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Journal of Applied Mathematics
Volume 2014, Article ID 273567, 14 pages
Research Article

The Nonpermutation Flowshop Scheduling Problem: Adjustment and Bounding Procedures

Department of Industrial Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

Received 13 April 2014; Revised 8 October 2014; Accepted 14 October 2014; Published 26 November 2014

Academic Editor: Yuri N. Sotskov

Copyright © 2014 Anis Gharbi 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.


We consider the makespan minimization in a flowshop environment where the job sequence does not have to be the same for all the machines. Contrarily to the classical permutation flowshop scheduling problem, this strongly NP-hard problem received very scant attention in the literature. In this paper, some improved single-machine-based adjustment procedures are proposed, and a new two-machine-based one is introduced. Based on these adjustments, new lower and upper bounding schemes are derived. Our experimental analysis shows that the proposed procedures provide promising results.