International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 39, Pages 2475-2486

Two-machine flowshop scheduling problem to minimize makespan or total completion time with random and bounded setup times

Ali Allahverdi,1 Tariq Aldowaisan,1 and Yuri N. Sotskov2

1Department of Industrial and Management Systems Engineering, College of Engineering and Petroleum, Kuwait University, P. O. Box 5969, Safat, Kuwait
2Institute of Engineering Cybernetics, 6 Surganova Street, Minsk 220012, Belarus

Received 21 October 2002

Copyright © 2003 Ali Allahverdi 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.


This paper addresses the two-machine flowshop scheduling problem with separate setup times to minimize makespan or total completion time (TCT). Setup times are relaxed to be random variables rather than deterministic as commonly used in the OR literature. Moreover, distribution-free setup times are used where only the lower and upper bounds are given. Global and local dominance relations are developed for the considered flowshops and an illustrative numerical example is given.