An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem

The consideration of this paper is given to address the straight and U-shaped assembly line balancing problem. Although many attempts in the literature have been made to develop deterministic version of the assembly line model, the attention is not considerably given to those in uncertain environment. In this paper, a novel bi-objective fuzzy mixed-integer linear programming model (BOFMILP) is developed so that triangular fuzzy numbers (TFNs) are employed in order to represent uncertainty and vagueness associated with the task processing times in the real production systems. In this proposed model, two conflicting objectives (minimizing the number of stations as well as cycle time) are considered simultaneously with respect to set of constraints. For this purpose, an appropriate strategy in which new two-phase interactive fuzzy programming approach is proposed as a solution method to find an efficient compromise solution. Finally, validity of the proposed model as well as its solution approach are evaluated though numerical examples. In addition, a comparison study is conducted over some test problems in order to assess the performance of the proposed solution approach. The results demonstrate that our proposed interactive fuzzy approach not only can be applied in ALBPs but also is capable to handle any practical MOLP models. Moreover, in light of these results, the proposed model may constitute a framework aiming to assist the decision maker (DM) to deal with uncertainty in assembly line problem.     

A branch-and-bound algorithm for assembly line worker assignment and balancing problems

In this paper, we studied the assembly line worker assignment and balancing problem, which is an extension of the classical assembly line balancing problem in which an optimal partition of the assembly work among the stations is sought along with the assignment of the operators to the stations. The relationship between this problem and several other well-studied problems is explored, and new lower bounds are derived. Additionally, an exact enumeration algorithm, which makes use of the lower bounds, is developed to solve the problem. The algorithm is tested by using a standard benchmark set of instances. The results show that the algorithm improves upon the best-performing methods from the literature in terms of solution quality, and verifies more optimal solutions than the other available exact methods.     

Multi-objective optimization of a stochastic assembly line balancing: A hybrid simulated annealing algorithm

This paper deals with multi-objective optimization of a single-model stochastic assembly line balancing problem with parallel stations. The objectives are as follows: (1) minimization of the smoothness index and (2) minimization of the design cost. To obtain Pareto-optimal solutions for the problem, we propose a new solution algorithm, based on simulated annealing (SA), called m_SAA. m_SAA implements a multinomial probability mass function approach, tabu list, repair algorithms and a diversification strategy. The effectiveness of m_SAA is investigated comparing its results with those obtained by another SA (using a weight-sum approach) on a suite of 24 test problems. Computational results show that m_SAA with a multinomial probability mass function approach is more effective than SA with weight-sum approach in terms of the quality of Pareto-optimal solutions. Moreover, we investigate the effects of properties (i.e., the tabu list, repair algorithms and diversification strategy) on the performance of m_SAA.     

A beam search approach for solving type II robotic parallel assembly line balancing problem

In a robotic assembly line, a series of stations are arranged along a conveyor belt and a robot performs on tasks at each station. Parallel assembly lines can provide improving line balance, productivity and so on. Combining robotic and parallel assembly lines ensure increasing flexibility of system, capacity and decreasing breakdown sensitivity. Although aforementioned benefits, balancing of robotic parallel assembly lines is lacking – to the best knowledge of the authors- in the literature. Therefore, a mathematical model is proposed to define/solve the problem and also iterative beam search (IBS), best search method based on IBS (BIBS) and cutting BIBS (CBIBS) algorithms are presented to solve the large-size problem due to the complexity of the problem. The algorithm also tested on the generated benchmark problems for robotic parallel assembly line balancing problem. The superior performances of the proposed algorithms are verified by using a statistical test. The results show that the algorithms are very competitive and promising tool for further researches in the literature.     

A decomposition based solution algorithm for U-type assembly line balancing with interval data

Balancing U-type assembly lines under uncertainty is addressed in this paper by formulating a robust problem and developing its optimization model and algorithm. U-type assembly layouts are shown to be more efficient than conventional straight lines. A great majority of studies on U-lines assume deterministic environments and ignore uncertainty in operation times. We aim to fill this research gap and, to the best of our knowledge, this study will be the first application of robust optimization to U-type assembly planning.We assume that the operation times are not fixed but they can vary. We employ robust optimization that considers worst case situations. To avoid over-pessimism, we consider that only a subset of operation times take their worst case values. To solve this problem, we suggest an iterative approximate solution algorithm. The efficiency of the algorithm is evaluated with some computational tests.     

多目标拆卸线平衡问题的Pareto细菌觅食算法*

拆卸线平衡问题的优化涉及多个目标,为克服传统方法在求解多目标拆卸线平衡问题时不能很好处理各子目标间冲突及易于早熟等不足,提出了一种多目标细菌觅食优化算法。算法采用Pareto非劣排序技术对种群进行分级,并结合拥挤距离机制评价同级个体的优劣。为提高算法收敛性能,在趋向性操作结束后引入精英保留策略保留优秀个体,并采用全局信息共享策略引导菌群不断向均匀分布的Pareto最优前沿趋近。通过不同规模算例的对比验证表明了算法的有效性与优越性。     

Robust assembly line balancing with heterogeneous workers

Assembly lines are manufacturing systems in which a product is assembled progressively in workstations by different workers or machines, each executing a subset of the needed assembly operations (or tasks). We consider the case in which task execution times are worker-dependent and uncertain, being expressed as intervals of possible values. Our goal is to find an assignment of tasks and workers to a minimal number of stations such that the resulting productivity level respects a desired robust measure. We propose two mixed-integer programming formulations for this problem and explain how these formulations can be adapted to handle the special case in which one must integrate a particular set of workers in the assembly line. We also present a fast construction heuristic that yields high quality solutions in just a fraction of the time needed to solve the problem to optimality. Computational results show the benefits of solving the robust optimization problem instead of its deterministic counterpart.     

Multi-criteria decision making for assembly line balancing

Assembly line balancing often has significant impact on performance of manufacturing systems, and is usually a multiple-objective problem. Neither an algorithmic nor a procedural assembly line balancing methodology is usually effective in solving these problems. This article proposes a data envelopment analysis (DEA) approach to solve an assembly line balancing problem. A computer-aided assembly line balancing tool as Flexible Line Balancing software is used to generate a considerable number of solutions alternatives as well as to generate quantitative decision-making unit outputs. The quantitative performance measures were considered in this article. Then DEA was used to solve the multiple-objective assembly line balancing problem. An illustrative example shows the effectiveness of the proposed methodology.     

Type II robotic assembly line balancing problem: An evolution strategies algorithm for a multi-objective model

In this paper a different type II robotic assembly line balancing problem (RALB-II) is considered. One of the two main differences with the existing literature is objective function which is a multi-objective one. The aim is to minimize the cycle time, robot setup costs and robot costs. The second difference is on the procedure proposed to solve the problem. In addition, a new mixed-integer linear programming model is developed. Since the problem is NP-hard, three versions of multi-objective evolution strategies (MOES) are employed. Numerical results show that the proposed hybrid MOES is more efficient.     

A new hybrid improvement heuristic approach to simple straight and U-type assembly line balancing problems

This paper presents a new hybrid improvement heuristic approach to simple straight and U-type assembly line balancing problems which is based on the idea of adaptive learning approach and simulated annealing. The proposed approach uses a weight parameter to perturb task priorities of a solution to obtain improved solutions. The weight parameters are then modified using a learning strategy. The maximization of line efficiency (i.e., the minimization of the number of stations) and the equalization of workloads among stations (i.e., the minimization of the smoothness index or the minimization of the variation of workloads) are considered as the performance criteria. In order to clarify the proposed solution methodology, a well known problem taken from literature is solved. A computational study is conducted by solving a large number of benchmark problems available in the literature to compare the performance of the proposed approach to the existing methods such as simulated annealing and genetic algorithms. Some test instances taken from literature are also solved by the proposed approach. The results of the computational study show that the proposed approach performs quite effectively. It also yields optimal solutions for all test problems within a short computational time.     

Multi-objective optimization of stochastic disassembly line balancing with station paralleling

One of the major activities performed in product recovery is disassembly. Disassembly line is the most suitable setting to disassemble a product. Therefore, designing and balancing efficient disassembly systems are important to optimize the product recovery process. In this study, we deal with multi-objective optimization of a stochastic disassembly line balancing problem (DLBP) with station paralleling and propose a new genetic algorithm (GA) for solving this multi-objective optimization problem. The line balance and design costs objectives are simultaneously optimized by using an AND/OR Graph (AOG) of the product. The proposed GA is designed to generate Pareto-optimal solutions considering two different fitness evaluation approaches, repair algorithms and a diversification strategy. It is tested on 96 test problems that were generated using the benchmark problem generation scheme for problems defined on AOG as developed in literature. In addition, to validate the performance of the algorithm, a goal programming approach and a heuristic approach are presented and their results are compared with those obtained by using GA. Computational results show that GA can be considered as an effective and efficient solution algorithm for solving stochastic DLBP with station paralleling in terms of the solution quality and CPU time.     

Evolutionary optimization using epsilon method for resource-constrained multi-robotic disassembly line balancing

This paper concentrates on a resource-constrained multi-robotic disassembly line balancing (RC-MDLB) problem. In this RC-MDLB problem, different types of end-of-life products are disassembled simultaneously on the same line under the following conditions: allocating multiple robots to a workstation to simultaneously process the disassembly tasks that have no precedence relationship with each other, each robot needs a fixed number of limited resources to process tasks, and the total resources for each workstation is fixed. A mathematical model is presented for the RC-MDLB problem to minimize the cycle time and the number of robots being occupied simultaneously. A constrained multi-objective evolutionary algorithm framework and a constrained NSGA-II (E-NSGA-II) algorithm with epsilon method are proposed to handle the constraints of the RC-MDLB problem. The proposed E-NSGA-II is applied to a set of RC-MDLB problem instances introduced in this paper and compared with five representative multi-objective evolutionary algorithms. The experimental results reveal that the proposed E-NSGA-II presents outstanding performance on most of the cases analyzed.     

How to design effective priority rules: Example of simple assembly line balancing

Priority rule-based methods (PRBMs) rely on problem-specific knowledge to construct good solutions in a very short time. They can be used as stand-alone procedures or can be integrated into (partial) enumeration procedures, like branch and bound or dynamic programming, and heuristic solution methods. PRBMs are especially important for solving NP-hard optimization problems.In this paper, we formulate general design principles on how to construct good-performing PRBMs, based on a thorough computational investigation. Our principles allow to construct effective PRBMs already ad hoc, i.e. without time-consuming data mining algorithms. We conduct our analysis on the example of the NP-hard Simple Assembly Line Balancing Problem (SALBP), on which with small modifications most situations in the planning of assembly lines are based. We also provide a cross-validation of our results and illustrate the application of the formulated principles.     

Assembly line balancing under uncertainty: Robust optimization models and exact solution method

This research deals with line balancing under uncertainty and presents two robust optimization models. Interval uncertainty for operation times was assumed. The methods proposed generate line designs that are protected against this type of disruptions. A decomposition based algorithm was developed and combined with enhancement strategies to solve optimally large scale instances. The efficiency of this algorithm was tested and the experimental results were presented. The theoretical contribution of this paper lies in the novel models proposed and the decomposition based exact algorithm developed. Moreover, it is of practical interest since the production rate of the assembly lines designed with our algorithm will be more reliable as uncertainty is incorporated. Furthermore, this is a pioneering work on robust assembly line balancing and should serve as the basis for a decision support system on this subject.     

An efficient branch and bound algorithm for assembly line balancing problems with parallel multi-manned workstations

In the event that big-sized complex products (containing a large number of assembly tasks most of which have long task times) are produced in simple or two-sided assembly lines, hundreds of stations are essentially required. Long product flow time, a large area for establishment of the line, a high budget for the investment of equipment, and tools in stations and several work-in-process are also required for these kinds of products. In order to avoid these disadvantages, assembly lines with parallel multi-manned workstations can be utilized. In this paper, these lines and one of their balancing problems are addressed, and a branch and bound algorithm is proposed. The algorithm is composed of a branching scheme, some efficient dominance and feasibility criteria based on a problem-specific knowledge. A heuristic-based guidance for enumeration process is included as an efficient component of the algorithm as well. VWSolver algorithm proposed for a special version of the problem in the literature has been modified and compared with the proposed algorithm. Results show that proposed algorithm outperforms VWSolver in terms of both CPU times and quality of feasible solutions found.     

An advanced multiobjective genetic algorithm design for the time and space assembly line balancing problem

Time and space assembly line balancing considers realistic multiobjective versions of the classical assembly line balancing industrial problems involving the joint optimization of conflicting criteria such as the cycle time, the number of stations, and/or the area of these stations. In addition to their multi-criteria nature, the different problems included in this field inherit the precedence constraints and the cycle time limitations from assembly line balancing problems, which altogether make them very hard to solve. Therefore, time and space assembly line balancing problems have been mainly tackled using multiobjective constructive metaheuristics. Global search algorithms in general - and multiobjective genetic algorithms in particular - have shown to be ineffective to solve them up to now because the existing approaches lack of a proper design taking into account the specific characteristics of this family of problems. The aim of this contribution is to demonstrate the latter assumption by proposing an advanced multiobjective genetic algorithm design for the 1/3 variant of the time and space assembly line balancing problem which involves the joint minimization of the number and the area of the stations given a fixed cycle time limit. This novel design takes the well known NSGA-II algorithm as a base and considers the use of a new coding scheme and sophisticated problem specific operators to properly deal with the said problematic questions. A detailed experimental study considering 10 different problem instances (including a real-world instance from the Nissan plant in Barcelona, Spain) will show the good yield of the new proposal in comparison with the state-of-the-art methods.     

A meta-heuristic algorithm for the fuzzy assembly line balancing type-E problem

Consideration is given to a single-model assembly line balancing problem with fuzzy task processing times. The problem referred to herein as f-SALBP-E consists of finding a combination of the number of workstations and the cycle time as well as a respective line balance such that the efficiency of the line is maximized. f-SALBP-E is an extension of the classical SALBP-E under fuzziness. First, a formulation of the problem is given with the tasks processing times presented by triangular fuzzy membership functions. Then, since the problem is known to be NP-hard, a meta-heuristic based on a Genetic Algorithm (GA) is developed for its solution. The performance of the proposed solution approach is studied and discussed over multiple benchmarks test problems taken from the open literature. The results demonstrate very satisfactory performance for the developed approach in terms of both solution time and quality.     

Firing sequences backward algorithm for simple assembly line balancing problem of type 1

The objective of simple assembly line balancing problem type-1 (SALBP-1) is to minimize the number of workstations on an assembly line for a given cycle time. Since SALBP-1 is NP-hard, many iterative backtracking heuristics based on branch and bound procedure, tabu search, and genetic algorithms were developed to solve SALBP-1. In this study, a new heuristic algorithm based on Petri net approach is presented to solve the problem. The presented algorithm makes an order of firing sequence of transitions from Petri net model of precedence diagram. Task is assigned to a workstation using this order and backward procedure. The algorithm is coded in MATLAB, and its efficiency is tested on Talbot’s and Hoffmann’s benchmark datasets according to some performance measures and classifications. Computational study validates its effectiveness on the benchmark problems. Also comparison results show that the algorithm is efficiency to solve SALBP-1.     

拆卸线平衡问题的改进细菌觅食优化算法

拆卸是产品回收过程中最重要的环节,拆卸过程高效与否直接影响产品的回收效率。为克服传统算法求解拆卸线平衡问题时性能不稳定的缺陷,在构建基于工作站利用率、负荷均衡,尽早拆卸有危害、高需求的零件,最小化拆卸成本等方面的拆卸线平衡问题多目标优化模型的基础上,提出一种改进的细菌觅食优化算法对问题求解。通过改进细菌的移动规则扩大搜索空间,引入全局信息共享策略增强算法收敛性能,定义了一种自适应驱散概率防止驱散操作中解的退化。在对不同规模算例的对比分析中,验证了该算法的有效性。     

A solution procedure for type E simple assembly line balancing problem

This paper presents a type E simple assembly line balancing problem (SALBP-E) that combines models SALBP-1 and SALBP-2. Furthermore, this study develops a solution procedure for the proposed model. The proposed model provides a better understanding of management practice that optimizes assembly line efficiency while simultaneously minimizing total idle time. Computational results indicated that, under the given upper bound of cycle time (ct_max), the proposed model can solve problems optimally with minimal variables, constraints, and computing time.