Scheduling with Rejection to Minimize the Makespan

Authors:
Yuzhong Zhang;Jianfeng Ren;Chengfei Wang
Affiliations:
Institute of Operations Research, Qufu Normal University, Rizhao, China 276826;Institute of Operations Research, Qufu Normal University, Rizhao, China 276826;Institute of Operations Research, Qufu Normal University, Rizhao, China 276826
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

Citing 5
Cited 3

Multiprocessor Scheduling with Rejection

SIAM Journal on Discrete Mathematics
On-line uniform machine scheduling with rejection

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Preemptive multiprocessor scheduling with rejection

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Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On-line scheduling of unit time jobs with rejection: minimizing the total completion time

Operations Research Letters

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
A survey on offline scheduling with rejection

Journal of Scheduling

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Abstract

In this paper, we consider the scheduling with rejection. The objective functions are to minimize the maximum completion time of the processed ones when the total compression cost is given. Firstly, we prove that the problem 1|rej | C max /TCP is NP-hard, which implying that P m |rej | C max /TCP , 1 |rej , r j |C max /TCP , 1 |rej , on *** line |C max /TCP are all NP-hard. Secondly, for problem P m |rej | C max /TCP , we design a pseudopolynomial time dynamic programming algorithm that solves it exactly and an FPTAS (full polynomial time approximation scheme) when m is a constant. We also design a pseudopolynomial time dynamic programming algorithm and an FPTAS for the case of non-identical job arrival problem 1 |rej , r j |C max /TCP . In the end, we consider the on-line problem 1 |rej , on *** line |C max /TCP and prove that there doesn't exist any on-line algorithm with a constant competitive ratio for it, even if the jobs only have two different release times.