 
Summary: Scheduling with Unexpected Machine Breakdowns
Susanne Albers Gunter Schmidty
Abstract
We investigate an online version of a basic scheduling problem where a set of jobs has
to be scheduled on a number of identical machines so as to minimize the makespan. The
job processing times are known in advance and preemption of jobs is allowed. Machines
are noncontinuously available, i.e., they can break down and recover at arbitrary time
instances not known in advance. New machines may be added as well. Thus machine
availabilities change online.
We rst show that no online algorithm can construct optimal schedules. We also
show that no online algorithm can achieve a bounded competitive ratio if there may be
time intervals where no machine is available. Then we present an online algorithm that
constructs schedules with an optimal makespan of COPTmax if a lookahead of one is given,
i.e., the algorithm always knows the next point in time when the set of available machines
changes. Finally we give an online algorithm without lookahead that constructs schedules
with a nearly optimal makespan of COPTmax + , for any > 0, if at any time at least one
machine is available. Our results demonstrate that not knowing machine availabilities in
advance is of little harm.
1 Introduction
In scheduling theory the basic model assumes that a xed set of machines is continuously
