Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
Preemptive multiprocessor scheduling with rejection
Theoretical Computer Science
Single machine scheduling to minimize total compression plus weighted flow cost is NP-hard
Information Processing Letters
Techniques for Scheduling with Rejection
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Single machine scheduling with discretely controllable processing times
Operations Research Letters
On-line scheduling of unit time jobs with rejection: minimizing the total completion time
Operations Research Letters
A PTAS for parallel batch scheduling with rejection and dynamic job arrivals
Theoretical Computer Science
Minimizing the makespan on a single parallel batching machine
Theoretical Computer Science
Single-machine scheduling under the job rejection constraint
Theoretical Computer Science
Two-machine flow-shop scheduling with rejection
Computers and Operations Research
A bicriteria approach to scheduling a single machine with job rejection and positional penalties
Journal of Combinatorial Optimization
International Journal of Applied Evolutionary Computation
A survey on offline scheduling with rejection
Journal of Scheduling
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In the traditional scheduling problems, it is always assumed that any job has to be processed and the processing time is pre-given and fixed. In this paper, we address the scheduling problems with rejection or with discretely compressible processing times in which we can choose a subset of jobs to process or discretely compress the original processing times. Of course, choosing not to process any job or to process it with a compressed processing time incurs a corresponding penalty or cost. We consider the following problems for the first time: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost, scheduling with rejection to minimize the total weighted completion time with the constraint of total penalties and scheduling with discretely compressible processing times to minimize the sum of total weighted completion time plus total compression cost. We show that they are all NP-hard and design pseudo-polynomial time algorithms through dynamic programming and FPTASs for the first two problems. For the third problem, we present a greedy heuristic. Theoretical analysis shows that it has a bounded worst case performance ratio for a special case and large numbers of simulations tell us that it works very well for the general problem.