Scheduling with Testing on Multiple Identical Parallel Machines
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by
Susanne Albers, Alexander Eckl
2021
Abstract
Scheduling with testing is a recent online problem within the framework of
explorable uncertainty motivated by environments where some preliminary action
can influence the duration of a task. Jobs have an unknown processing time that
can be explored by running a test. Alternatively, jobs can be executed for the
duration of a given upper limit. We consider this problem within the setting of
multiple identical parallel machines and present competitive deterministic
algorithms and lower bounds for the objective of minimizing the makespan of the
schedule. In the non-preemptive setting, we present the SBS algorithm whose
competitive ratio approaches 3.1016 if the number of machines becomes large.
We compare this result with a simple greedy strategy and a lower bound which
approaches 2. In the case of uniform testing times, we can improve the SBS
algorithm to be 3-competitive. For the preemptive case we provide a
2-competitive algorithm and a tight lower bound which approaches the same
value.
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