A note on the SPT heuristic for solving scheduling problems with generalized due dates

Two NP-hard scheduling problems on parallel identical machines with generalized due dates are studied. We focus on two objectives: (i) minimizing maximum tardiness and (ii) minimizing total tardiness. In both cases, we introduce a shortest processing time first (SPT)-based heuristic and simple lower bounds on the optimal cost. Our numerical study indicates that the SPT heuristic performs extremely well in all settings. In traditional scheduling literature, due dates are job dependent, i.e., a specific job has to be completed by a given due date. When generalized due dates are considered, a certain number of jobs must be completed by each specified due date. The identity of the jobs is immaterial. In this note, we address two hard multi-machine scheduling problems with generalized due dates. We introduce a simple and efficient heuristic, which is shown numerically to produce very close to optimal schedules.