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This paper presents a review of single machine scheduling to minimize the weighted number of tardy jobs. The problem involves processing n jobs on a single machine, each having processing time $p_j$ and due date $d_j$. The aim is to schedule the jobs to meet their due date. A job is tardy if the completion time of job $j$ is $C_j>d_j$ and on-time otherwise. This paper assesses works done to minimize the weighted number of tardy jobs by providing an extensive review of authors, methods and techniques used. Finally, the possible direction for future research is presented.

A survey of single machine scheduling to minimize weighted number of tardy jobs