Rescheduling for new orders on a single machine with setup times

We focus on some single machine scheduling problems for which a set of new jobs have to be scheduled after a schedule of old jobs has been set. Each new and old job belongs to a family and changing the production from one family to another requires a setup. The initial schedule of old jobs is assumed to minimize the sum of setup times. The new jobs can be either scheduled after the old jobs or inserted within the existing schedule, which results in a disruption cost that has to be minimized together with the sum of setup times of the overall schedule. In this paper we tackle several simple setup time configurations yielding different scheduling problems for which we propose optimal polynomial time algorithms or provide NP-hardness proofs. In the former case we consider the problem of enumerating the set of strict Pareto optima for the sum of setup times and disruption cost criteria.