A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements

In this study we consider a U-shaped assembly line balancing problem where each task uses a specified set of equipments and each type of equipment has a specified cost. Our problem is to assign the tasks together with their equipments to the workstations so as to minimize the total equipment cost. We formulate the problem as a mixed integer linear programming model that is capable of solving small sized instances. We propose a branch and bound algorithm that uses efficient precedence relations and lower bounds. We find that the algorithm is able to solve moderate sized problem instances in reasonable times.     

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 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.     

An efficient hybrid genetic algorithm to solve assembly line balancing problem with sequence-dependent setup times

In this paper the setup assembly line balancing and scheduling problem (SUALBSP) is considered. Since this problem is NP-hard, a hybrid genetic algorithm (GA) is proposed to solve the problem. This problem involves assigning the tasks to the stations and scheduling them inside each station. A simple permutation is used to determine the sequence of tasks. To determine the assignment of tasks to stations, the algorithm is hybridized using a dynamic programming procedure. Using dynamic programming, at any time a chromosome can be converted to an optimal solution (subject to the chromosome sequence).     

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.     

Generating subproblems in branch and bound algorithms for parallel machines scheduling problem

A branch and bound algorithm (B&B) has been widely used in various discrete and combinatorial optimization fields. To obtain optimal solutions as soon as possible for scheduling problems, three tools, which are branching, bounding and dominance rules, have been developed in the B&B algorithm. One of these tools, a branching is a method for generating subproblems and directly determines size of solution to be searched in the B&B algorithm. Therefore, it is very important to devise effective branching scheme for the problem.In this note, a survey of branching schemes is performed for parallel machines scheduling (PMS) problems with n independent jobs and m machines and new branching schemes that can be used for identical and unrelated PMS problems, respectively, are suggested. The suggested branching methods show that numbers of generated subproblems are much smaller than that of other methods developed earlier and therefore, it is expected that they help to reduce a lot of CPU time required to obtain optimal solutions in the B&B algorithm.     

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 branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property

We focus on the problem of scheduling n independent jobs on m identical parallel machines with the objective of minimizing total tardiness of the jobs considering a job splitting property. In this problem, it is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. We develop several dominance properties and lower bounds for the problem, and suggest a branch and bound algorithm using them. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of moderate sizes in a reasonable amount of computation time.     

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 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.     

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.     

Decomposition-based bi-objective optimization for sustainable robotic assembly line balancing problems

Due to the increasing greenhouse gas emissions and the energy crisis, the manufacturing industry which is one of the most energy intensive sector is paying close attention to the improvement of environmental performance efficiency. Therefore, in this paper the automated assembly line is balanced in a sustainable way which aims to optimize a green manufacturing objective (the total energy consumption) and a productivity-related objective (similar working load) simultaneously. A comprehensive total energy consumption of each processing stage was analyzed and modeled. To make the model more practical, a sequence-based changeover time and robots with different efficiencies and energy consuming rates are considered and optimized. To properly solve the problem, the proposed novel optimal solution takes the well-known MOEA/D as a base and incorporates a well-designed coding scheme and a problem-specific local search mechanism. Computational experiments are conducted to evaluated each improving strategies of the algorithm and its superiority over two other high-performing multi-objective optimization methods. The model allows decision makers to select more sustainable assembly operations based on their decision impacts in both productivity and energy-saving.     

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.     

Accumulated risk of body postures in assembly line balancing problem and modeling through a multi-criteria fuzzy-genetic algorithm

Monotonous body postures during repetitive jobs negatively affect assembly-line workers with the developing of Work-related Musculoskeletal Disorders (WMSDs). Ergonomics specialists have offered auxiliary posture diversity to deal with the lack of varieties, especially for high-risk ones. Meanwhile, Assembly Line Balancing (ALB) problem has been recognized as a prior thinking to (re)configure assembly lines via the balancing of their tasks among their workstations. Some conventional criteria, cycle time and overall workload are often considered during the balancing. This paper presents a novel model of ALB problem that incorporates assembly worker postures into the balancing. In addition to the conventional ALB criteria, a new criterion of posture diversity is defined and contributes to enhance the model. The proposed model suggests configurations of assembly lines via the balancing; so that the assigned workers encounter the opportunities of changing their body postures, regularly. To address uncertainties in the conventional criteria, a fuzzy goal programming is used, and an appropriate genetic algorithm is developed to deal with the model. Various computational tests are performed on the different models made with combinations of the three criteria mentioned above. Comparing the pay-offs among the combinations, results show that well balanced task allocation can be obtained through the proposed model.     

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.     

On solving the assembly line worker assignment and balancing problem via beam search

Certain types of manufacturing processes can be modelled by assembly line balancing problems. In this work we deal with a specific assembly line balancing problem that is known as the assembly line worker assignment and balancing problem (ALWABP). This problem appears in settings where tasks must be assigned to workers, and workers to work stations. Task processing times are worker specific, and workers might even be incompatible with certain tasks. The ALWABP was introduced to model assembly lines typical for sheltered work centers for the Disabled.     

A hybrid algorithm for allocating tasks,operators, and workstations in multi-manned assembly lines

In a car, there are approximately 30,000 parts produced by many different industries. This is due to the complexity and enormity of the automotive industry chain. The vehicle assembly process comprises welding, painting, prefabrication, and final entire-vehicle assembly. The assembly line has the largest labor force, which should be arranged and balanced to increase production efficiency and reduce labor force requirements. Unlike traditional studies on assembly line balancing problems (ALBPs), this study considers the characteristics of the automotive industry, such as multi-manned workstations, minimization in terms of the numbers of operators and workstations for streamlined production, budget constraints, the optimization of both task and operator allocation among workstations, and the determination of the start/end processing time of each task at different workstations. To address these NP-hard problems, a hybrid heuristic approach that combines the procedure of building feasible balancing solutions and the simulated annealing algorithm is proposed to map out an optimal line balancing plan for multi-manned workstations and to reduce the required workspace for shop operations. Based on the design and analysis of experiments, the effects of the maximum number of allowed operators per workstation and those of the cycle time on ALBP solutions are explored. The optimal combination of algorithm parameters is also determined. The results of this study can serve as a practical reference in planning the allocation of tasks, workstations, and operators in the industry.     

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.     

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.