| dc.description.abstract | We study a scheduling problem in which jobs
may be split into parts, where the parts of a split job may be
processed simultaneously on more than one machine. Each
part of a job requires a setup time, however, on the machine
where the job part is processed. During setup, a machine
cannot process or set up any other job. We concentrate on
the basic case in which setup times are job-, machine- and
sequence-independent. Problems of this kind were encountered
when modelling practical problems in planning disaster relief operations. Our main algorithmic result is a
polynomial-time algorithm for minimising total completion
time on two parallel identical machines. We argue, why the
same problem with threemachines is not an easy extension of
the two-machine case, leaving the complexity of this case as a
tantalising open problem. We give a constant-factor approximation
algorithm for the general case with any number of
machines and a polynomial-time approximation scheme for
a fixed number of machines. For the version with the objective
to minimise total weighted completion time, we prove
NP-hardness. Finally, we conclude with an overview of the
state of the art for other split scheduling problems with job-,
machine- and sequence-independent setup times. | |
