A Cardinality-constrained Approach for Robust Machine Loading Problems

The Machine Loading Problem (MLP) refers to the allocation of operative tasks and tools to machines for the production of parts. Since the uncertainty of processing times might affect the quality of the solution, this paper proposes a robust formulation of an MLP, based on the cardinality-constrained approach, to evaluate the optimal solution in the presence of a given number of fluctuations of the actual processing time with respect to the nominal one. The applicability of the model in the practice has been tested on a case study

Robust optimization for U-shaped assembly line worker assignment and balancing problem with uncertain task times

Awareness of the importance of U-shaped assembly line balancing problems is all on the rise. In the U-shaped assembly line, balancing is affected by the uncertainty associated with the assembly task times. Therefore, it is crucial to develop an approach to respond to the uncertainty caused by the task times. When the great majority of existing literature related to uncertainty in the assembly line is considered, it is observed that the U-shaped assembly line balancing problem under uncertainty is scarcely investigated. That being the case, we aim to fill this research gap by proposing a robust counterpart formulation for the addressed problem. In this study, a robust optimization model is developed for the U-shaped assembly line worker assignment and balancing problem (UALWABP) to cope with the task time uncertainty characterized by a combined interval and polyhedral uncertainty set. A real case study is conducted through data from a company producing water meters

Improving the resolution of the simple assembly line balancing problem type E

The simple assembly line balancing problem type E (abbreviated as SALBP-E) occurs when the number of workstations and the cycle time are variables and the objective is to maximise the line efficiency. In contrast with other types of SALBPs, SALBP-E has received little attention in the literature. In order to solve optimally SALBP-E, we propose a mixed integer liner programming model and an iterative procedure. Since SALBP-E is NP-hard, we also propose heuristics derived from the aforementioned procedures for solving larger instances. An extensive experimentation is carried out and its results show the improvement of the SALBP-E resolution

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

Resolució del problema d’equilibrat de línia de muntatge amb tasques amb deterioració

El present treball té la finalitat de resoldre el problema de l’equilibrat de línia de muntatge considerant l’efecte de la deterioració de les tasques. Definint la deterioració d’una tasca com el fet de que una tasca processada després d’un cert temps consumeix més temps de processament que si la mateixa es processada més aviat. Tot i que és un problema que es troba present en certes línies de muntatge reals, se’n troben pocs estudis a la literatura científica. Amb tal fi, s’ha desenvolupat un procediment heurístic que, donades unes determinades característiques de la línia de producció, concretament el nombre de tasques, els temps de procés constants de cada tasca, les seves relacions de precedència i el temps de cicle màxim de la línia, realitzi la seva distribució a les estacions de treball de la manera més eficient possible i minimitzant el nombre d’estacions utilitzades (el que es coneix com a ALBP-1). El procediment proposat es basa en una heurística de millora coneguda com a optimització local. Aquest mètode parteix d’una solució inicial (en aquest cas trobada a partir d’heurísitiques constructives greedy) i utilitza com a idea fonamental l’exploració del veïnatge per trobar solucions millors. S’han creat 12 variants basades en aquest algorisme que resulten de canvis en els mètodes per obtenir la solució inicial, és a dir, 12 heurístiques amb regles de prioritat diferents per distribuir les tasques en les estacions. Per tal d’avaluar el funcionament del procediment de resolució proposat s’ha realitzat una experiència computacional a partir d’un conjunt d’exemplars de testatge. Per dur a terme l’experimentació, s’ha escollit utilitzar un banc de dades dirigit per la resolució de problemes d’equilibrat de línia de muntatge simple al que se li ha afegit com a dada la taxa de creixement de la deterioració. En concret s’han estudiat 5 variants diferents de taxa de deterioració per tal de poder analitzar la incidència que té en l’equilibrat de la línia. Finalment s’ha fet una comparativa entre les diferents heurístiques aplicades per veure quina d’elles és la més eficaç per resoldre aquest problema