Online and Semi–Online Scheduling on Two Hierarchical Machines with a Common Due Date to Maximize the Total Early Work

In this study, we investigate several online and semi-online scheduling problems related to two hierarchical machines with a common due date to maximize the total early work. For the pure online case, we design an optimal online algorithm with a competitive ratio of . Additionally, for the cases when the largest processing time is known, we give optimal algorithms with a competitive ratio of 6/5 if the largest job is a lower-hierarchy one, and of − 1 if the largest job is a higher-hierarchy one.