Deterministic and random single machine sequencing with variance minimization
Operations Research
One-processor scheduling with symmetric earliness and tardiness penalties
Mathematics of Operations Research
Single machine flow-time scheduling with a single breakdown
Acta Informatica
Sequencing with earliness and tardiness penalties: a review
Operations Research
Stochastic single machine scheduling with quadratic early-tardy penalties
Operations Research
Probability in the Engineering and Informational Sciences
Stochastic single machine scheduling with an exponentially distributed due date
Operations Research Letters
Analysis of computer job control under uncertainty
Journal of Computer and Systems Sciences International
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We study a stochastic scheduling problem of processing a set of jobs on a single machine. Each job has a random processing time Pi and a random due date Di, which are independently and exponentially distributed. The machine is subject to stochastic breakdowns in either preempt-resume or preempt-repeat patterns, with the uptimes following an exponential distribution and the downtimes (repair times) following a general distribution. The problem is to determine an optimal sequence for the machine to process all jobs so as to minimize the expected total cost comprising asymmetric earliness and tardiness penalties, in the form of E[∑&agr;i max{0,Di − Ci} + &bgr;i max{0,Ci − Di}]. We find sufficient conditions for the optimal sequences to be V-shaped with respect to {E(Pi)/&agr;i} and {E(Pi)/&bgr;i}, respectively, which cover previous results in the literature as special cases. We also find conditions under which optimal sequences can be derived analytically. An algorithm is provided that can compute the best V-shaped sequence.