reveal that IGA, which has the decreased decision-making space for the second level, outperforms GA. Moreover, to validate the proposed model and the efficiency of the proposed algorithms, a real-life example is presented and solved.

Dominance rule and opposition-based particle swarm optimization for two-stage assembly scheduling with time cumulated learning effect

This paper introduces a two-stage assembly flowshop scheduling model with time cumulated learning effect, which exists in many realistic scheduling settings. By the time cumulated learning effect, we mean that the actual job processing time of a job depends on its scheduled position as well as the processing times of the jobs already processed. The first stage consists of two independently working machines where each machine produces its own component. The second stage consists of a single assembly machine. The objective is to identify a schedule that minimizes the total completion time of all jobs. With analysis on the discussed problem, some dominance rules are developed to optimize the solving procedure. Incorporating with the developed dominance rules, a dominance rule and opposition-based particle swarm optimization algorithm (DR-OPSO) and branch-and-bound are devised. Computational experiments have been conducted to compare the performances of the proposed DR-OPSO and branch-and-bound through comparing with the standard O-PSO and PSO. The results fully demonstrate the efficiency and effectiveness of the proposed DR-OPSO algorithm, providing references to the relevant decision-makers in practice.

Memetic social spider optimization algorithm for scheduling two-stage assembly flowshop in a distributed environment

Abstract This paper studies the distributed two-stage assembly flowshop problem with separate setup times, which is a generalisation for the regular two-stage assembly flowshop problem in the distributed manufacturing environment. The optimization objective is to find a suitable job schedule such that the criterion of total completion time is minimized. To deal with such a problem, we propose a novel memetic algorithm (MA) based on a recently developed social spider optimization (SSO). To the best of our knowledge, it is the first effort to explore the SSO-based MA (MSSO) and to apply SSO in the field of combinational optimization. In the proposed MSSO algorithm, we first modify the original version of SSO to adapt to the distributed problems, and then integrate two improvement techniques, problem-special local search and self-adaptive restart strategy, within MA framework. In the numerical experiment, the parameters used in MSSO are calibrated and suitable parameter values are suggested based on the Taguchi method. Experimental results and comparisons with the existing algorithms validate the effectiveness and efficiency of the proposed MSSO for addressing the considered problem. In addition, the effect of problem scale parameters on MSSO and the effectiveness of the proposed improvement techniques are also investigated and demonstrated.

Modeling and Scheduling Two-stage Assembly Flow Shop Problems with Non-Identical Assembly Machines

Modeling and Scheduling Two-stage Assembly Flow Shop Problems with Non-Identical Assembly Machines

Multi objective two-stage assembly flow shop with release time

Abstract Two-stage assembly flow shops are integral part of several manufacturing systems such as computer and engine manufacturing lines. This paper explores three objectives of makespan, total tardiness, and total completion times for two-stage assembly flow shop with release time. To the best of our knowledge, these performance measures have not been addressed simultaneously in assembly flow shops. We derive polynomial optimal solutions for special cases of this problem with a single objective and then develop heuristics with promising starting solutions for the multi-objective case. Due to NP-hardness of the problem, we apply a customized reference-based Non-dominated Sorting Genetic Algorithm (NSGA-III) and Multi-Objective Particle Swarm Optimization (MOPSO) as solution procedures. Finally, we present extensive computational analysis to compare the performance of employed heuristic and metaheuristics on randomly generated instances. Results show that both NSGA-III and MOPSO generate competitive solutions for the presented problem. However, NSGA-III generates significantly better results than MOPSO based on one of the three performance metrics.

A two-stage three-machine assembly flow shop scheduling with learning consideration to minimize the flowtime by six hybrids of particle swarm optimization

Abstract There have been many applications of two-stage three-machine assembly flow shop in query scheduling, such as fire engine assembly, personal computer manufacturing, and distributed database system. Moreover, learning phenomenon has been shown present in many two-stage assembly flow shop environments. In conjunction with this learning phenomenon, we addressed, in this study, a two-stage three-machine flow shop scheduling problem with a cumulated learning function. Our objective was to search an optimal sequence for minimizing the flowtime (or total completion time). We developed some dominance propositions with a lower bound used in a branch-and-bound algorithm for small-size jobs. We also proposed six versions of hybrid particle swam optimization (PSO) algorithms to find approximate solutions for small-size and big-size jobs, and for three different data types. In addition, analysis of variance (ANOVA) was employed to examine the performances of the six PSOs for each data type. Subsequently, Fisher's least significant difference tests were carried out to further make pairwise comparisons among the performances of the six algorithms.

Minimizing the Makespan for a Two-Stage Three-Machine Assembly Flow Shop Problem with the Sum-of-Processing-Time Based Learning Effect

Two-stage production process and its applications appear in many production environments. Job processing times are usually assumed to be constant throughout the process. In fact, the learning effect accrued from repetitive work experiences, which leads to the reduction of actual job processing times, indeed exists in many production environments. However, the issue of learning effect is rarely addressed in solving a two-stage assembly scheduling problem. Motivated by this observation, the author studies a two-stage three-machine assembly flow shop problem with a learning effect based on sum of the processing times of already processed jobs to minimize the makespan criterion. Because this problem is proved to be NP-hard, a branch-and-bound method embedded with some developed dominance propositions and a lower bound is employed to search for optimal solutions. A cloud theory-based simulated annealing (CSA) algorithm and an iterated greedy (IG) algorithm with four different local search methods are used to find near-optimal solutions for small and large number of jobs. The performances of adopted algorithms are subsequently compared through computational experiments and nonparametric statistical analyses, including the Kruskal–Wallis test and a multiple comparison procedure.

Minimising maximum tardiness in assembly flowshops with setup times

This paper addresses a two-stage assembly flowshop scheduling problem with the objective of minimising maximum tardiness where set-up times are considered as separate from processing times. The performance measure of maximum tardiness is important for some scheduling environments, and hence, it should be taken into account while making scheduling decisions for such environments. Given that the problem is strongly NP-hard, different algorithms have been proposed in the literature. The algorithm of Self-Adaptive Differential Evolution (SDE) performs as the best for the problem in the literature. We propose a new hybrid simulated annealing and insertion algorithm (SMI). The insertion step, in the SMI algorithm, strengthens the exploration step of the simulated annealing algorithm at the beginning and reinforces the exploitation step of the simulated annealing algorithm towards the end. Furthermore, we develop several dominance relations for the problem which are incorporated in the proposed SMI algorithm. We compare the performance of the proposed SMI algorithm with that of the best existing algorithm, SDE. The computational experiments indicate that the proposed SMI algorithm performs significantly better than the existing SDE algorithm. More specifically, under the same CPU time, the proposed SMI algorithm, on average, reduces the error of the best existing SDE algorithm over 90%, which indicates the superiority of the proposed SMI algorithm.

The 2-stage assembly flowshop scheduling problem with total completion time: Efficient constructive heuristic and metaheuristic

In this paper, we address the 2-stage assembly scheduling problem where there are m machines in the first stage to manufacture the components of a product and one assembly station (machine) in the second stage. The objective considered is the minimisation of the total completion time. Since the NP-hard nature of this problem is well-established, most previous research has focused on finding approximate solutions in reasonable computation time. In our paper, we first review and derive a number of problem properties and, based on these ideas, we develop a constructive heuristic that outperforms the existing constructive heuristics for the problem, providing solutions almost in real-time. Finally, for the cases where extremely high-quality solutions are required, a variable local search algorithm is proposed. The computational experience carried out shows that the algorithm outperforms the best existing metaheuristic for the problem. As a summary, the heuristics presented in the paper substantially modify the state-of-the-art of the approximate methods for the 2-stage assembly scheduling problem with total completion time objective.

The two stage assembly flow-shop scheduling problem with batching and delivery

This paper investigates the two-stage assembly flow shop scheduling problem with a batched delivery system where there are m independent machines at the first stage doing the components of a job and multiple identical assembly machines at the second stage, each of which can assemble the components and complete the job. The objective is to schedule the jobs, to form them into batches so as to minimize the sum of tardiness plus delivery costs. To the best of our knowledge, the assembly flow shop scheduling problem with this objective function has not been addressed so far. A mathematical model for this problem is presented. However, due to the fact that this model happens to be a mixed integer nonlinear programming model and cannot guarantee to reach the solution at reasonable time we developed the imperialist competitive algorithm (ICA) and a hybrid algorithm (HICA) by incorporating the dominance relations. Computational results show that HICA performs better than ICA with respect to the value of the objective function, However the runtime of the ICA is less than HICA.