Polynomial Time Algorithms for Minimizing the Weighted Number of Late Jobs on a Single Machine with Equal Processing Times

We study the problem of minimizing the weighted number of late jobs to be scheduled on a single machine when processing times are equal. In this paper, we show that this problem, as well as its preemptive variant, are both strongly polynomial. When preemption is not allowed 1 | pj = p, rj | Σ wj Uj, the problem can be solved in O(n). In the preemptive case, 1 | pj = p, pmtn, rj | Σ wj Uj, the problem can be solved in O(n). Both algorithms are based upon dynamic programming.