Robust Single Machine Scheduling Problem with Weighted Number of Late Jobs Criterion

This paper deals with a single machine scheduling problem with the weighted number of late jobs criterion, where some job parameters, such as: processing times, due dates, and weights, may be uncertain. This uncertainty is modeled by specifying a scenario set containing all vectors of the job parameters, called scenarios, which may occur. The min-max criterion is adopted to compute a solution under uncertainty. In this paper some of the recent negative complexity and approximability results for the problem are extended and strengthened. Moreover, some positive approximation results for the problem in which the maximum criterion is replaced with the OWA operator are presented.