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The simple assembly line balancing problem with parallel workstations - A simulated annealing approach
Abstract
This work presents a new mathematical programming model for the simple assembly line balancing problem with parallel workstations that allows the user to control the way workstations are 'parallelised'. As in the conventional procedures the user can limit the number of replicas allowed for each workstation, but in this novel approach the user can also define a minimum task time to trigger the replication of the workstations. Another important characteristic of the model is that it simultaneously minimises the number of workstation and smoothes the workload among them. Due to the model complexity a simulated annealing approach is proposed to solve it. An example is used for illustration and computational experience is provided. The computational tests show that the performance of the proposed procedure is quite good, taking into account the problem complexity. Significance: Assembly lines are employed for high volumes of output, so the global savings that result from a small reduction in unit costs, fostered by a correctly balanced line, can be important, The proposed model introduces a more realistic approach to assembly line balancing than previous ones.
... Some researchers have used the simulated annealing method in their approach [28][29][30][31][32][33][34][35]. ...
... Hong and Cho [29] applied SA to generate linebalanced assembly sequences for robotic assembly in a single-model and deterministic ALBP, considering assembly constraints and assembly cost and idle time. McMullen and Frazier [30] and Simaria and Vilarinho [31] developed a simulated annealing based technique to solve a multi-objective ALBP when paralleling of workstations is permitted. ...
The purpose of this report is to review and outline the methodologies and tools in assembly process planning developed during the past ten years, such as the application of meta-heuristics methods to find the optimal/near optimal assembly plans and assembly line balancing, the evaluation methods for Design for Assembly (DFA), and collaborative assembly process planning systems. Based on the review, the future trends in this area are also identified and discussed.
... We note from the previous studies that the parallelism concept in ALB can be divided into different categories such as paralleling assembly lines (Suer, 1998;Gokcen et al., 2006), workstations (Bard, 1989;Askin and Zhou, 1997;Simaria and Vilarinho, 2001;Tiacci et al., 2006), tasks (Pinto et al., 1975;Kaplan, 2004;Kazemi et al., 2011) and works (Bartholdi, 1993;Kim et al., 2000;Lee et al., 2001). We also note that paralleling tasks as considered in our study is defined as assigning a task to more than one workstation, which is different from some other schemes where it is possible to divide tasks into smaller units assigned to different stations. ...
In this study, a mathematical programming model for using dynamically-positioned-rework stations for performing parallel tasks in assembly line balancing is proposed. We first introduce a nonlinear programming model, which is quadratic in constraints resulting from the modeling of the parallel task assignment and dynamic positioning of the rework station. We also establish some novel logical conditions in the model building process while deriving the proposed formulation. In the next step, we present appropriate variable transformations for linearization to take advantage of the algorithms for solving linear programs by noting that the quadratic expressions of the model are present as either the multiplications of binaries or binaries multiplied by continuous variables. After implementing the corresponding variable transformations, the model is transformed to a linear-mixed-integer program. A numerical example is then presented using the resulted linear model for illustration. We also perform some computational experiments using sample problems from the related literature to analyze the performance of the model.
... It is noted that one of the factors affecting the cycle time of an assembly line is about the parallelism concept that can be classified into different categories such as paralleling assembly lines (Suer 1998;Gokcen et al., 2006), workstations (Bard, 1989;Askin and Zhou, 1997, Tiacci et al., 2006, Simaria and Vilarinho., 2001, tasks (Pinto et al., 1975;Kaplan, 2004;Kazemi et al., 2011) and works (Bartholdi, 1993;Kim et al., 2000;Lee et al., 2001) considering the previous studies in the literature. Note that paralleling tasks as considered in this study is defined as the assignment of a task to more than one workstation. ...
p>In assembly lines, rework stations are generally used for reprocessing defective items. On the other hand, using rework stations for this purpose only might cause inefficient usage of the resources in this station especially in an assembly line with a low defective rate. In this study, a mixed-integer programming model for cycle time minimization is proposed by considering the use of rework stations for performing parallel tasks. By linearizing the non-linear constraint about parallel tasks using a variate transformation, the model is transformed to a linear-mixed-integer form. In addition to different defective rates, different rework station positions are also considered using the proposed model. The performance of the model is analyzed on several test problems from the related literature . </p
... The recommended approach is implemented to an ALBP in a textile firm and to a select set of benchmark problems from the literature to show the influences of PWLs. Simaria and Vilarinho (2001) considered minimizing the number of workstations and the variability of workload among workstations simultaneously. Choi (2009) presented a zero-one integer programming model that integrates PW with different risk factors and processing times for the ALBP. ...
This paper investigates Assembly Line Worker Assignment and Balancing Problem (ALWABP), focusing specifically on productive workload differences due to age and gender of workers, to minimize the number of workstations. Most of the published papers on assembly line balancing problems (ALBP) are focused only on the task processing times. However, this may cause an overload in work assignments for certain workers. A work-overload may cause fatigue and thus lead to a decrease in line efficiency and factory productivity, and also result in an increase in quality problems and work-related injuries. To avoid the negative implications of work-overload conditions, this paper assigns tasks among workstations without exceeding the cycle time or the age and gender-adjusted physical workload capacity (PWLC). We propose a regression model to determine age and gender-based PWLC. Six different age categories are analyzed to show the impacts of age and gender on PWLC. We propose a binary (0-1) integer linear programming (BILP) for ALWABP, where age and gender-adjusted PWLC is considered. The efficiency of the model is shown on test problems and a real-life application in a textile firm. An ALWABP is considered taking into account the processing times and physical workloads for a textile factory assembly line of 53 tasks. The numbers of stations for ALWABP without and with the physical workload in the textile firm assembly line case are 5 and 6, respectively. All workstations are balanced in terms of physical workload and processing times. The results show that advancing average age increases the number of stations (NS), and this situation triggers a reduction in line efficiency (LE) and PWLC utilization ratio.
... However, only few studies are reported on parallel assembly line. A state of art review on multiple and parallel assembly lines has been presented by Lusa [7].A new mathematical model for assembly line balancing problem with parallel workstations to control the way workstations are 'parallelised' is proposed by Simaria and Vilarinho [8]. Bard [9] has proposed analgorithm for solving an assembly line-balancing problem with parallel workstations. ...
: Assembly line balancing is a production policy that sets a planned rate of production to yield a product within a
particular time frame. Productivity enhancement in assembly lines is vital as it increases the capacity and at the same time
reduces the cost. One possible means to increase the capacity is to used parallel assembly lines.
The paper presents a new method to solve assembly line balancing problems in case of multiple lines. The procedure is explained
with the help of suitable example. In many cases an industry utilizes more than one line to make same or different products at
the same time independently. Working of the lines concurrently with common resources plays a vital role in minimization of the
resource resulting in reduced production cost. The proposed system offers a substantial improvement in the assembly line
efficiency when more than one line is necessary.
... There are literally various methods for solving SALB problem such as branch and bound (Pinto et al., 1975;Bukchin & Rabinowitch, 2006;Miralles et al. 2008;Ege et al., 2009) and dynamic programming (Henig, 1986;Bautista & Pereira, 2007). There are also several heuristics (Shin, 1990) and metaheuristics to solve this type problem including genetic algorithm (Rubinovitz & Levitin, 1995;Kim et al., 1996;Levitin et al., 2006;Tasan, & Tunali, 2008), Simulated annealing (Simaria & Vilarinho, 2001;Özcan, 2010;Seyed-Alagheband et al., 2011), tabu search (Lapierre et al., 2006), Ant Colony (Chica et al., 2011;McMullen & Tarasewich, 2003), differential evolution algorithm (Nourmohammadi & Zandieh, 2011;Zhang et al., 2016), There are also different techniques to tackle uncertainty associated with parameters in SALB (Reeve & Thomas, 1973;Andres et al., 2008;Silverman & Carter, 1986). Moreover, a class of SALB problem can be analyzed using simulation methods (Driscolla & Abdel-Shafi, 1985). ...
Modeling the simple assembly line balancing (SALB) problem has covered a wide range of real-world applications. The recent advances in optimization problems have created the opportunities to tackle more challenging problems. This paper presents a multi-objective decision making problem to consider two objectives, cost and cycle time, for simple assembly line balancing. The problem is formulated as a mixed integer nonlinear optimization and the proposed study of this paper uses two metaheuristics to solve the resulted problem on some benchmark problems. The preliminary results have indicated that multi objective particle swarm optimization (MOPSO) has provided better quality solutions while the hybrid method based on MOPSO and simulated annealing has yielded more non-dominated Pareto solutions.
... Much research has been conducted on the SDM as a general ALB problem (Baybars [16], Erel and Sarin [20], Jin and Wu [22], Simaria and Vilarinho [23]). Meanwhile research on the stochastic model has been remarkably limited. ...
In uncertain cases, the result and efficiency of a current period (or production cycle) are in?uenced not only by the risks which exist in current period but also by the risks which exist in the previous ones. What is more, the risk itself is also affected greatly by the risks which exist in the earlier periods. This kind of problem is called a limited-cycle problem with multiple periods. Normally, workers ’efficiency is different on different tasks. How can we get an optimal assignment to minimize the total expected costs? In this paper, we consider the optimal worker assignment considering two kinds of efficiency, clever or poor efficiency on tasks. The regularity will be described that n-1 workers have two clever tasks of all, 1 worker has no clever task by contrast. Also, some numerical experiments will be done to check out the regularity of the optimal assignment that each worker has two or three clever tasks.
The simple assembly line balancing problem (SALBP) considers work division among different workstations of a serially arranged assembly process to maximise its efficiency under workload (cumulative) and technological (precedence) constraints. In this work, we consider a variant of the SALBP which allows parallel workstations. To study the effect of parallel stations, we propose a new problem (the parallel station assembly line balancing problem or PSALBP) in which the objective is to minimise the number of parallel stations required to obtain the maximum theoretical efficiency of the assembly process. We study the complexity of the problem and identify a polynomially solvable case. This result is then used as a building block for the development of a heuristic solution procedure. Finally, we carry out a computational experiment to identify the characteristics of assembly lines that may benefit from station paralleling and to evaluate the performance of the proposed heuristic.
In turbulent times featuring increased customisation, higher demand volatility, and shortened product life cycles, companies gain a competitive advantage by adopting a single yet highly flexible assembly line. A cornerstone of today's production systems is determining the optimal takt time (or cycle time) by aligning the assembly pace with the desired level of output. In practice, most companies rely on a fixed takt time, even when the work content between models varies considerably. We show that, in contrast to a fixed takt system, variable takt times reduce not only labour inefficiencies but also the complexity of the mixed-model assembly line balancing problem. Inspired by our industry partner Fendt, an innovation leader in the global agricultural machinery market and benchmark for a wide range of industries, we define a generalisable mixed-integer programming model that accounts for key conditions neglected in previous research – in particular, random customisation through configuration-specific task times and assembly quality by assigning operator workloads to ‘zones’. Introducing such operator work zones reveals that firms need not face a time–quality trade-off whereby takt time must be prioritised over how well work is performed. Our numerical study and takt time sensitivity analysis document the effectiveness of this approach when its results are compared with those under Fendt's current takt times.
The problem of assembly sequence generation is complex and has proven to be difficult to solve. Various method have been used in attempting to solve the problem, including mathematical modeling and search techniques. This paper presents an investigation for analyzing assembly sequences of assembly systems with a proposed neural network predictor. The proposed neural network has three layers with recurrent structure. A fast learning algorithm Backpropagation (BP) algorithm is employed for updating the weight parameters of the proposed network. Significance: An ordered and sequenced connection process of parts existing in a system is known as assembly. Assembly sequence planning is the choice of the most optimum one. Although much research has been conducted in the field, there are still some shortcomings related to the sequence planning of large system. The developed assembly sequence planning system is graph based and automatic. By optimization, the best assembly sequences are determined. Due to parallel structure and fast learning with small errors, the neural network can be employed as an algorithm for this kind of assembly systems.
This paper presents a dynamic programming (DP) algorithm for solving an assembly line-balancing )ALB( problem with parallel workstations. Solutions represent a trade-off between the minimum number of stations required to achieve a balance and the cost of installing additional facilities. Both task costs and equipment costs are considered. A second feature of the algorithm is that it takes into account unproductive time during a cycle.The advantage of the DP approach is that it readily permits the recursive relationship associated with the serial ALB problem to be modified to accommodate the cost of paralleling. Solutions are obtained with an enumeration scheme that exploits known lower bounds. Two examples, and the results from a series of industry-based test problems, are presented to highlight the computations. In general, the algorithm performs well, but runs into trouble when the order strength of the underlying precedence graph is close to one or zero.
In this paper we investigate and depict the similarities and the performance of simulated annealing and tabu search. Different modern search methods which are used for combinatorial problems have a common structure. The realisation of both methods is shown for the assembly line balancing problem and the performance is compared. The problem set consists of well known literature problems. In this comparison tabu search is successful and superior to other methods.
The problem of balancing assembly lines with stochastic task processing times is addressed. The size of the problems that can be solved by optimal methods is limited and hence many heuristics have been developed, which give sub-optimal solutions. An approach for solving the problem using the simulated annealing technique is presented here. The proposed approach tries to reach the global optimum by not getting trapped at the different local optimum points. Another feature of this method is the non-dependence of the final solution on the initial solution. Solutions for line balancing problems obtained using the above method compare favourably with the results of other greedy heuristics.
A critical assumption in balancing assembly lines is that the line is ‘ serial ’ with no ‘ paralleling’ of tasks allowed. This constrains the cycle time to be at least equal to the maximum task time, which in turn limits the production rate. One alternative to increasing the production rate (hence lowering the cycle time) is by allowing parallel tasks in the assembly line at the cost of additional facilities. In this case, the problem becomes one of selecting the tasks to be paralleled such that the total cost is minimized. This problem is formulated as a mixed integer programme, and a branch and bound algorithm is presented for its solution. The structural properties of this programming problem are discussed, which con be used to improve the computational efficiency of our branch and bound algorithm. An illustrative problem and preliminary computational results are provided.
An efficient single-pass heuristic method capable of finding good solutions for the single-model deterministic line balancing problem is presented. The method involves four phases for simplifying a given problem, reducing its size and decomposing it into smaller subproblems when appropriate. The solution is then found by using combinations of various heuristic rules. The procedure is illustrated on the 70-task problem of Tonge (1960)and computational results on well-known test problems are reported.
This paper describes a generalized heuristic to balance an assembly line where the task times may be smaller or greater than the specified cycle time. The tasks are primarily assigned to different stages by choosing different stage cycle times so as to have the stage idleness within the specified limit. Later, the line is further balanced and the stage idleness is smoothed by trading and transferring the tasks, or crashing the worst stages. The line is then balanced by adjusting the manpower at different stages. Several proofs and models have been formulated regarding the generalization of paralleling to serial line balance, some design aspects of manpower utilization, the superiority rule of strategic policy for choosing stage cycle times, etc. The balance is chosen through cost optimization.
A comparative investigation is performed on the (optimizing) algorithms which have appeared in the literature to solve the basic assembly line balancing problem. Each algorithm is subjected to a series of test problems, and the computation times are notedIt was observed that problems of 20 tasks were within the capabilities of most algorithms studied. Solutions could he found for 40-task problems if the average number of tasks per station was no more than four. For the 20-task problems, branch and bound algorithms performed the best for problems with four or more tasks per station, while a particular dynamic programming formulation performed best on problems with an average of two tasks per stationDetails of a newest node search branch and bound algorithm, where arcs represent stations is presented. This algorithm performed successfully in the investigation.
A critical assumption made in formulating the classical assembly line balancing model is that the line is ‘serial’ with no ‘paralleling’ of stations allowed. A model is proposed here which allows the paralleling of stations, thereby achieving a higher production rate and lower labour costs. The mathematical formulation of the proposed model results in a mixed integer program. A branch and bound and a heuristic solution procedure, derived from the branch and bound method, are presented. An example problem is used for illustration. Some computational experience is also provided.
A case is stated for extending the techniques of assembly line balancing to provide for the parallel operation of identical stations, where this leads to a reduction in idle time. The practical implications of operating with this type of system are discussed, both for the stations themselves and the line as a whole, with reference to various classifications of assembly line, and ways in which balancing can be made to fit into an overall strategy for production line design are touched upon. Two distinct types of computer program have been developed to enable multiple stations to become a recognised feature incorporated into "heuristic" line balancing, rather than an appendage to be applied ad hoc by industrial engineers when current techniques have proven inadequate. One approach is based on a more sophisticated version of the `positional weight' method while the other relies on the contrasting philosophy of the "random generation" method, and a comparison is made of their relative success in solving two assembly line problems, and their potential from an industrial viewpoint.