Solving a time-indexed formulation for an unrelated parallel machine scheduling problem by preprocessing and cutting planes

We consider a time-indexed formulation for the unrelated parallel machine scheduling problem. show that all polyhedral knowledge known from single problem (in particular, valid inequalities) is applicable to this formulation. present new facet-inducing inequalities and preprocessing technique involving fixing variables based on reduced costs. combine both techniques in basic cutting-plane algorithm test performance of resulting by running it randomly generated instances.