Hybrid metaheuristics for the accessibility windows assembly line balancing problem level 2 (AWALBP-L2)

This paper addresses an assembly line balancing problem in which the length of the workpieces is larger than the width of the workstations. The problem differs from traditional variants of assembly line balancing in the sense that only a portion of the workpiece, or portions of two consecutive workpieces, can be reached from any workstation. Consequently, at any stationary stage of the cycle, each workstation can only process a portion of the tasks, namely, those which are inside the area of a workpiece that is reachable from the workstation. The objective is to find a (cyclic) movement scheme of the workpieces along the line and a task assignment to stationary stages of the production process, while minimizing the cycle time. We propose three hybrid approaches of metaheuristics and mathematical programming - one based on simulated annealing and the other two based on tabu search, relying on different neighborhood definitions. The two former approaches make use of a classical neighborhood, obtained by applying local changes to a current solution. The latter approach, in contrast, draws ideas from the corridor method to define a corridor around the current solution, via the imposition of exogenous constraints on the solution space of the problem. An extensive computational experiment is carried out to test the performance of the proposed approaches, improving the best results published to date.Postprint (author's final draft

AWALBP-L2 : the Accessibility Windows Assembly Line Balancing Problem Level 2 : formalization and solution methods

This doctoral thesis tackles an assembly line balancing problem with restricted access to the workpieces that has been entitled AWALBP: the Accessibility Windows Assembly Line Balancing Problem. The problem is described and a general classification for its main optimization levels is proposed. The thesis focuses on a specific case of the optimization level AWALBP-L2. The AWALBP-L2 consists of two subproblems that need to be solved simultaneously: (i) the computation of a feasible movement scheme and (ii) the assignment of each task to one workstation and one stationary stage of the cycle. In the particular case of AWALBP-L2 addressed in this thesis, for each task a single workstation is compatible. The review of the state of the art reveals that relatively few studies have been published concerning the AWALBP. Regarding the solution of the AWALBP-L2, the only available previous work is a mathematical programming model, but the model is not tested or validated. In order to fill this research gap, the aim of this thesis is three-fold: i) to describe the AWALBP and characterize its main optimization levels, ii) to propose exact methods for the case of AWALBP-L2 considered, and iii) to develop solution procedures for the challenging instances that are out of reach of the former methods. Consequently, in this doctoral thesis the AWALBP is characterized and the AWALBP-L2 case is addressed through four main approaches. First, the problem is formalized and solved via two mixed integer linear programming (MILP) models. Second, an approach combining a matheuristic and a MILP model is proposed. The third approach considers hybridizing metaheuristics with mathematical programming models. Finally, the fourth approach proposes sequential combinations of the aforementioned hybrid metaheuristics and a MILP model. The performance of all approaches is evaluated via an extensive computational experiment based on realistic instances, and an optimal solution could be found for a large number of them. Future research work may include additional assumptions on the problem, such as precedence relationships among tasks or several workstations compatible for each task. The methods proposed in this thesis are open in nature and extend perspectives for combining (meta)heuristics and mathematical programming models, either for improving the solution of the AWALBP-L2 or for tackling other combinatorial optimization problems.Esta tesis doctoral aborda un problema de equilibrado de líneas con acceso limitado a las piezas que ha sido titulado AWALBP: Accessibility Windows Assembly Line Balancing Problem. Se describe el problema y se propone una clasificación general de sus principales niveles de optimización. La tesis se centra en un caso específico del nivel AWALBP-L2. El AWALBP-L2 consta de dos subproblemas que deben ser resueltos simultáneamente: (i) cálculo de un esquema de movimiento factible y (ii) asignación de cada tarea a una estación y a una de las etapas estacionarias del ciclo. En el caso particular de AWALBP-L2 tratado en esta tesis, para cada tarea existe una única estación compatible. La revisión del estado del arte revela que relativamente pocos estudios han sido publicados sobre el AWALBP. Respecto a la resolución del AWALBP-L2, el único trabajo anterior disponible es un modelo de programación matemática, el cual no está probado o validado. Con tal de cubrir este hueco de investigación, el objetivo de la presente tesis es triple: i) describir el AWALBP y caracterizar sus principales niveles de optimización, ii) proponer métodos exactos para el caso considerado de AWALBP-L2, y iii) desarrollar métodos de resolución para los ejemplares más difíciles que quedaron fuera del alcance de los métodos anteriores. Por consiguiente, en esta tesis doctoral se caracteriza el AWALBP y se aborda el caso de AWALBP-L2 mediante cuatro enfoques principales. En primer lugar, el problema se formaliza y se resuelve mediante dos modelos de programación lineal entera mixta (PLEM). En segundo lugar se propone una mateheurística combinada con un modelo de PLEM. El tercer enfoque consiste en hibridizar metaheurísticas con modelos de programación matemática. Finalmente, el cuarto enfoque propone combinaciones secuenciales de las mencionadas metaheurísticas híbridas con un modelo de PLEM. Los enfoques propuestos se evalúan mediante una extensa experiencia computacional con ejemplares realistas, y se obtuvo una solución óptima para un gran número de ellos. Las líneas propuestas de investigación futura incluyen supuestos adicionales tales como relaciones de precedencia entre tareas o varias estaciones compatibles para una misma tarea. Los métodos propuestos en esta tesis son de naturaleza abierta y ofrecen perspectivas para la combinación de (meta)heurísticas con modelos de programación matemática, tanto para mejorar la solución del AWALBP-L2 como para abordar otros problemas de optimización combinatoria

Solving the accessibility windows assembly line problem level 1 and variant 1 (AWALBP-L1-1) with precedence constraints

Assembly line balancing problems (ALBPs) are among the most studied combinatorial optimization problems due to their relevance in many production systems. In particular, the accessibility windows ALBP (AWALBP) may arise when the workpieces are larger than the workstations, which implies that at a given instant the workstations have access to only a portion of the workpieces. Thus, the cycle is split into forward steps and stationary stages. The workpieces advance during the forward steps and the tasks are processed during the stationary stages. Several studies have dealt with the AWALBP assuming that there are no precedence relationships between tasks. However, this assumption is not always appropriate. In this work we solve the first level of AWALBP (AWALBP-L1) considering the existence of precedence relationships. Specifically, this work deals with variant 1 (AWALBP-L1-1), in which each task can be performed at only one workstation and, therefore, only the stationary stages and the starting instants in which the tasks are performed have to be decided. We design a solution procedure that includes pre-processing procedures, a matheuristic and a mixed integer linear programming model. An extensive computational experiment is carried out to evaluate its performance.Peer ReviewedPostprint (author's final draft

Articles publicats per investigadors de l'ETSEIB. Producció científica a Futur 2015

Postprint (author's final draft

Articles publicats per investigadors de l'ETSEIB. Producció científica a Futur 2015

Postprint (author's final draft

Hybrid metaheuristics for the accessibility windows assembly line balancing problem level 2 (AWALBP-L2)

This paper addresses an assembly line balancing problem in which the length of the workpieces is larger than the width of the workstations. The problem differs from traditional variants of assembly line balancing in the sense that only a portion of the workpiece, or portions of two consecutive workpieces, can be reached from any workstation. Consequently, at any stationary stage of the cycle, each workstation can only process a portion of the tasks, namely, those which are inside the area of a workpiece that is reachable from the workstation. The objective is to find a (cyclic) movement scheme of the workpieces along the line and a task assignment to stationary stages of the production process, while minimizing the cycle time. We propose three hybrid approaches of metaheuristics and mathematical programming - one based on simulated annealing and the other two based on tabu search, relying on different neighborhood definitions. The two former approaches make use of a classical neighborhood, obtained by applying local changes to a current solution. The latter approach, in contrast, draws ideas from the corridor method to define a corridor around the current solution, via the imposition of exogenous constraints on the solution space of the problem. An extensive computational experiment is carried out to test the performance of the proposed approaches, improving the best results published to date