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.     

Erratum to “A solution procedure for type E simple assembly line balancing problem”

The objective of SALBP-E is to minimize the product on the number of workstations by the cycle time. Recently Wei and Chao [Comput. Ind. Eng. 61 (2011) 824–830] have proposed an exact procedure for solving this problem. It is based on solving iteratively SALBP-2 by means of a MILP model. SALBP-E has not been much studied and hence the high interest of their work. However, the article has several errors that make its understanding harder and, moreover, impede the correct implementation of their procedure for solving SALBP-E. Therefore, it is important to correct them.     

Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model

This paper is the first one of the two papers entitled “modeling and solving mixed-model assembly line balancing problem with setups”, which has the aim of developing the mathematical programming formulation of the problem and solving it with a hybrid meta-heuristic approach. In this current part, a mixed-integer linear mathematical programming (MILP) model for mixed-model assembly line balancing problem with setups is developed. The proposed MILP model considers some particular features of the real world problems such as parallel workstations, zoning constraints, and sequence dependent setup times between tasks, which is an actual framework in assembly line balancing problems. The main endeavor of Part-I is to formulate the sequence dependent setup times between tasks in type-I mixed-model assembly line balancing problem. The proposed model considers the setups between the tasks of the same model and the setups because of the model switches in any workstation. The capability of our MILP is tested through a set of computational experiments. Part-II tackles the problem with a multiple colony hybrid bees algorithm. A set of computational experiments is also carried out for the proposed approach in Part-II.     

Improved integer programming models for simple assembly line balancing and related problems

We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations using impulse variables, and produces solutions of significantly better quality in practice. The improved formulation can be used to strengthen related problems with similar restrictions. We demonstrate their effectiveness on the U‐shaped assembly line balancing problem and on the bin packing problem with precedence constraints.     

Two-sided assembly line balancing problem of type I: Improvements,a simple algorithm and a comprehensive study

Many meta-heuristic methods have been applied to solve the two-sided assembly line balancing problem of type I with the objective of minimizing the number of stations, but some of them are very complex or intricate to be extended. In addition, different decoding schemes and different objectives have been proposed, leading to the different performances of these algorithms and unfair comparison. In this paper, two new decoding schemes with reduced search space are developed to balance the workload within a mated-station and reduce sequence-depended idle time. Then, graded objectives are employed to preserve the minor improvements on the solutions. Finally, a simple iterated greedy algorithm is extended for the two-sided assembly line balancing problem and modified NEH-based heuristic is introduced to obtain a high quality initial solution. And an improved local search with referenced permutation and reduced insert operators is developed to accelerate the search process. Computational results on benchmark problems prove the efficiency of the proposed decoding schemes and the new graded objectives. A comprehensive computational comparison among 14 meta-heuristics is carried out to demonstrate the efficiency of the improved iterated greedy algorithm.     

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.     

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

Two-sided assembly lines are especially used at the assembly of large-sized products, such as trucks and buses. In this type of a production line, both sides of the line are used in parallel. In practice, it may be necessary to optimize more than one conflicting objectives simultaneously to obtain effective and realistic solutions. This paper presents a mathematical model, a pre-emptive goal programming model for precise goals and a fuzzy goal programming model for imprecise goals for two-sided assembly line balancing. The mathematical model minimizes the number of mated-stations as the primary objective and it minimizes the number of stations as a secondary objective for a given cycle time. The zoning constraints are also considered in this model, and a set of test problems taken from literature is solved. The proposed goal programming models are the first multiple-criteria decision-making approaches for two-sided assembly line balancing problem with multiple objectives. The number of mated-stations, cycle time and the number of tasks assigned per station are considered as goals. An example problem is solved and a computational study is conducted to illustrate the flexibility and the efficiency of the proposed goal programming models. Based on the decision maker's preferences, the proposed models are capable of improving the value of goals.     

Optimisation of mixed-model assembly line balancing problem under uncertain demand

Assembly lines play a crucial role in determining the profitability of a company. Market conditions have increased the importance of mixed-model assembly lines. Variations in the demand are frequent in real industrial environments and often leads to failure of the mixed-model assembly line balancing scheme. Decision makers have to take into account this uncertainty. In an assembly line balancing problem, there is a massive amount of research in the literature assuming deterministic environment, and many other works consider uncertain task times. This research utilises the uncertainty theory to model uncertain demand and introduces complexity theory to measure the uncertainty of assembly lines. Scenario probability and triangular fuzzy number are used to describe the uncertain demand. The station complexity was measured based on information entropy and fuzzy entropy to assist in balancing systems with robust performances, considering the influence of multi-model products in the station on the assembly line. Taking minimum station complexity, minimum workload difference within station, maximum productivity as objective functions, a new optimization model for mixed-model assembly line balancing under uncertain demand was established. Then an improved genetic algorithm was applied to solve the model. Finally, the effectiveness of the model was verified by several instances of mixed-model assembly line for automobile engine.     

A hybrid genetic algorithm for mixed model assembly line balancing problem with parallel workstations and zoning constraints

In this paper, we propose a hybrid genetic algorithm to solve mixed model assembly line balancing problem of type I (MMALBP-I). There are three objectives to be achieved: to minimize the number of workstations, maximize the workload smoothness between workstations, and maximize the workload smoothness within workstations. The proposed approach is able to address some particular features of the problem such as parallel workstations and zoning constraints. The genetic algorithm may lack the capability of exploring the solution space effectively. We aim to improve its exploring capability by sequentially hybridizing the three well known heuristics, Kilbridge & Wester Heuristic, Phase-I of Moodie & Young Method, and Ranked Positional Weight Technique, with genetic algorithm. The proposed hybrid genetic algorithm is tested on 20 representatives MMALBP-I and the results are compared with those of other algorithms.     

A genetic algorithm based approach to the mixed-model assembly line balancing problem of type II

Mixed-model assembly lines allow for the simultaneous assembly of a set of similar models of a product, which may be launched in the assembly line in any order and mix. As current markets are characterized by a growing trend for higher product variability, mixed-model assembly lines are preferred over the traditional single-model assembly lines.

This paper presents a mathematical programming model and an iterative genetic algorithm-based procedure for the mixed-model assembly line balancing problem (MALBP) with parallel workstations, in which the goal is to maximise the production rate of the line for a pre-determined number of operators.

The addressed problem accounts for some relevant issues that reflect the operating conditions of real-world assembly lines, like zoning constraints and workload balancing and also allows the decision maker to control the generation of parallel workstations.     

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.     

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.     

用改进的遗传算法解决ALB问题

针对生产装配线平衡问题,提出一种改进的遗传算法.算法采用缩放适应度法、随机普遍取样的选择策略、线性可变的杂交和变异算子.使用PB语言实现了这一应用平台,给出了系统的功能结构图和主要的数据结构,并结合实例给出了ALB-2问题的解决方案.实例对比证明,改进的算法很好地解决了简单遗传算法易早熟的问题,大大改善了简单算法的性能.     

单一产品复杂装配线启发式平衡排产方法

提出了一种基于Excel的单一产品复杂装配线启发式平衡排产方法。给出了基于Excel的单一产品复杂装配线启发式平衡排产方法的总体技术方案;阐述了该方法中的五个关键技术,包括将装配优先图映射为工作表,工序后接数及阶位值计算,工序排序,装配线平衡,装配线排产;通过案例分析验证了该方法的有效性。     

Modeling and solving constrained two-sided assembly line balancing problem via bee algorithms

Designing and operating two-sided assembly lines are crucial for manufacturing companies which assemble large-sized products such as trucks, buses and industrial refrigerators. This type of assembly line structure has several advantages over one-sided assembly lines such as shortened line length and reduced throughput time. The research area has recently focused on balancing two-sided assembly lines owing to these advantages. However, due to the complex structure of this problem, some practical constraints have been disregarded or have not been fully incorporated. In order to overcome these deficiencies, a fully constrained two-sided assembly line balancing problem is addressed in this research paper. Initially, a mathematical programming model is presented in order to describe the problem formally. Due to the problem complexity, two different swarm intelligence based search algorithms are implemented to solve large-sized instances. Bees algorithm and artificial bee colony algorithm have been applied to the fully constrained two-sided assembly line balancing problem so as to minimize the number of workstations and to obtain a balanced line. An extensive computational study has also been performed and the comparative results have been evaluated.     

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 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.     

Two-sided assembly line balancing considering the relationships between tasks

Previous studies of the two-sided assembly line balancing problem assumed equal relationships between each two tasks assignable to a side of the line. In practice, however, this relationship may be related to such factors as the distance between the implementation place and the tools required for implementation. We know that the more relationships exist between the tasks assigned to each station, the more efficient will be the assembly line. In this paper, we suggest an index for calculating the value of the relationship between each two tasks, and define a performance criterion called ‘assembly line tasks consistency’ for calculating the average relationship between the tasks assigned to the stations of each solution. We propose a simulated annealing algorithm for solving the two-sided assembly line balancing problem considering the three performance criteria of number of stations, number of mated-stations, and assembly line tasks consistency. Also, the simulated annealing algorithm is modified for solving the two-sided assembly line balancing problem without considering the relationships between tasks. This modification finds five new best solutions for the number of stations performance criterion and ten new best solutions for the number of mated-stations performance criterion for benchmark instances.     

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 mathematical model and a genetic algorithm for two-sided assembly line balancing

A two-sided assembly line is a type of production line where tasks are performed in parallel at both sides of the line. The line is often found in producing large products such as trucks and buses. This paper presents a mathematical model and a genetic algorithm (GA) for two-sided assembly line balancing (two-ALB). The mathematical model can be used as a foundation for further practical development in the design of two-sided assembly lines. In the GA, we adopt the strategy of localized evolution and steady-state reproduction to promote population diversity and search efficiency. When designing the GA components, including encoding and decoding schemes, procedures of forming the initial population, and genetic operators, we take account of the features specific to two-ALB. Through computational experiments, the performance of the proposed GA is compared with that of a heuristic and an existing GA with various problem instances. The experimental results show that the proposed GA outperforms the heuristic and the compared GA.