Inverse interval scheduling via reduction on a single machine

Abstract

We consider an inverse counterpart of the interval scheduling problem. In the problem, we are given a set of machines and the objective is to reduce the non-preemptive job intervals with a least cost so that all jobs with positive processing times may be scheduled on the machines. The paper focuses on the single machine case. We establish the strong NP-hardness of the problem and show however it admits a polynomial time approximation scheme.