Anzeige
Erschienen in:
2009 | OriginalPaper | Buchkapitel
A Mathematical Programming Approach for Online Hierarchical Scheduling
verfasst von : Zhiyi Tan, An Zhang
Erschienen in: Combinatorial Optimization and Applications
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of
m
machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize makespan. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both algorithm and lower bounds are based on solutions of mathematical programming. For any given
m
, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any
m
, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for
m
= 4 and 5, respectively.