Sequencing with earliness and tardiness penalties: a review
Operations Research
Multiprocessor scheduling with rejection
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Theoretical Computer Science
An Optimal Incremental Algorithm for Minimizing Lateness with Rejection
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Bounded single-machine parallel-batch scheduling with release dates and rejection
Computers and Operations Research
A PTAS for parallel batch scheduling with rejection and dynamic job arrivals
Theoretical Computer Science
Scheduling with Rejection to Minimize the Makespan
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
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
Two-machine flow-shop scheduling with rejection
Computers and Operations Research
Scheduling on parallel identical machines with job-rejection and position-dependent processing times
Information Processing Letters
A survey on offline scheduling with rejection
Journal of Scheduling
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Single machine scheduling problems have been extensively studied in the literature under the assumption that all jobs have to be processed. However, in many practical cases, one may wish to reject the processing of some jobs in the shop, which results in a rejection cost. A solution for a scheduling problem with rejection is given by partitioning the jobs into a set of accepted and a set of rejected jobs, and by scheduling the set of accepted jobs among the machines. The quality of a solution is measured by two criteria: a scheduling criterion, F1, which is dependent on the completion times of the accepted jobs, and the total rejection cost, F2. Problems of scheduling with rejection have been previously studied, but usually within a narrow framework--focusing on one scheduling criterion at a time. This paper provides a robust unified bicriteria analysis of a large set of single machine problems sharing a common property, namely, all problems can be represented by or reduced to a scheduling problem with a scheduling criterion which includes positional penalties. Among these problems are the minimization of the makespan, the sum of completion times, the sum and variation of completion times, and the total earliness plus tardiness costs where the due dates are assignable. Four different problem variations for dealing with the two criteria are studied. The variation of minimizing F1+F2 is shown to be solvable in polynomial time, while all other three variations are shown to be $\mathcal{NP}$ -hard. For those hard problems we provide a pseudo polynomial time algorithm. An FPTAS for obtaining an approximate efficient schedule is provided as well. In addition, we present some interesting special cases which are solvable in polynomial time.