We consider the online scheduling with job rejection to minimize the total weighted completion time of the scheduled jobs plus the total rejection penalty of the rejected jobs.In the problem,a set of independent jobs arriving online over time has to be scheduled with the flexibility of rejecting some of the jobs,where preemption is not allowed and the information of each job,including its processing time,release date,weight,and rejection penalty,is not known in advance.For this problem,using a technique named Greedy-Interval-Rejection,we provide an online algorithm with a competitive ratio of at most 4+εon identical machines and an online algorithm with a competitive ratio of at most 8 on unrelated machines,respectively。
Online scheduling is a rapidly developed branch in scheduling theory.In this paper,we present an extensive survey for online over time scheduling on parallel-batch machines.Some open problems are proposed for further research.
We study a scheduling problem with incompatible job families and rejection on a parallel-batching machine,where the objective is to minimize the makespan of all accepted jobs plus the total penalty of all rejected jobs.We provide a polynomial-time algorithm for the case where all jobs have identical release dates and a pseudo-polynomial-time algorithm for the case where the number of distinct release dates is fixed.We also present a 2-approximation algorithm and a polynomial-time approximation scheme for the general problem.
In this paper,we study the Pareto optimization scheduling problem on a single machine with positional due indices of jobs to minimize the total completion time and a maximum cost.For this problem,we give two O(n^(4))-time algorithms.
