On the tractability of hard scheduling problems with generalized due-dates with respect to the number of different due-dates

Abstract We study two $$\mathcal {NP}$$ NP -hard single-machine scheduling problems with generalized due-dates. In such problems, due-dates are associated positions in the job sequence rather than jobs. Accordingly, that is assigned to position j processing order (job sequence), a predefined due-date, $$\delta _{j}$$ ? j . first problem, objective consists of finding schedule minimizes maximal absolute lateness, while second we aim maximize weighted number jobs completed exactly at their due-date. Both known be strongly when instance includes an arbitrary different Our tractability both respect instance, $$\nu _{d}$$ ? d show remain $$ \mathcal even _{d}=2$$ = 2 , and solvable pseudo-polynomial time value upper bounded by constant. To complement our results, fixed parameterized tractable ( FPT ) combine parameters times _{p}$$ p ).