Minimizing the weighted number of tardy task units

Minimizing the Number of Tardy Jobs

Minimizing Weighted Number of Tardy Jobs and Weighted Completion Time 1

In this paper, we present a novel O(N) algorithm to minimize the weighted number of tardy jobs with unit processing times, integer ready times and deadlines, and M homogeneous parallel machines, where N is the number of jobs to be scheduled. wi is the weight re ecting job i's importance, and Ui is 1 if job i is tardy and 0 otherwise, so P wiUi is the measure of performance. (In standard notatio...

Heterogeneous-criteria scheduling: Minimizing weighted number of tardy jobs and weighted completion time

In this paper, we present a novel O(N) algorithm to minimize the weighted number of tardy jobs with unit processing times, integer ready times and deadlines, and M homogeneous parallel machines, where N is the number of jobs to be scheduled. wi is the weight re ecting job i's importance, and Ui is 1 if job i is tardy and 0 otherwise, so P wiUi is the measure of performance. (In standard notatio...

Minimizing the number of tardy job units under release time constraints

We study two single-machine scheduling problems: Minimizing the weighted and unweighted number of tardy units, when release times are present. Fast strongly polynomial algorithms are given for both problems: For problems with n jobs, we give algorithms which require O(n log n) and O(n2) steps, for the unweighted and weighted problems respectively. Our results also imply an extension of the fami...

New Algorithms for Minimizing the Weighted Number of Tardy Jobs On a Single Machine

In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or is taken as a parameter in the sense of parameterized complexity. These three parameters are the number of different due dates, processing times, and weigh...