Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
Preemptive multiprocessor scheduling with rejection
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Theoretical Computer Science
Bounded single-machine parallel-batch scheduling with release dates and rejection
Computers and Operations Research
On several scheduling problems with rejection or discretely compressible processing times
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Approximate minimization algorithms for the 0/1 Knapsack and Subset-Sum Problem
Operations Research Letters
On-line scheduling of unit time jobs with rejection: minimizing the total completion time
Operations Research Letters
A survey on offline scheduling with rejection
Journal of Scheduling
| Hi-index | 5.23 |
In this paper, we consider single-machine scheduling problems under the job rejection constraint. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the single machine. However, the total rejection penalty of the rejected jobs cannot exceed a given upper bound. The objective is to find a schedule such that a given criterion f is minimized, where f is a non-decreasing function on the completion times of the accepted jobs. We analyze the computational complexities of the problems for distinct objective functions and present pseudo-polynomial-time algorithms. In addition, we provide a fully polynomial-time approximation scheme for the makespan problem with release dates. For other objective functions related to due dates, we point out that there is no approximation algorithm with a bounded approximation ratio.