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Article

Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval

by
Lili Zuo
1,
Zhenxia Sun
1,
Lingfa Lu
1,* and
Liqi Zhang
2
1
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
2
College of Information and Management Science, Henan Agricultural University, Zhengzhou 450002, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 668; https://doi.org/10.3390/math7080668
Submission received: 8 July 2019 / Revised: 20 July 2019 / Accepted: 24 July 2019 / Published: 26 July 2019
(This article belongs to the Special Issue Advances and Novel Approaches in Discrete Optimization)
Versions Notes

Abstract

In this paper, we study two scheduling problems on a single machine with rejection and an operator non-availability interval. In the operator non-availability interval, no job can be started or be completed. However, a crossover job is allowed such that it can be started before this interval and completed after this interval. Furthermore, we also assume that job rejection is allowed. That is, each job is either accepted and processed in-house, or is rejected by paying a rejection cost. Our task is to minimize the sum of the makespan (or the total weighted completion time) of accepted jobs and the total rejection cost of rejected jobs. For two scheduling problems with different objective functions, by borrowing the previous algorithms in the literature, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme (FPTAS), respectively.
Keywords: scheduling with rejection; machine non-availability; operator non-availability; dynamic programming; FPTAS scheduling with rejection; machine non-availability; operator non-availability; dynamic programming; FPTAS

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MDPI and ACS Style

Zuo, L.; Sun, Z.; Lu, L.; Zhang, L. Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval. Mathematics 2019, 7, 668. https://doi.org/10.3390/math7080668

AMA Style

Zuo L, Sun Z, Lu L, Zhang L. Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval. Mathematics. 2019; 7(8):668. https://doi.org/10.3390/math7080668

Chicago/Turabian Style

Zuo, Lili, Zhenxia Sun, Lingfa Lu, and Liqi Zhang. 2019. "Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval" Mathematics 7, no. 8: 668. https://doi.org/10.3390/math7080668

APA Style

Zuo, L., Sun, Z., Lu, L., & Zhang, L. (2019). Single-Machine Scheduling with Rejection and an Operator Non-Availability Interval. Mathematics, 7(8), 668. https://doi.org/10.3390/math7080668

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