A Single-machine Scheduling with Generalized Due Dates to Minimize Total Weighted Late Work

Abstract

In the paper, we consider a single-machine scheduling problem with generalized due dates, in which the objective is to minimize total weighted work. This problem was proven to be NP-hard by Mosheiov et al. [1]. However, the exact complexity remains open. We show that the problem is strongly NP-hard, and is weakly NP-hard if the lengths of the intervals between the consecutive due dates are identical.