Restricted Duplication Based MILP Formulation for Scheduling Task Graphs on Unrelated Parallel Machines

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 (U B - LB)/U B where U B and LB are the upper and lower bounds achieved by the MILPs respectively.