A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

AbstractThis research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective

Minimizing the weighted sum of maximum earliness and maximum tardiness costs on a single machine with periodic preventive maintenance

[IF=1.718]International audienceWe consider the problem of scheduling a set of jobs on a single machine against a common and restrictive due date. In particular, we are interested in the problem of minimizing the weighted sum of maximum earliness and maximum tardiness costs. This kind of objective function is related to the just-in-time environment where penalties, such as storage cost and additional charges for late delivery, should be avoided. First we present a mixed integer linear model for the problem without availability constraints and we prove that this model can be reduced to a polynomial-time model. Secondly, we suppose that the machine undergoes a periodic preventive maintenance. We present then a second mixed integer linear model to solve the problem to optimality. Although the latter problem can be solved to optimality for small instances, we show that the problem reduces to the one-dimensional bin packing problem. Computational results show that the proposed algorithm best fit decreasing performs well

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

Aplicação do Particle Swarm Optimization a um problema de escalonamento de máquinas paralelas não relacionadas com tempos de setup dependentes da sequência

Dissertação de mestrado em Engenharia de SistemasEsta dissertação aborda um problema de escalonamento de máquinas paralelas não relacionadas com tempos de setup dependentes da sequência e o objetivo é minimizar o makespan de um conjunto de trabalhos. Para tal, é implementado o algoritmo Particle Swarm Optimization, que é usado para resolver um problema da literatura, dividido em pequenos e grandes problemas, consoante o número de trabalhos que são utilizados. O desempenho deste algoritmo foi avaliado através de uma análise comparativa das suas soluções com as soluções obtidas usando o Ant Colony Optimization, o Simulated Annealing e o Genetic Algorithm. Na implementação do algoritmo em estudo foi utilizado a toolbox particleswarm do software MATLAB, que tenta otimizar utilizando o algoritmo Particle Swarm Optimization. Os resultados da implementação mostram que para pequenos problemas o Particle Swarm consegue superar o Genetic Algorithm em algumas instâncias, sendo que os outros três algoritmos apresentam valores de makespan inferiores. Para grandes problemas, é clara a superioridade do Particle Swarm em relação ao Genetic Algorithm, no entanto, relativamente aos restantes algoritmos o mesmo não acontece. Existe também a tendência crescente da variação percentual entre os algoritmos à medida que o número de máquinas aumenta para o mesmo número de trabalhos.This dissertation addresses the unrelated parallel machine scheduling problem with sequence-dependent setup times and the objective is to minimize the makespan of a set of jobs. It is implemented the Particle Swarm Optimization, used to solve a problem from the literature, divided into small and large problems, depending on the number of jobs that are used. Particle Swarm performance is evaluated through a comparative analysis between its solutions and the solutions obtained using Ant Colony Optimization, Simulated Annealing and Genetic Algorithm. For implementing the algorithm under study, the particle swarm toolbox from the MATLAB software was used, which tries to optimize using the Particle Swarm Optimization. The results of the implementation show that for small problems the Particle Swarm can overcome the Genetic Algorithm in some instances, with the other three algorithms having lower makespan values. For large problems, the Particle Swarm superiority over Genetic Algorithm is clear, however, in relation to the other algorithms the same does not happen. There is also as increasing trend in the percentage variation between the algorithms as the number of machines increases for the same number of jobs