Single machine scheduling to minimize maximum earliness/tardiness cost with job rejection

We study a single machine due-date assignment problem with a common due-date. The objective function is minimizing the maximum earliness/tardiness cost. The scheduler may process only a subset of the jobs and the remaining jobs are rejected. Job-dependent rejection-costs are considered, and an upper bound on the total permitted rejection cost is assumed. The problem is proved to be NP-Hard. We present and test a pseudo-polynomial dynamic programming solution algorithm. An extension to the setting containing additional due-date cost component is also discussed. An efficient implementation of the algorithm is introduced, and medium size problems (containing hundreds of jobs) are shown to be solved in very reasonable running time. In addition, an intuitive heuristic is introduced, tested numerically, and is shown to produce very small optimality gaps.