Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection

We study a single machine scheduling problem, where the goal is to maximize the weighted number of jobs completed exactly at their due-dates. The option of job-rejection is considered, i.e., the scheduler may perform only a subset of the jobs. An upper bound on the total permitted rejection cost is assumed. The problem is proved to be NP-hard, and a pseudo-polynomial dynamic programming algorithm is introduced. Our numerical tests indicate that the proposed algorithm performs well: medium size instances (of up to 100 jobs) are solved in less than 1 s.