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Mathematical Problems in Engineering
Volume 2016, Article ID 3203728, 5 pages
Research Article

Parallel Machine Scheduling with Nested Processing Set Restrictions and Job Delivery Times

1Key Laboratory of Intelligent Information Processing in Universities of Shandong (Shandong Institute of Business and Technology), Yantai 264005, China
2College of Computer Science and Technology, Shandong Institute of Business and Technology, Yantai 264005, China

Received 7 June 2016; Accepted 4 September 2016

Academic Editor: Bruno G. M. Robert

Copyright © 2016 Shuguang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of scheduling jobs with delivery times on parallel machines is studied, where each job can only be processed on a specific subset of the machines called its processing set. Two distinct processing sets are either nested or disjoint; that is, they do not partially overlap. All jobs are available for processing at time 0. The goal is to minimize the time by which all jobs are delivered, which is equivalent to minimizing the maximum lateness from the optimization viewpoint. A list scheduling approach is analyzed and its approximation ratio of 2 is established. In addition, a polynomial time approximation scheme is derived.