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The purpose of this paper is to develop a computer simulation model to evaluate the bowl phenomenon and the allocation at the end of the line of stations with either greater mean operation times or higher variability of operation times.

The model was developed on the basis of a realistic case problem and applied to a six‐station assembly line. The evaluation criteria were the: minimization of the total elapsed time; maximization of the average percentage of working time; and minimization of the average time in the system.

The performance of an assembly line with independently normally distributed operation times could be improved by applying the bowl phenomenon. The allocation of large operation mean times to stations located near the end of the line did not produce improved results. Instead a more balanced allocation proved to be more significantly effective. On the other hand, the assignment of larger variability of operation times to the stations near the end of the line improved the performance of the assembly line.

The investigation contributed to the computer simulation approach to solving assembly line problems that dealt with the impact of normally distributed operation times on the bowl phenomenon and assembly lines with increasing mean operation times and higher variability of operation times at the end of the line of stations.

This paper aims to develop a new differential evolution algorithm (DEA) for solving the simple assembly line balancing problem of type 2 (SALBP-2).

Novel approaches of mutation operator and crossover operator are presented. A self-adaptive double mutation scheme is implemented and an elitist strategy is used in the selection operator.

Test and comparison results show that the proposed IDEA obtains better results for SALBP-2.

The presented DEA is called the integer-coded differential evolution algorithm (IDEA), which can directly deal with integer variables of SALBP-2 on a discrete space without any posterior conversion. The proposed IDEA will be an alternative in evolutionary algorithms, especially for various integer/discrete-valued optimization problems.

Due to the market trend of low-volume and high-variety, the manufacturing industry is paying close attention to improve the ability to hedge against variability. Therefore, in this paper the assembly line with limited resources is balanced in a robust way that has good performance under all possible scenarios. The proposed model allows decision makers to minimize a posteriori regret of the selected choice and hedge against the high cost caused by variability.

A generalized resource-constrained assembly line balancing problem (GRCALBP) with an interval data of task times is modeled and the objective is to find an assignment of tasks and resources to the workstations such that the maximum regret among all the possible scenarios is minimized. To properly solve the problem, the regret evaluation, an exact solution method and an enhanced meta-heuristic algorithm, Whale Optimization Algorithm, are proposed and analyzed. A problem-specific coding scheme and search mechanisms are incorporated.

Theory analysis and computational experiments are conducted to evaluated the proposed methods and their superiority. Satisfactory results show that the constraint generation technique-based exact method can efficiently solve instances of moderate size to optimality, and the performance of WOA is enhanced due to the modified searching strategy.

For the first time a minmax regret model is considered in a resource-constrained assembly line balancing problem. The traditional Whale Optimization Algorithm is modified to overcome the inferior capability and applied in discrete and constrained assembly line balancing problems.

In this study, a mixed-model assembly line (MMAL) balancing problem is applied in a make-to-order (MTO) environment. One of the important problems in MTO systems is identifying the control points, which is considered by designing a control system. Furthermore, the worker assignment problem is defined by considering abilities and operating costs of workers. The proposed model is solved in two stages. First, a multi-objective model by simultaneously minimizing the number of stations and the total cost of the task duplication and workers assignment is considered. The second stage is designing a control system to minimize the work in process.

To solve this problem, a non-dominated sorting genetic algorithm (NSGA-II) is introduced and the proposed model is compared with four multi-objective algorithms (MOAs).

The proposed model is compared with four MOAs, i.e. multi-objective particle swarm optimization, multi-objective ant colony optimization, multi-objective firefly algorithm and multi-objective simulated annealing algorithm. The computational results of the NSGA-II algorithm are superior to the other algorithms, and multi-objective ant colony optimization has the best running time of the four MOA algorithms.

With attention to workers assignment in a MTO environment for the MMAL balancing problem, the present research has several significant implications for the rapidly changing manufacturing challenge.

To the best of the authors’ knowledge, no study has provided for the MMAL balancing problem in a MTO environment considering control points. This study provides the first attempt to fill this research gap. Also, a usual assumption in the literature that common tasks of different models must be assigned to a single station is relaxed and different types of real assignment restrictions like resource restrictions and tasks restrictions are described.

The purpose of this paper is to introduce robust optimization approaches to balance mixed model assembly lines with uncertain task times and daily model mix changes.

Scenario planning approach is used to represent the input data uncertainty in the decision model. Two kinds of robust criteria are provided: one is min‐max related; and the other is α‐worst scenario based. Corresponding optimization models are formulated, respectively. A genetic algorithm‐based robust optimization framework is designed. Comprehensive computational experiments are done to study the effect of these robust approaches.

With min‐max related robust criteria, the solutions can provide an optimal worst‐case hedge against uncertainties without a significant sacrifice in the long‐run performance; α‐worst scenario‐based criteria can generate flexible robust solutions: through rationally tuning the value of α, the decision maker can obtain a balance between robustness and conservatism of an assembly line task elements assignment.

This paper is an attempt to robust mixed model assembly line balancing. Some more efficient and effective robust approaches – including robust criteria and optimization algorithms – may be designed in the future.

In an assembly line with significant uncertainty, the robust approaches proposed in this paper can hedge against the risk of poor system performance in bad scenarios.

Using robust optimization approaches to balance mixed model assembly line.

The balancing of robotic weld assembly lines has a significant influence on achievable production efficiency. This paper aims to investigate the most suitable way to assign both assembly tasks and type of robots to every workstation, and present an optimal method of robotic weld assembly line balancing (ALB) problems with the additional concern of changeover times. An industrial case of a robotic weld assembly line problem is investigated with an objective of minimizing cycle time of workstations.

This research proposes an optimal method for balancing robotic weld assembly lines. To solve the problem, a low bound of cycle time of workstations is built, and on account of the non-deterministic polynomial-time (NP)-hard nature of ALB problem (ALBP), a genetic algorithm (GA) with the mechanism of simulated annealing (SA), as well as self-adaption procedure, was proposed to overcome the inferior capability of GA in aspect of local search.

Theory analysis and simulation experiments on an industrial case of a car body welding assembly line are conducted in this paper. Satisfactory results show that the performance of GA is enhanced owing to the mechanism of SA, and the proposed method can efficiently solve the real-world size case of robotic weld ALBPs with changeover times.

The additional consideration of tool changing has very realistic significance in manufacturing. Furthermore, this research work could be modified and applied to other ALBPs, such as worker ALBPs considering tool-changeover times.

For the first time in the robotic weld ALBPs, the fixtures’ (tools’) changeover times are considered. Furthermore, a mathematical model with an objective function of minimizing cycle time of workstations was developed. To solve the proposed problem, a GA with the mechanism of SA was put forth to overcome the inferior capability of GA in the aspect of local search.

In pursuit of zero‐defect quality, a growing number of JIT manufacturing firms often consider a line‐stop strategy that allows workers to stop the assembly line when abnormalities occur during production process, and to repair defects immediately as they occur. The line‐stop strategy contrasts with a traditional off‐line repair strategy that either scraps the defects or sends them to a separate repair station. Develops an expected total cost model to demonstrate the cost‐effectiveness of the line‐stop strategy over the off‐line repair strategy in JIT environments. Computational experiments indicate that cost savings resulting forum using the line‐stop strategy are greater than those using the off‐line repair strategy.

Parallel two-sided assembly lines are usually designed to produce large-sized products such as trucks and buses. In parallel two-sided assembly lines, both left and right sides of the line are used for manufacturing one or more products on two or more assembly lines located parallel to each other. The purpose of this paper is to develop a new mathematical model for the parallel two-sided assembly line balancing problem that helps to evaluate and validate the balancing operations of the machines such as removal of tools and fixtures and reallocating the operators.

The proposed approach is explained with the help of an example problem. In all, 22 test problems are formed using the benchmark problems P9, P12, P16 and P24. The results obtained are compared among approaches of the task(s) shared, tool(s) shared and both tool(s) and task(s) shared for effect on efficiency as the performance measure. The solution presented here follows the exact solution procedure that is solved by Lingo 16 solver.

Based on the experiments, line efficiency decreases when only tools are shared and increases when only tasks are shared. Results indicate that by sharing tasks and tools together, better line efficiency is obtained with less cost of tools and fixtures.

According to the industrial aspect, the result of the study can be beneficial for assembly of the products, where tools and tasks are shared between parallel workstations of two or more parallel lines.

According to the author’s best knowledge, this paper is the first to address the tools and tasks sharing between any pair of parallel workstations.

This paper aims to discuss the sequence-dependent forward setup time (FST) and backward setup time (BST) consideration for the first time in two-sided assembly lines. Sequence-dependent FST and BST values must be considered to compute all of the operational times of each station. Thus, more realistic results can be obtained for real-life situations with this new two-sided assembly line balancing (ALB) problem with setups consideration. The goal is to obtain the most suitable solution with the least number of mated stations and total stations.

The complex structure it possesses has led to the use of certain assumptions in most of the studies in the ALB literature. In many of them, setup times have been neglected or considered superficially. In the real-life assembly process, potential setup configurations may exist between each successive task and between each successive cycle. When two tasks are in the same cycle, the setup time required (forward setup) may be different from the setup time required if the same two tasks are in consecutive cycles (backward setup).

Algorithm steps have been studied in detail on a sample solution. Using the proposed algorithm, the literature test problems are solved and the algorithm efficiency is revealed. The results of the experiments revealed that the proposed approach finds promising results.

The sequence-dependent FST and BST consideration is applied in a two-sided assembly line approach for the first time. A genetic algorithm (GA)-based algorithm with ten different heuristic rules was used in this proposed model.

This paper aims to review and discuss four aspects of mixed-model assembly line balancing (MMALB) problem mainly on the optimization angle. MMALB is a non-deterministic polynomial-time hard problem which requires an effective algorithm for solution. This problem has attracted a number of research fields: manufacturing, mathematics and computer science.

This paper review 59 published research works on MMALB from indexed journal. The review includes MMALB problem varieties, optimization algorithm, objective function and constraints in the problem.

Based on research trend, this topic is still growing with the highest publication number observed in 2016 and 2017. The review indicated that the future research direction should focus on human factors and sustainable issues in the problem modeling. As the assembly cost becomes crucial, resource utilization in the assembly line should also be considered. Apart from that, the growth of new optimization algorithms is predicted to influence the MMALB optimization, which currently relies on well-established algorithms.

The originality of this paper is on the research trend in MMALB. It provides the future direction for the researchers in this field.