Assembly Flow Shop Research Articles

Improved discrete cuckoo optimization algorithm for the three-stage assembly flowshop scheduling problem

The three-stage assembly flow shop scheduling problem, where the first stage has parallel machines and the second and the third stages have a single machine, is addressed in this study. Each product has made of several components that after processing at the first stage are collected and transferred to the third stage to assemble them as the product. The goal is to find products’ sequence to minimize completion time of the last product, makespan. Since the problem is NP-hard, an improved version of Cuckoo Optimization Algorithm (COA), a bio-inspired meta-heuristic, is proposed which incorporates new adjustments such as clustering, egg laying and immigration of the cuckoos based on a discrete representation scheme. These novel features result in an Improved Discrete version of COA, called IDCOA, which works efficiently. Also, for the addressed problem, a lower bound and some dispatching rules are proposed. The performance of the employed algorithms through randomly generated instances is evaluated which endorses the capability of the proposed IDCOA algorithm.

An efficient meta-heuristic algorithm for scheduling a two-stage assembly flow shop problem with preventive maintenance activities and reliability approach

This paper investigates integrated two-stage assembly flow shop problem with preventive maintenance (PM) activities under the multi-objective optimisation approaches. Reliability models are employed to carry out the maintenance activities. This paper attempts to find the appropriate sequence of jobs on machines in order to minimise the makespan and determining when to perform the PM activities in order to minimise the system unavailability. As this problem is proven to be NP-hard two multi-objective optimisation methods that are named non-dominated sorting genetic algorithm II (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are employed to find the Pareto-optimal front. The parameters of proposed algorithms are calibrated by artificial neural network (ANN) and the performances of the algorithms on the problem of various sizes are analysed based on four metrics. The computational results reveal NRGA is statistically better than NSGA-II.

An efficient meta-heuristic algorithm for scheduling a two-stage assembly flow shop problem with preventive maintenance activities and reliability approach

This paper investigates integrated two-stage assembly flow shop problem with preventive maintenance (PM) activities under the multi-objective optimisation approaches. Reliability models are employed to carry out the maintenance activities. This paper attempts to find the appropriate sequence of jobs on machines in order to minimise the makespan and determining when to perform the PM activities in order to minimise the system unavailability. As this problem is proven to be NP-hard two multi-objective optimisation methods that are named non-dominated sorting genetic algorithm II (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are employed to find the Pareto-optimal front. The parameters of proposed algorithms are calibrated by artificial neural network (ANN) and the performances of the algorithms on the problem of various sizes are analysed based on four metrics. The computational results reveal NRGA is statistically better than NSGA-II.

Scheduling of assembly flow shop problem and machines with random breakdowns

We investigate two-stage assembly flow shop problems (TAFSP) with considering machines breakdown and minimisation of the expected the weighted sum of makespan and mean of completion time is as objective value. This problem is NP-hard, hence we presented genetic algorithm (GA) and new self adapted differential evolutionary (NSDE) for solving random generated test problems. Artificial neural network (ANN) is applied to set parameters of two proposed algorithms also Taguchi method is used for analysing the effect of parameters of problem. The computational results reveal that NSDE is better than GA and achieve to good solutions in a shorter time.

Scheduling of assembly flow shop problem and machines with random breakdowns

Scheduling of assembly flow shop problem and machines with random breakdowns

Two-stage assembly scheduling problem for processing products with dynamic component-sizes and a setup time

In this paper, two-stage assembly flow shop scheduling problem (TSAFSP) to assemble products having dynamic component-sizes is considered. In the machining stage, a single machining machine produces various types of components to assemble the products. During the machining process, a setup time is required whenever the machining machine starts to process a new component or processes a different component. When the required components are available for the associated product from the machining stage, a single assembly machine can assemble these components into the product in the assembly stage. To solve the problem, a novel mixed integer linear programming model is derived. Three genetic algorithms (GAs) with different chromosome representations are proposed due to the intractability of the optimal solution for large-sized problems. One GA has a chromosome to represent a complete solution. Two hybrid genetic algorithms (HGAs) have a simple chromosome to represent a partial solution, and the rest of the solution is provided by an effective local search heuristic given the partial solution. The performance of the GAs is compared by using randomly generated examples.

Coordinated scheduling of production and transportation in a two-stage assembly flowshop

To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.

Bi-objective optimization for integrating production and preventive maintenance scheduling in two-stage assembly flow shop problem

This paper presents a new bi-objective mixed integer programming model for the two-stage assembly flow shop scheduling problem with preventive maintenance (PM) activities, in which the reliability/availability approach is employed to model the maintenance concepts of a problem. PM activities carry out the operations on machines and tools before the breakdown takes place. Therefore, it helps to prevent failures before they happen. After developing a new bi-objective model, an Epsilon-constraint method is proposed to solve the problem. This problem has been known as Np-hard. Therefore, three multi-objective optimization methods, namely fast non-dominated sorting genetic algorithm, Multi-objective imperialist competitive algorithm, and non-dominated ranking genetic algorithm (NRGA) are employed to find the pareto-optimal front for large sized problems. The parameters of the proposed algorithms are calibrated using artificial neural network (ANN) and the performances of the proposed algorithms on the problems of various sizes are analyzed and the computational results reveal that NRGA outperform than two other proposed algorithms in quality of solutions and computational time.

Two-stage assembly scheduling problem for minimizing total tardiness with setup times

The two-stage assembly flowshop scheduling problem has received much attention from researchers because it is applicable to many real-life environments. The objective of minimizing total tardiness is important because the fulfillment of due dates for customers must be considered when making scheduling decisions. However, the setup times were assumed to be zero in previous studies, which may not be realistic or appropriate for some scheduling environments because treating the setup times separately from the processing times increases the level of machine utilization and reduces total tardiness. In this study, we investigate the two-stage assembly flowshop scheduling problem with separate setup times to minimize the total tardiness. We propose two new algorithms and adapt four existing algorithms, which are different versions of simulated annealing, genetic, and insertion algorithms. Moreover, we formulate the problem mathematically, where we develop a dominance relation and we utilize the dominance relation in our proposed algorithms. Extensive computational experiments indicated that one of the proposed algorithms performed much better than the others on average, i.e., the error using the best algorithm was 54% to 98% less than that with the other algorithms. Computational experiments were also conducted with zero setup times in order to compare the performance of our proposed algorithms with that of the best known previously reported algorithm in the zero setup time case. When the setup times were zero, the best proposed algorithm reduced the error of the best previously reported algorithm by 48% when both algorithms were run for the same computational time. Therefore, our best proposed algorithm can be used for both zero and non-zero setup times. Hence, for the first time, the present study considers the problem with separate setup times as well as proposing much better algorithms for the zero setup time case.

Minimizing the number of tardy jobs on a two-stage assembly flowshop

The objective of minimizing the number of tardy jobs is important as it is directly related to the percentage of on-time shipments, which is often used to rate managers’ performance in many manufacturing environments. To the best of our knowledge, the assembly flowshop scheduling problem with this objective has not been addressed so far, and thus is addressed in this paper. Given that the problem is NP-hard, different heuristics are proposed for the problem in this paper. The proposed heuristics are genetic algorithm (GA), improved genetic algorithm (IGA), simulated annealing algorithm with three different neighborhood structures (SA-1, SA-2, SA-3), Dhouib et al.’s simulated annealing algorithm (DSA), and an improved cloud theory-based simulated annealing algorithm (CSA). The heuristics are evaluated based on extensive computational experiments and all the heuristics were run for the same computational time for a fair comparison. The experiments reveal that the overall average errors of DSA, GA, IGA, CSA, SA-1, SA-2, SA-3 were 20.53, 13.49, 11.64, 3.27, 2.81, 1.92, and 0.56, respectively. Therefore, the proposed heuristic of SA-3 reduces the error of DSA, GA, IGA, CSA, SA-1, SA-2 by about 97, 96, 95, 83, 80, and 71%, respectively. All the results are statistically confirmed.

Grey Wolf Optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time

This article addresses the two-stage assembly flow shop scheduling problem with release time of jobs which is applicable in many industrial areas, such as computer manufacturing industry, fire engine assembly plant, etc. The first stage of the problem is called “fabrication stage” and includes identical parallel machines while the second stage is called “assembly stage” with a single assembly machine. The jobs have components which they need to be firstly processed at the fabrication stage and then they should go under assembly operation at the assembly stage. The goal of this research is to find the jobs sequence such that completion time of the last processed job is minimized. For this problem, several heuristic techniques as well as a lower bound are developed. Also, a novel meta-heuristic algorithm called Grey Wolf Optimizer (GWO), which is inspired by living and haunting behavior of wolves, is then proposed. An extensive statistical analysis is conducted to compare the performance of the employed algorithms on randomly generated instances. The obtained results indicate that the methods based on Johnson’s algorithm yield better results than the other heuristic algorithms. Moreover, the consequences show that the proposed LB is tight enough. Finally, the experiments show that the GWO outperforms the other employed well-known meta-heuristic algorithms.

Simulated imperialist competitive algorithm in two-stage assembly flow shop with machine breakdowns and preventive maintenance

This article deals with the two-stage assembly flow shop problem considering preventive maintenance activities and machine breakdowns. The objective is to minimize the makespan. This problem is proven to be NP-hard; thus, we proposed two meta-heuristic algorithms, namely, imperialist competitive algorithm and genetic algorithm, to obtain solutions of the problem. This article describes an approach incorporating simulation with imperialist competitive algorithm for the scheduling purpose having machine breakdowns and preventive maintenance activities. The results obtained are analyzed using Taguchi experimental design, and the parameters of proposed algorithms are calibrated by artificial neural network. The computational results demonstrate that imperialist competitive algorithm is statistically better than genetic algorithm in quality of solution and reaches to better solutions at the same computational time.

Synchronisation of production scheduling and shipment in an assembly flowshop

This paper studies a synchronised scheduling problem of production simultaneity and shipment punctuality in a two-stage assembly flowshop system. Production simultaneity seeks to ensure all products belonging to a same customer order are simultaneously completed (at least as close as possible). Shipment punctuality attempts to satisfy orders’ individual shipment due dates. We provide two criteria, i.e. mean longest waiting duration and mean earliness and tardiness, for measuring production simultaneity and shipment punctuality, respectively. A synchronised scheduling model is developed by balancing the two criteria using linear weighted sum method. A modified genetic algorithm (GA) is then proposed for solving this model. Numerical studies demonstrate the effectiveness of the proposed approach. The results indicate that considering production simultaneity can remarkably reduce finished products inventory. A prioritised weight combination interval for production simultaneity and shipment punctuality has been suggested. Production simultaneity is affected by the production system configuration, especially in peak seasons.

Multi-objective meta-heuristics to solve three-stage assembly flow shop scheduling problem with machine availability constraints

In this paper, a three-stage assembly flow shop scheduling problem with machine availability constraints is taken into account. Two objectives of minimising total weighted completion times (flow time) and minimising sum of weighted tardiness and earliness are simultaneously considered. To describe this problem, a mathematical model is presented. The problem is generalisation of three-machine flow shop scheduling problem and two-stage assembly flow shop scheduling problem. Since these problems are known to be NP-hard, the considered problem is also strongly NP-hard. Therefore, two multi-objective meta-heuristics are presented to efficiently solve this problem in a reasonable amount of time. Comprehensive computational experiments are performed to illustrate the performance of the presented algorithms.

A hybrid electromagnetism-like algorithm for two-stage assembly flow shop scheduling problem

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation.

Minimizing the total completion time in a distributed two stage assembly system with setup times

In this paper, a novel distributed two stage assembly flowshop scheduling problem (DTSAFSP) is addressed. The objective is to assign jobs to several factories and schedule the jobs in each factory with the minimum total completion time (TCT). In view of the NP-hardness of the DTSAFSP, we develop heuristics method to deal with the problem and propose three hybrid meta-heuristics (HVNS, HGA-RVNS, and HDDE-RVNS). The parameters of HGA-RVNS and HDDE-RVNS are tuned by using the Taguchi method and that of HVNS is done by using the single factor ANOVA method. Computational experiments have been conducted to compare the performances of the proposed algorithms. The analyses of computational results show that, for the instances with small numbers of jobs, HDDE-RVNS obtains better performances than HGA-RVNS and HVNS; whereas for the instances with large numbers of jobs, HGA-RVNS is the best one in all the proposed algorithms. Computational results indicate that the performances of the HDDE-RVNS and HGA-RVNS are not much affected by the number of machines at the first stage and factories. The experimental results also show that the RVNS-based local search steps in both HGA-RVNS and HDDE-RVNS are efficient and effective.

Meta-heuristics for the distributed two-stage assembly scheduling problem with bi-criteria of makespan and mean completion time

This paper focuses on the distributed two-stage assembly flowshop scheduling problem for minimising a weighted sum of makespan and mean completion time. This problem involves two inter-dependent decision sub-problems: (1) how to allocate jobs among factories and (2) how to schedule the assigned jobs at each factory. A mathematical model is formulated for solving the small-sized instances of the problem. Since the NP-hardness of the problem, we also proposed a variable neighbourhood search (VNS) algorithm and a hybrid genetic algorithm combined with reduced variable neighbourhood search (GA-RVNS) to solve the distributed two-stage assembly flowshop scheduling problems and approximately optimise makespan and mean completion time simultaneously. Computational experiments have been conducted to compare the performances of the model and proposed algorithms. For a set of small-sized instances, both the model and the proposed algorithms are effective. The proposed algorithms are further evaluated on a set of large-sized instances. The results statistically show that both GA-RVNS and VNS obtain much better performances than the GA without RVNS-based local search step (GA-NOV). For the instances with small numbers of jobs, VNS achieves better performances than GA-RVNS. However, for the instances with large numbers of jobs, GA-RVNS yields better performances than the VNS. It is also shown that the overall performances of VNS are very close to GA-RVNS with different numbers of factories, weights given to makespan and numbers of machines at the first stage.

Finite capacity material requirement planning system for assembly flow shop with alternative work centres

This paper aims to develop a new finite capacity material requirement planning (FCMRP) system for an assembly flow shop with alternative work centres. It is a four-step procedure that firstly uses a variable lead-time MRP system to generate material and manufacturing plans. Secondly, dispatching rules are applied to determine sequence of customer orders. Thirdly, operations of orders are scheduled on the first and second priority work centres using various scheduling heuristics. Finally, the start times of operations are optimally adjusted by the LP model considering the finite capacity of all work centres and precedence of operations. Three industrial case studies are used to analyse the performances of the proposed system. The results show that the scheduling options/methods and dispatching rules significantly affect the performances of the proposed FCMRP system and the proposed FCMRP system greatly outperforms the FCMRP system of Wuttipornpun et al. (2006) considering overall performance index. In addition, the system requires short computational time when applied to industrial situations.

Heuristics for an assembly flow-shop with non-identical assembly machines and sequence dependent setup times to minimize sum of holding and delay costs

This paper addresses the two-stage assembly flow-shop scheduling problem with non-identical assembly machines at the second stage to minimize a sum of holding and delay costs. Although there are more than one assembly machine in many manufacturing systems, to the best of our knowledge, the two-stage assembly flow-shop scheduling problem (TSAFSP) has never been addressed with more than one assembly machine at stage two. Moreover, setup time is an inevitable factor in many cases and so in this paper, for more reality, sequence dependent setup times are considered for both stages. After extending mathematical modeling, to solve the addressed problem, four hybrid meta-heuristics are developed. A simulated annealing algorithm (SA) and an imperialist competitive algorithm (ICA) in order to find a sequence of jobs at the first stage and a heuristic (HEU) and again SA for assigning addressed jobs to assembly machines in stage two; therefore, these hybrid meta-heuristics are SA+HEU, ICA+HEU, SA+SA and ICA+SA. Computational results reveal that ICA+HEU outperforms all other algorithms; however, the run time of SA+HEU is the smallest among the algorithms.

An efficient imperialist competitive algorithm for scheduling in the two-stage assembly flow shop problem

This paper considers a two-stage assembly flow shop problem where m parallel machines are in the first stage and an assembly machine is in the second stage. The objective is to minimise a weighted sum of makespan and mean completion time for n available jobs. As this problem is proven to be NP-hard, therefore, we employed an imperialist competitive algorithm (ICA) as solution approach. In the past literature, Torabzadeh and Zandieh (2010) showed that cloud theory-based simulated annealing algorithm (CSA) is an appropriate meta-heuristic to solve the problem. Thus, to justify the claim for ICA capability, we compare our proposed ICA with the reported CSA. A new parameters tuning tool, neural network, for ICA is also introduced. The computational results clarify that ICA performs better than CSA in quality of solutions.