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Mathematical Problems in Engineering
Volume 2014, Article ID 260415, 9 pages
Research Article

Optimal Rules for Single Machine Scheduling with Stochastic Breakdowns

1School of Economics and Management, Shanghai University of Electric Power, Shanghai 200090, China
2School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
3School of Electrical and Computer Engineering, Georgia Institute of Technology, GA 31407, USA
4Research Institute of Automation, East China University of Science and Technology, Shanghai 200237, China

Received 2 June 2014; Accepted 4 September 2014; Published 29 September 2014

Academic Editor: Kang Li

Copyright © 2014 Jinwei Gu 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 studies the problem of scheduling a set of jobs on a single machine subject to stochastic breakdowns, where jobs have to be restarted if preemptions occur because of breakdowns. The breakdown process of the machine is independent of the jobs processed on the machine. The processing times required to complete the jobs are constants if no breakdown occurs. The machine uptimes are independently and identically distributed (i.i.d.) and are subject to a uniform distribution. It is proved that the Longest Processing Time first (LPT) rule minimizes the expected makespan. For the large-scale problem, it is also showed that the Shortest Processing Time first (SPT) rule is optimal to minimize the expected total completion times of all jobs.