Abstract:
Duplication has proved to be a vital technique
for scheduling task graphs on a network of unrelated parallel
machines. Few attempts have been made to model duplication in a
Mixed Integer Linear Program (MILP) to reduce schedule length.
Other known optimal MILPs duplicate a job on all the available
processing elements and this increases their complexities. This
paper proposes a new REStricted Duplication (RESDMILP)
approach to model duplication in a MILP. The complexity of this
model increases with the increase in the amount of duplication.
Experiments conducted have revealed that RESDMILP achieves
better runtimes when the problem instance is solved optimally
and provides better lower bound and percentage gap if it is run
for a fixed amount of time. The percentage gap is defined as,
(UB − LB)/UB where UB and LB are the upper and lower
bounds achieved by the MILPs respectively
