Stochastic single machine scheduling with quadratic early-tardy penalties
Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
General stochastic single-machine scheduling with regular cost functions
Mathematical and Computer Modelling: An International Journal
Probability in the Engineering and Informational Sciences
CAR'10 Proceedings of the 2nd international Asia conference on Informatics in control, automation and robotics - Volume 2
Scheduling deteriorating jobs on a single machine subject to breakdowns
Journal of Scheduling
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We study a stochastic scheduling problem with a single machine subject to random breakdowns. We address the preemptive-repeat model; that is, if a breakdown occurs during the processing of a job, the work done on this job is completely lost and the job has to be processed from the beginning when the machine resumes its work. The objective is to complete all jobs so that the the expected weighted flow time is minimized. Limited results have been published in the literature on this problem, all with the assumption that the machine uptimes are exponentially distributed. This article generalizes the study to allow that (1) the uptimes and downtimes of the machine follow general probability distributions, (2) the breakdown patterns of the machine may be affected by the job being processed and are thus job dependent; (3) the processing times of the jobs are random variables following arbitrary distributions, and (4) after a breakdown, the processing time of a job may either remain a same but unknown amount, or be resampled according to its probability distribution. We derive the necessary and sufficient condition that ensures the problem with the flow-time criterion to be well posed under the preemptive-repeat breakdown model. We then develop an index policy that is optimal for the problem. Several important situations are further considered and their optimal solutions are obtained.