One machine scheduling to minimize the maximum earliness with minimum number of tardy jobs

In this study we consider the problem of sequencing n jobs on one machine under the dual objective of minimizing the maximum earliness (Emax) with minimum number of tardy jobs (nT). A procedure is first proposed to schedule for minimizing the maximum earliness when the set of non-tardy jobs is specified. A branch and bound algorithm is presented to obtain the optimal schedule that minimizes the maximum earliness with minimum number of tardy jobs by connecting Moore's algorithm.