New approximation algorithms for machine scheduling with rejection on single and parallel machine

Peihai Liu () and Xiwen Lu ()
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Peihai Liu: East China University of Science and Technology
Xiwen Lu: East China University of Science and Technology

Journal of Combinatorial Optimization, 2020, vol. 40, issue 4, No 6, 929-952

Abstract: Abstract In this paper we consider three machine scheduling problems with the special feature that jobs may be rejected at a certain penalty. There are n jobs which are characterized by a release date, a processing time and a penalty. Each job is either accepted and then processed by one machine, or rejected and then a rejection penalty is paid. The objective is to minimize the maximum completion time of all accepted job plus the total penalties of all rejected jobs. When jobs have identical release dates, we present a ( $$\frac{3}{2}-\frac{1}{2m}$$ 3 2 - 1 2 m )-approximation algorithm for the parallel machine problem. When jobs have general release dates, we propose a $$\frac{4}{3}$$ 4 3 -approximation algorithm for the single machine problem and a ( $$1+\max \{0.618,1-\frac{1}{m}\}$$ 1 + max { 0.618 , 1 - 1 m } )-approximation algorithm for the parallel machine problem, respectively.

Keywords: Scheduling; Rejection; Release date; Approximation algorithm; Worst-case ratio (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-020-00642-9

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