Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 280560, 15 pages
Research Article

A Three-Stage Optimization Algorithm for the Stochastic Parallel Machine Scheduling Problem with Adjustable Production Rates

School of Economics and Management, Nanchang University, Nanchang 330031, China

Received 17 October 2012; Accepted 15 January 2013

Academic Editor: Xiang Li

Copyright © 2013 Rui Zhang. 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.


We consider a parallel machine scheduling problem with random processing/setup times and adjustable production rates. The objective functions to be minimized consist of two parts; the first part is related with the due date performance (i.e., the tardiness of the jobs), while the second part is related with the setting of machine speeds. Therefore, the decision variables include both the production schedule (sequences of jobs) and the production rate of each machine. The optimization process, however, is significantly complicated by the stochastic factors in the manufacturing system. To address the difficulty, a simulation-based three-stage optimization framework is presented in this paper for high-quality robust solutions to the integrated scheduling problem. The first stage (crude optimization) is featured by the ordinal optimization theory, the second stage (finer optimization) is implemented with a metaheuristic called differential evolution, and the third stage (fine-tuning) is characterized by a perturbation-based local search. Finally, computational experiments are conducted to verify the effectiveness of the proposed approach. Sensitivity analysis and practical implications are also discussed.