Efficient local search limitation strategy for single machine total weighted tardiness scheduling with sequence-dependent setup times

International audienceThis paper concerns the single machine total weighted tardiness scheduling with sequence-dependent setup times, usually referred as 1|sij|∑wjTj. In this NP-hard problem, each job has an associated processing time, due date and a weight. For each pair of jobs i and j, there may be a setup time before starting to process j in case this job is scheduled immediately after i. The objective is to determine a schedule that minimizes the total weighted tardiness, where the tardiness of a job is equal to its completion time minus its due date, in case the job is completely processed only after its due date, and is equal to zero otherwise. Due to its complexity, this problem is most commonly solved by heuristics. The aim of this work is to develop a simple yet effective limitation strategy that speeds up the local search procedure without a significant loss in the solution quality. Such strategy consists of a filtering mechanism that prevents unpromising moves to be evaluated. The proposed strategy has been embedded in a local search based metaheuristic from the literature and tested in classical benchmark instances. Computational experiments revealed that the limitation strategy enabled the metaheuristic to be extremely competitive when compared to other algorithms from the literature, since it allowed the use of a large number of neighborhood structures without a significant increase in the CPU time and, consequently, high quality solutions could be achieved in a matter of seconds. In addition, we analyzed the effectiveness of the proposed strategy in two other well-known metaheuristics. Further experiments were also carried out on benchmark instances of problem 1|sij|∑Tj

Formulações matemáticas para o problema de sequenciamento de tarefas com manutenções periódicas e tempos de setup

The single-machine scheduling problem with periodic maintenances and sequencedependent setup times aims at scheduling jobs on a single machine in which periodic maintenances and setups are required. The objective is the minimization of the makespan. We propose an exact algorithm based on the iterative solution of three alternative arc-time-indexed models. Extensive computational experiments are carried out on 420 benchmark instances with up to 50 jobs, and on 360 newly proposed instances involving up to 125 jobs. We compare the results found by all formulations with those obtained by the best available mathematical formulation. All instances from the existing dataset are solved to optimality for the first time.O problema de sequenciamento em uma m´aquina estudado neste trabalho tem como objetivo ordenar tarefas em apenas uma m´aquina com per´ıodos de indisponibilidade fixos, levando em considera¸c˜ao tempos de setup dependentes da sequˆencia. O objetivo ´e minimizar o makespan. Neste trabalho ´e proposto um algoritmo exato que resolve, iterativamente, uma de trˆes formula¸c˜ao matem´aticas de arcos indexados no tempo apresentadas. Experimentos computacionais extensivos s˜ao conduzidos em 420 instˆancias da literatura de at´e 50 tarefas, e em 360 instˆancias, envolvendo at´e 125 tarefas, propostas neste trabalho. Os resultados s˜ao comparados com aqueles obtidos pela melhor formula¸c˜ao matem´atica dispon´ıvel na literatura. Pela primeira vez, todas as instˆancias do conjunto existente foram resolvidas na otimalidade

Programación de la producción para la sección de formado y lijado en una empresa de fabricación de cepillos profesionales para peluquerías

La programación de la producción se entiende como el proceso que tiene una empresa para la toma de decisiones respecto a la fabricación de sus productos. En este proyecto se estudiará el problema de programación de la producción para la Etapa 2: formado y lijado, la cual se identificó como cuello de botella en la empresa Irca Ltda. Como principal objetivo, se desarrollará un aplicativo en Microsoft Excel ®. El cual se apoyará en un algoritmo genético que logre reducir la sumatoria de las diferencias entre el tiempo de terminación de un trabajo y la fecha de entrega del mismo; entendida como la minimización de la tardanza total. Se tomaron restricciones propias del sistema, las cuales están relacionadas con máquinas en paralelo, elegibilidad de máquina, permutación e interrupción de las órdenes de producción. Este algoritmo genético aplica un enfoque de variabilidad logrando hallar una solución factible y de calidad para el problema. Este enfoque comienza utilizando reglas de despacho como SPT, LPT, EDD y LIFO para el caso de la población inicial, para la selección de padres una probabilidad asociada al de menor tardanza, para el cruce se utiliza aleatoriedad en las particiones a intercambiar y en la mutación se presenta la probabilidad que los tipos de cabo se agrupen para reducción de tiempos de alistamiento. Respecto a los resultados obtenidos es posible evidenciar como el algoritmo propuesto mejora la tardanza en un rango entre el 40-90%, además de mejor solución en comparación con la programación actual de la compañía, al igual que con las reglas de despacho evaluadas.Scheduling is understood as the decision process that a company has to make regarding the manufacture of its products. This project will study the production scheduling problem for Stage 2: formed and sanding, which was identified as a bottleneck in the company Irca Ltda. As an objective, an application will be developed in Microsoft Excel ®. Which will be based on a genetic algorithm that reduces the sum of the differences between the time of completion of a work and the date of delivery of the same, Understood as the minimization of total tardiness. The constraints of this system were applied, this are related to parallel machines, machine eligibility, permutation and interruption of production orders. This genetic algorithm applies a variability approach to find a feasible and quality solution for the problem. This approach starts using dispatch rules such as SPT, LPT, EDD and LIFO for the initial population case, for the selection of parents a probability associated to the lesser delay, for the crossing is used randomness in the partitions to be exchanged and in the Mutation we present the probability that the types of cable are grouped for reduction of enlistment times. Regarding the results obtained, it is possible to show how the proposed algorithm improves the Total Tardiness in a range between 40-90%, as well as a better solution in comparison with the current schedule of the company, as well as with the dispatch rules evaluated.Ingeniero (a) IndustrialPregrad