Single machine scheduling with maximum earliness and number tardy

In this paper, we study the bicriteria scheduling problem of minimizing the maximum earliness and the number of tardy jobs on a single machine. We assume idle time insertion is not allowed. We first examine the problem of minimizing maximum earliness while keeping the number of tardy jobs to its minimum value. We then propose a general procedure for generating all efficient schedules for bicriteria problems. We also develop a general procedure to find the efficient schedule that minimizes a composite function of the two criteria by evaluating only a small fraction of the efficient solutions. We adapt the general procedures for the bicriteria problem of minimizing maximum earliness and the number of tardy jobs.