误工排序问题是经典排序论中最基本的问题之一。1968年Moore提出解决这个问题的算法,可以在时间O(nlogn)内得到最优解。误工问题推广到以下情况:或者某些工件必须不误工;或者工件的加工时间与工件的权有反向一致性;或者工件的加工时间与工件的权具有反向一致性,并且某些工件必须不误工等等。对于这些误工问题及其推广问题提出了多项式时间算法,证明了算法的最优性,并且证明了算法得到的最优解是所有最优解中不误工工件加工时间之和是最小的。
The single machine scheduling to minimize the number of tardy jobs is one of the most fundamental scheduling problems in scheduling theory. The famous Moore-Hodgson algorithm could get the problem's optimal solution in O (n log n). It have been generalized to some issues as follow: some jobs must be early; or the job's processing times and weights are reverse agreeable, or both the job's processing times and weights are reverse agreeable, and some jobs must be early. In this paper a new polynomial time algorithm of the last problem is proposed, its optimality is proved, and the optimum gotten by the algorithm has the shortest total processing time of on-time jobs among all optima.