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We consider a model for scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to traditional stochastic scheduling models, we assume that jobs arrive online, and there is no knowledge about the jobs that will arrive in the future. The model incorporates both, stochastic scheduling and online scheduling
as a special case. The particular setting we consider is non-preemptive parallel machine scheduling, with the objective to
minimize the total weighted completion times of jobs. We analyze
simple, combinatorial online scheduling policies for that model, and
derive performance guarantees that match performance guarantees previously
known for stochastic and online parallel machine scheduling, respectively.
For processing times that follow NBUE distributions, we
improve upon previously best known performance bounds from
stochastic scheduling, even though we consider a more general
setting.
We consider a non-preemptive, stochastic parallel machine
scheduling model with the goal to minimize the weighted completion
times of jobs. In contrast to the classical stochastic model where jobs
with their processing time distributions are known beforehand, we assume
that jobs appear one by one, and every job must be assigned
to a machine online. We propose a simple online scheduling policy for
that model, and prove a performance guarantee that matches the currently
best known performance guarantee for stochastic parallel machine
scheduling. For the more general model with job release dates we derive
an analogous result, and for NBUE distributed processing times we
even improve upon the previously best known performance guarantee for
stochastic parallel machine scheduling. Moreover, we derive some lower
bounds on approximation.