Single machine scheduling to minimize total late work

In the problem of scheduling a single machine to minimize total late work, there are n jobs to be processed for which each has an integer processing time and a due date. The objective is to minimize the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. For the preemptive total late work problem, an O(n log n) algorithm is derived. The nonpreemptive total late work problem is shown to be NP-hard, although efficient algorithms are derived for the special cases in which all processing times are equal and all due dates are equal. A pseudopolynomial dynamic programming algorithm is presented for the general nonpreemptive total late work problem; it requires O(nUB) time, where UB is any upper bound on the total late work. Computational results for problems with up to 10,000 jobs are given.