Optim Lett DOI 10.1007/s11590-009-0163-4 ORIGINAL PAPER An optimal online algorithm for two-machine open shop preemptive scheduling with bounded processing times Ming Liu · Chengbin Chu · Yinfeng Xu · Feifeng Zheng Received: 7 May 2009 / Accepted: 10 November 2009 © Springer-Verlag 2009 Abstract This paper deals with a two-machine open shop scheduling problem. The objective is to minimize the makespan. Jobs arrive over time. We study preemption- resume model, i.e., the currently processed job may be preempted at any moment in necessary and be resumed some time later. Let p 1, j and p 2, j denote the processing time of a job J j on the two machines M 1 and M 2 , respectively. Bounded processing times mean that 1 ≤ p i , j ≤ α (i = 1, 2) for each job J j , where α ≥ 1 is a constant number. We propose an optimal online algorithm with a competitive ratio 5α-1 4α . Keywords Open shop scheduling · Bounded processing times · Competitive analysis · Online algorithm M. Liu · C. Chu · Y. Xu · F. Zheng School of Management, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China M. Liu (B ) · C. Chu Laboratoire Génie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry Cedex, France e-mail: minyivg@gmail.com C. Chu e-mail: chengbin.chu@ecp.fr Y. Xu · F. Zheng State Key Laboratory for Manufacturing Systems Engineering, 710049 Xi’an, Shaanxi, People’s Republic of China e-mail: yfxu@mail.xjtu.edu.cn F. Zheng e-mail: zhengff@mail.xjtu.edu.cn 123