60 research outputs found

    A simple, fast, and effective heuristic for the single-machine total weighted tardiness problem

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    We consider the single-machine total weighted tardiness problem (TWT) where a set of n jobs with general weights w_1,…, w_n, integer processing times p_1,…, p_n, and integer due dates d_1,…, d_n has to be scheduled non-preemptively. If C_j is the completion time of job j then T_j = max(0, C_j - d_j) denotes the tardiness of this job. The objective is to find a schedule S^{*}_{WT} that minimizes the weighted sum of the tardiness costs of all jobs computed as \sum_{j=1}^{n} w_j T_j. This problem is known to be unary NP-hard. Our goal is to design a constructive heuristic for this problem that yields excellent feasible solutions in short computational times by exploiting the structural properties of a preemptive relaxation

    A Cluster-based Evolutionary Algorithm for the Single Machine Total Weighted Tardiness-scheduling Problem

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    In this paper a new evolutionary algorithm is described for the single machine total weighted tardiness problem. The operation of this method can be divided in three stages: a cluster forming and two local search stages. In the first stage it approaches some locally optimal solutions by grouping based on similarity. In the second stage it improves the accuracy of the approximation of the solutions with a local search procedure while periodically generating new solutions. In the third stage the algorithm continues the application of the local search procedure. We tested our algorithm on all the benchmark problems of ORLIB. The algorithm managed to find, within an acceptable time limit, the best-known solution for the problems, or found solutions within 1% of the best-known solutions in 99 % of the tasks

    Dominance-Based Heuristics for One-Machine Total Cost Scheduling Problems

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    International audienceWe study the one-machine scheduling problem with release dates and we look at several objective functions including total (weighted) tardiness and total (weighted) completion time. We describe dominance rules for these criteria, as well as techniques for using these dominance rules to build heuristic solutions. We use them to improve certain well-known greedy heuristic algorithms from the literature. Finally, we introduce a Tabu Search method with a neighborhood based on our dominance rules. Experiments show the effectiveness of our techniques in obtaining very good solutions for all studied criteria

    Two exponential neighborhoods for single machine scheduling

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    We study the problem of minimizing total completion time on a single machine with the presence of release dates. We present two different approaches leading to exponential neighborhoods in which the best improving neighbor can be determined in polynomial time. Furthermore, computational results are presented to get insight in the performance of the developed neighborhoods

    Evaluación de funciones de utilidad de GRASP en la programación de producción para minimizar la tardanza total ponderada en una máquina

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    This paper considers the total weighted tardiness minimization in a single machineenvironment (1|| wj Tj ) a scheduling problem which has been proved to be NP-Hard. The solution approach uses the Greedy Randomized Adaptive Search Procedure (GRASP) meta-heuristic known for the quality of the solutions it can generate and the selective ability of its utility function during the construction phase. This work proposes and analyses three different utility functions for the problem in question. A statistical study showed significant differences between the mean values obtained from the proposed utility functions. The computational experiments were carried out using problems instances found in the OR-LIBRARY, and the outcome of these experiments were competitive solutions compared to the best known values of the instances involved. This work also shows the ease of developing GRASP methods for solving scheduling problems in a simple spreadsheet software such as MS Excel.Este artículo aborda la minimización de la tardanza total ponderada en un entorno de producción (1|| wj Tj ) que es conocido en complejidad como de tipo NP-hard. El enfoque de solución propuesto utiliza la metaheurística Greedy Randomized Adaptive Search Procedure (GRASP), la cual es reconocida por la correlación existente entre la calidad de las soluciones y la capacidad discriminante de la función de utilidad empleada en su fase constructiva. Este trabajo propone y analiza tres diferentes funciones de utilidad para este problema en particular. El desempeño de estas funciones se evaluó mediante un estudio estadístico que evidenció diferencias significativas en los valores medios de tardanza total ponderada, explicadas por el factor función de utilidad. La fase experimental se desarrolló usando instancias de la librería OR-LIBRARY y permitió obtener soluciones competitivas en calidad con respecto a los mejores valores conocidos para las instancias de este problema. Este trabajo ilustra la potencialidad de uso de métodos GRASP implementados en una hoja de cálculo normal para hallar soluciones a problemas de programación de la producción
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