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Alvarez-Miranda, E., & Pereira, J. (2019). On the complexity of assembly line balancing problems. Comput. Oper. Res., 108, 182–186.
Abstract: Assembly line balancing is a family of combinatorial optimization problems that has been widely studied in the literature due to its simplicity and industrial applicability. Most line balancing problems are NP-hard as they subsume the bin packing problem as a special case. Nevertheless, it is common in the line balancing literature to cite [A. Gutjahr and G. Nemhauser, An algorithm for the line balancing problem, Management Science 11 (1964) 308-315] in order to assess the computational complexity of the problem. Such an assessment is not correct since the work of Gutjahr and Nemhauser predates the concept of NP-hardness. This work points at over 50 publications since 1995 with the aforesaid error. (C) 2019 Elsevier Ltd. All rights reserved.
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Alvarez-Miranda, E., Chace, S., & Pereira, J. (2021). Assembly line balancing with parallel workstations. Int. J. Prod. Res., 59(21), 6486–6506.
Abstract: 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.
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Alvarez-Miranda, E., Pereira, J., Torrez-Meruvia H., & Vila, M. (2021). A Hybrid Genetic Algorithm for the Simple Assembly Line Balancing Problem with a Fixed Number of Workstations. Mathematics, 9(17), 2157.
Abstract: The assembly line balancing problem is a classical optimisation problem whose objective is to assign each production task to one of the stations on the assembly line so that the total efficiency of the line is maximized. This study proposes a novel hybrid method to solve the simple version of the problem in which the number of stations is fixed, a problem known as SALBP-2. The hybrid differs from previous approaches by encoding individuals of a genetic algorithm as instances of a modified problem that contains only a subset of the solutions to the original formulation. These individuals are decoded to feasible solutions of the original problem during fitness evaluation in which the resolution of the modified problem is conducted using a dynamic programming based approach that uses new bounds to reduce its state space. Computational experiments show the efficiency of the method as it is able to obtain several new best-known solutions for some of the benchmark instances used in the literature for comparison purposes.
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Alvarez-Miranda, E., Pereira, J., Vargas, C., & Vila, M. (2022). Variable-depth local search heuristic for assembly line balancing problems. Int. J. Prod. Res., 61(9), 3103–3121.
Abstract: Assembly lines are production flow systems wherein activities are organised around a line consisting of various workstations through which the product flows. At each station, the product is assembled through a subset of operations. The assembly line balancing problem (ALBP) consists of allocating operations between stations to maximise the system efficiency. In this study, a variable-depth local search algorithm is proposed for solving simple assembly line balancing problems (SALBPs), which are the most widely studied versions of the ALBP. Although the state-of-the-art techniques for solving the SALBP consist of exact enumeration-based methods or heuristics, this paper proposes a local search-based heuristic using variable-length sequences that allow the solution space to be efficiently explored. The proposed algorithm improves the best solution known for multiple instances reported in the literature, indicating that its efficiency is comparable to those of the state-of-the-art method for solving the SALBP. Moreover, the characteristics of the instances for which the proposed procedure provides a better solution than previously reported construction procedures are investigated.
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Alvarez-Miranda, E., Pereira, J., & Vila, M. (2023). Analysis of the simple assembly line balancing problem complexity. Comput. Oper. Res., 159, 106323.
Abstract: The simple assembly line balancing problem (SALBP) involves the determination of the assignment of elementary assembly operations to the workstations of the assembly line for the manufacture of a final product, with the objective of maximising assembly efficiency. In addition to its practicality, the SALBP can be considered as an extension of the bin packing problem (BPP) to account for the precedence relations between items. These constraints introduce an ordering component to the problem, which increases the complexity of SALBP resolution. However, previous studies indicated that precedence constraints do not play an important role in the capacity of state-of-the-art procedures to solve benchmark instances to optimality. In this study, we analysed the influences of different features of an SALBP instance on the performance of state-of-the-art solution methods for the abovementioned problem. First, we provide an alternative proof of complexity for the SALBP that uses precedence constraints to demonstrate its non-deterministic polynomial time (NP)-complete status, followed by a new set of benchmark instances directed towards an empirical analysis of the different features of SALBP instances. The experimental results revealed that the packing features of the SALBP are a major source of the perceived difficulty for any instance; however, precedence constraints play a role in the performance of these solution procedures. Specifically, the number of precedence constraints plays an important role in the results obtained from state-of-the-art methods. In addition to the analysis, certain issues that were identified in the publicly available implementations of the state-of-the-art method for resolving this problem were addressed in this study.
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Pereira, J. (2018). Modelling and solving a cost-oriented resource-constrained multi-model assembly line balancing problem. Int. J. Prod. Res., 56(11), 3994–4016.
Abstract: A line balancing problem considers the assignment of operations to workstations in an assembly line. While assembly lines are usually associated to mass production of standardised goods, their advantages have led to their widespread use whenever a product-oriented production system is applicable and the benefits of the labour division and specialisation are significant, even when some of its characteristics may deviate from classical assembly lines. In this work, we study a line balancing problem found in the textile industry in which the line must be balanced for multiple types of goods taking into account resource requirements. In order to solve the problem, a hybrid method that combines classical methods for line balancing with an Estimation of Distribution Algorithm is proposed. Computational experiments show that the new procedure improves upon the state of the art when compared using a benchmark set derived from the literature, as well as when compared using data from the manufacturer that originated this research work.
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Pereira, J. (2018). The robust (minmax regret) assembly line worker assignment and balancing problem. Comput. Oper. Res., 93, 27–40.
Abstract: Line balancing aims to assign the assembly tasks to the stations that compose the assembly line. A recent body of literature has been devoted to heterogeneity in the assembly process introduced by different workers. In such an environment, task times depend on the worker performing the operation and the problem aims at assigning tasks and workers to stations in order to maximize the throughput of the line. In this work, we consider an interval data version of the assembly line worker assignment and balancing problem (ALWABP) in which it is assumed that lower and upper bounds for the task times are known, and the objective is to find an assignment of tasks and workers to the workstations such that the absolute maximum regret among all of the possible scenarios is minimized. The relationship with other interval data minmax regret (IDMR) problems is investigated, the inapplicability of previous approximation methods is studied, regret evaluation is considered, and exact and heuristic solution methods are proposed and analyzed. The results of the proposed methods are compared in a computational experiment, showing the applicability of the method and the theoretical results to solve the problem under study. Additionally, these results are not only applicable to the problem in hand, but also to a more general class of problems. (C) 2018 Elsevier Ltd. All rights reserved.
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Pereira, J., & Ritt, M. (2023). Exact and heuristic methods for a workload allocation problem with chain precedence constraints. Eur. J. Oper. Res., 309(1), 387–398.
Abstract: Industrial manufacturing is often organized in assembly lines where a product is assembled on a se-quence of stations, each of which executes some of the assembly tasks. A line is balanced if the maximum total execution time of any station is minimal. Commonly, the task execution order is constrained by precedences, and task execution times are independent of the station performing the task. Here, we con -sider a recent variation, called the “(Calzedonia) Workload Allocation Problem” (WAP), where the prece-dences form a chain, and the execution time of a task depends on the worker executing it. This problem was recently proposed by Battarra et al. (2020) and it is a special case of the Assembly Line Worker As-signment and Balancing Problem Miralles et al. (2007) where precedence relations are arbitrary. In this paper we consider the computational complexity of the problem and prove its NP-hardness. To solve the problem, we provide different lower bounds and exact and heuristic procedures. The performance of the proposed methods is tested on previously proposed instances and on new, larger instances with the same characteristics. The results show that the proposed methods can solve instances with up to about 40 0 0 tasks and 29 workers, doubling the size of the instances that previously could be solved to optimality.
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Pereira, J., & Alvarez-Miranda, E. (2018). An exact approach for the robust assembly line balancing problem. Omega-Int. J. Manage. Sci., 78, 85–98.
Abstract: This work studies an assembly line balancing problem with uncertainty on the task times. In order to deal with the uncertainty, a robust formulation to handle changes in the operation times is put forward. In order to solve the problem, several lower bounds, dominance rules and an enumeration procedure are proposed. These methods are tested in a computational experiment using different instances derived from the literature and then compared to similar previous approaches. The results of the experiment show that the method is able to solve larger instances in shorter running times. Furthermore, the cost of protecting a solution against uncertainty is also investigated. The results highlight that protecting an assembly line against moderate levels of uncertainty can be achieved at the expense of small quantities of additional resources (stations). (C) 2017 Elsevier Ltd. All rights reserved.
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Pereira, J., & Ritt, M. (2022). A note on “Algorithms for the Calzedonia workload allocation problem”. J. Oper. Res. Soc., 73(6), 1420–1422.
Abstract: Battarra et al. recently proposed a novel assembly line balancing problem with applications to the apparel industry, where the tasks are performed in a fixed order. To solve the problem, one has to assign workers and tasks to the workstations with the objective of maximising the throughput of the assembly line. In this paper, we provide dynamic programming formulations for the general problem and some special cases. We then use these formulations to develop an exact solution approach that optimally solves the instances in Battarra et al. within seconds.
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Pereira, J., & Vila, M. (2016). A new model for supply chain network design with integrated assembly line balancing decisions. Int. J. Prod. Res., 54(9), 2653–2669.
Abstract: Supply chain network design aims at the integration of the different actors of a supply chain within a single framework in order to optimise the total profit of the system. In this paper, we consider the integration of line balancing issues within the tactical decisions of the supply chain, and we offer a novel model and a solution approach for the problem. The new approach decomposes the problem into multiple line balancing problems and a mixed integer linear model, which is easier to solve than the previously available non-linear mixed integer formulation. The results show that the new method is able to solve previously studied models within a fraction of the reported running times, and also allows us to solve larger instances than those reported in earlier works. Finally, we also provide some analysis on the influence of the cost structure, the demand and the structure of the assembly process on the final configuration of the assemblies and the distribution network.
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Pereira, J., Ritt, M., & Vasquez, O. C. (2018). A memetic algorithm for the cost-oriented robotic assembly line balancing problem. Comput. Oper. Res., 99, 249–261.
Abstract: In order to minimize costs, manufacturing companies have been relying on assembly lines for the mass production of commodity goods. Among other issues, the successful operation of an assembly line requires balancing work among the stations of the line in order to maximize its efficiency, a problem known in the literature as the assembly line balancing problem, ALBP. In this work, we consider an ALBP in which task assignment and equipment decisions are jointly considered, a problem that has been denoted as the robotic ALBP. Moreover, we focus on the case in which equipment has different costs, leading to a cost-oriented formulation. In order to solve the problem, which we denote as the cost-oriented robotic assembly line balancing problem, cRALBP, a hybrid metaheuristic is proposed. The metaheuristic embeds results obtained for two special cases of the problem within a genetic algorithm in order to obtain a memetic algorithm, applicable to the general problem. An extensive computational experiment shows the advantages of the hybrid approach and how each of the components of the algorithm contributes to the overall ability of the method to obtain good solutions. (C) 2018 Elsevier Ltd. All rights reserved.
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