ASALBP: The Alternative Subgraphs Assembly Line Balancing Problem

The classic assembly line balancing problem basically consist in assigning a set of tasks to a group of workstations while maintaining the task’ precedence relations. Habitually, such relations are represented by a predetermined precedence graph. However, a product’s assembly process may admit, for one or more of its parts, alternative precedence subgraph. This may be due to the fact that the processing time for some task are dependent on their processing sequence, or because there are alternatives for such a subassembly. In general, because of the great difficulty of the problem and the impossibility of representing alternative subgraphs in a precedence graph, the system designer will decide to select, a priori, one of such alternative subgraphs, which sometimes imposes additional constrains other than technological ones. In this paper we present, characterize and formulate a new general assembly line balancing problem: the Alternative Subgraphs Assembly Line Balancing Problem (ASALBP). Its novel characteristic is that it considers the possibility of having alternative assembly subgraphs, in which the processing times and/or the precedence relations of certain task are dependent on the assembly subgraph selected. Therefore, solving this problem implies simultaneously selecting an assembly subgraph for each part of the assembly that allows alternatives and balancing the line (i.e., assigning the task to the workstations). The potentially positive effects of this on the solution of the problem are shown here in a numerical example. Finally, the mathematical programming model developed is described and the results of a brief computational experiment are presented

Assembly Line

An assembly line is a manufacturing process in which parts are added to a product in a sequential manner using optimally planned logistics to create a finished product in the fastest possible way. It is a flow-oriented production system where the productive units performing the operations, referred to as stations, are aligned in a serial manner. The present edited book is a collection of 12 chapters written by experts and well-known professionals of the field. The volume is organized in three parts according to the last research works in assembly line subject. The first part of the book is devoted to the assembly line balancing problem. It includes chapters dealing with different problems of ALBP. In the second part of the book some optimization problems in assembly line structure are considered. In many situations there are several contradictory goals that have to be satisfied simultaneously. The third part of the book deals with testing problems in assembly line. This section gives an overview on new trends, techniques and methodologies for testing the quality of a product at the end of the assembling line

The ASALB problem with processing alternatives involving different tasks: definition, formalization and resolution

The Alternative Subgraphs Assembly Line Balancing Problem (ASALBP) considers assembly alternatives that determine task processing times and/or precedence relations among the tasks. Capacho and Pastor formalized this problem and developed a mathematical programming model (MILP) in which the assembly alternatives are determined by combining all available processing alternatives of each existing sub-assembly. In this paper an extended definition of the ASALBP is presented in which assembly subprocesses involving different tasks are also considered. Additionally, a mathematical programming model is proposed to formalize and solve the extended version of the ASALBP, which also improves the performance of the former MILP model. Some computational results are included.Peer Reviewe

SALBPGen - A systematic data generator for (simple) assembly line balancing

Assembly line balancing is a well-known and extensively researched decision problem which arises when assembly line production systems are designed and operated. A large variety of real-world problem variations and elaborate solution methods were developed and presented in the academic literature in the past 60 years. Nevertheless, computational experiments examining and comparing the performance of solution procedures were mostly based on very limited data sets unsystematically collected from the literature and from some real-world cases. In particular, the precedence graphs used as the basis of former tests are limited in number and characteristics. As a consequence, former performance analyses suffer from a lack of systematics and statistical evidence. In this article, we propose SALPBGen, a new instance generator for the simple assembly line balancing problem (SALBP) which can be applied to any other assembly line balancing problem, too. It is able to systematically create instances with very diverse structures under full control of the experiment's designer. In particular, based on our analysis of real-world problems from automotive and related industries, typical substructures of the precedence graph like chains, bottlenecks and modules can be generated and combined as required based on a detailed analysis of graph structures and structure measures like the order strength. We also present a collection of new challenging benchmark data sets which are suited for comprehensive statistical tests in comparative studies of solution methods for SALBP and generalized problems as well. Researchers are invited to participate in a challenge to solve these new problem instances.manufacturing, benchmark data set, assembly line balancing, precedence graph, structure analysis, complexity measures

ASALBP: the Alternative Subgraphs Assembly Line Balancing Problem. Formalization and Resolution Procedures

Hoy en día, los problemas de equilibrado de líneas de montaje se encuentran comúnmente en la mayoría de sistemas industriales y de manufactura. Básicamente, estos problemas consisten en asignar un conjunto de tareas a una secuencia ordenada de estaciones de trabajo, de manera que se respeten las restricciones de precedencia y se optimice una medida de eficiencia dada (como, por ejemplo, el número de estaciones de trabajo o el tiempo ciclo). Dada la complejidad de los problemas de equilibrado de líneas, en los trabajos de investigación tradicionalmente se consideraban numerosas simplificaciones en las que, por ejemplo, una sola línea serial procesaba un único modelo de un solo producto. Además, los problemas estaban principalmente restringidos por las relaciones de precedencia y el tiempo ciclo. Sin embargo, la disponibilidad de recursos computacionales de hoy en día, así como la necesidad de las empresas a adaptarse a los rápidos cambios en los procesos de producción, han motivado tanto a investigadores como a gerentes a tratar problemas más realistas. Algunos ejemplos incluyen problemas que procesan modelos mixtos, estaciones de trabajo y líneas en paralelo, consideran múltiples objetivos y restricciones adicionales, como la capacidad de proceso de las estaciones de trabajo y la ubicación de los recursos en la línea de montaje.Esta tesis doctoral trata un nuevo problema de equilibrado de líneas, que ha sido titulado ASALBP: the Alternative Subgraphs Assembly Line Balancing Problem, en el que se consideran variantes alternativas para diferentes partes de un proceso de montaje o de manufactura. Cada alternativa puede ser representada por un subgrafo de precedencias, que determina las tareas requeridas para procesar un producto particular, las restricciones de precedencia y los tiempos de proceso. Para resolver eficientemente el ASALBP, se deben resolver dos problemas simultáneamente: (1) el problema de decisión para seleccionar un subgrafo de montaje para cada parte que admite alternativas y (2) el problema de equilibrado para asignar las tareas a las estaciones de trabajo. El análisis del estado del arte revela que este problema no ha sido estudiado previamente en la literatura, lo que ha conducido a la caracterización y a la definición de un nuevo problema. Por otra parte, dado que no es posible representar las variantes de montaje en un diagrama de precedencias estándar, se propone el S-grafo como una herramienta de diagramación, para representar en un único grafo todas las alternativas de montaje.Habitualmente, los problemas de equilibrado de líneas que consideran alternativas de montaje se resuelven en dos etapas. En la etapa inicial, el diseñador de sistema selecciona una de las variantes posibles utilizando cierto criterio de decisión como por ejemplo tiempo total de proceso. Una vez que se han seleccionado las alternativas de montaje, y se dispone de un diagrama de precedencias (es decir, el problema de planificación ha sido resuelto), la línea de montaje es equilibrada en una segunda etapa. Sin embargo, utilizando dicho procedimiento de dos etapas no se puede garantizar que una solución óptima del problema global se pueda obtener, porque las decisiones tomadas por el diseñador de sistema restringen el problema y causan perdida de información; es decir, cuando se selecciona una alternativa priori los efectos de las posibilidades restantes quedan sin explorar. Por ejemplo, si el diseñador de sistema utiliza tiempo total de proceso como criterio de decisión, la alternativa con el tiempo total de proceso más grande será descartada a pesar de que pueda ser la que proporcione la mejor solución del problema (es decir, requiere el mínimo número de estaciones de trabajo o el mínimo tiempo ciclo). Por lo tanto, pareciera razonable considerar que para solucionar eficientemente un ALBP que implica alternativas de proceso, todas las alternativas de montaje deben ser tomadas en cuenta en el proceso de equilibrado. Para este propósito, en esta tesis el problema de selección de una variante de montaje y el problema de equilibrado de la línea se consideran conjuntamente en lugar de independientemente.Para resolver el Problema de Equilibrado de Líneas con Alternativas de Montaje (ASALBP) se usan varios enfoques. El problema se formaliza y se resuelve de manera óptima a través de dos modelos de programación matemática. Un enfoque aproximativo es usado para resolver problemas de tamaño industrial. Además, se proponen procedimientos de optimización local con el objetivo de mejorar la calidad de las soluciones obtenidas por los métodos heurísticos desarrollados en este trabajo.Nowadays assembly line balancing problems are commonly found in most industrial and manufacturing systems. Basically, these problems seek to assign a set of assembly tasks to an ordered sequence of workstations in such a way that precedence constraints are maintained and a given efficiency measure (e.g. the number of workstations or the cycle time) is optimized.Because of the computational complexity of balancing problems, research works traditionally considered numerous simplifying assumptions in which, for example, a single model of a unique product were processed in a single line; moreover, problems were mainly restricted by precedence and cycle time constrains. Nevertheless, the current availability of computing resources and the enterprises need to adapt to rapid changes in production and manufacturing processes have encouraged researchers and decision-makers to address more realistic problems. Some examples include problems that involve mixed models, parallel workstations and parallel lines, multiple objectives and also further restrictions such as workstation processing capacity and resource allocation constraints. This doctoral thesis addresses a novel assembly line balancing problem, entitled here ASALBP: the Alternative Subgraphs Assembly Line Balancing Problem, which considers alternative variants for different parts of an assembly or manufacturing process. Each variant can be represented by a precedence subgraph that establishes the tasks required to process a particular product, their precedence requirements and their processing times. Therefore, to efficiently solve the Alternative Subgraphs Assembly Line Balancing Problem two subproblems need to be solved simultaneously: (1) the decision problem that selects one assembly variant for each part that admit alternatives and (2) the balancing problem that assigns the tasks to the workstations. The analysis of the state-of-the-art carried out revealed that the Alternative Subgraphs Assembly Line Balancing Problem has not been addressed before in literature studies, which leaded to the characterization and definition of this new problem. Moreover, due to the impossibility of representing assembly variants in a standard precedence graph, the S-Graph is proposed here as a diagramming tool to represent all available assembly alternatives in a unique diagram. Habitually, problems involving assembly alternatives are solved by using a two-stage based approach. In the initial stage, the system designer selects one of the possible variants according to criteria such as total processing time. Once the assembly alternatives have been selected, and a precedence graph is available (i.e. the assembly planning problem has been already solved), the line is then balanced in the second stage. However, by following this two-stage procedure it cannot be guaranteed that an optimal solution of the global problem can be obtained, because the decisions taken by the system designer restrict the problem and cause information loss; i.e., a priori selection of an alternative leaves the effects of the other possibilities unexplored. For instance, if the system designer uses total processing time as decision criterion, the alternative with largest total processing time will be discarded notwithstanding it may provide the best solution of the problem (i.e., it requires the minimum number of workstations or minimum cycle time). Therefore, it seems reasonable to consider that to solve efficiently an ALBP that involves processing alternatives all possibilities must be considered within the balancing process. For this purpose, in this thesis both the variant selection problem and the balancing problem are jointly considered instead of independently.Different approaches are used here to address the Alternative Subgraphs Assembly Line Balancing Problem (ASALBP). The problem is formalize and optimally solved by means of two mathematical programming models. An approximate approach is used to address industrial-scale problems. Furthermore, local optimization procedures are proposed aiming at improving the quality of the solutions provided by all heuristic methods developed here

Second order conic approximation for disassembly line design with joint probabilistic constraints

A problem of profit oriented disassembly line design and balancing with possible partial disassembly and presence of hazardous parts is studied. The objective is to design a production line providing a maximal revenue with balanced workload. Task times are assumed to be random variables with known normal probability distributions. The cycle time constraints are to be jointly satisfied with at least a predetermined probability level. An AND/OR graph is used to model the precedence relationships among tasks. Several lower and upper–bounding schemes are developed using second order cone programming and convex piecewise linear approximation. To show the relevance and applicability of the proposed approach, a set of instances from the literature are solved to optimality

Heuristic procedures for solving the General Assembly Line Balancing Problem with Setups (GALBPS)

The General Assembly Line Balancing Problem with Setups (GALBPS) was recently defined in the literature. It adds sequence-dependent setup time considerations to the classical Simple Assembly Line Balancing Problem (SALBP) as follows: whenever a task is assigned next to another at the same workstation, a setup time must be added to compute the global workstation time, thereby providing the task sequence inside each workstation. This paper proposes over 50 priority-rule-based heuristic procedures to solve GALBPS, many of which are an improvement upon heuristic procedures published to date