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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 928312, 20 pages
Research Article

Variable Neighborhood Search for Parallel Machines Scheduling Problem with Step Deteriorating Jobs

1School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
2School of Mechanical Engineering and Automation, Xihua University, Chengdu 610039, China

Received 20 February 2012; Revised 27 April 2012; Accepted 8 May 2012

Academic Editor: Jung-Fa Tsai

Copyright © 2012 Wenming Cheng et al. 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.


In many real scheduling environments, a job processed later needs longer time than the same job when it starts earlier. This phenomenon is known as scheduling with deteriorating jobs to many industrial applications. In this paper, we study a scheduling problem of minimizing the total completion time on identical parallel machines where the processing time of a job is a step function of its starting time and a deteriorating date that is individual to all jobs. Firstly, a mixed integer programming model is presented for the problem. And then, a modified weight-combination search algorithm and a variable neighborhood search are employed to yield optimal or near-optimal schedule. To evaluate the performance of the proposed algorithms, computational experiments are performed on randomly generated test instances. Finally, computational results show that the proposed approaches obtain near-optimal solutions in a reasonable computational time even for large-sized problems.