An Exact Method to Minimize the Number of Tardy Jobs in Single Machine Scheduling

This paper considers the problem of scheduling n jobs on a single machine to minimize the number of tardy (or late) jobs. Each job has a release date, a processing time and a due date. The general case with non-equal release dates and different due dates is considered. Using new and efficient lower bounds and several dominance rules, a branch and bound scheme is proposed based on the definition of a master sequence, i.e. a sequence containing at least one optimal sequence. With this procedure, 95% of 140-job instances are optimally solved in a maximum of one-hour CPU time.