Parallel-machine scheduling with potential disruption and positional-dependent processing times

Bin Zheng; Min Fan; Mengqi Liu; Shang-Chia Liu; Yunqiang Yin

doi:10.3934/jimo.2016041

Article Contents

2017, Volume 13, Issue 2: 697-711. Doi: 10.3934/jimo.2016041

This issue Previous Article Algorithms for single-machine scheduling problem with deterioration depending on a novel model Next Article Multiple common due-dates assignment and optimal maintenance activity scheduling with linear deteriorating jobs

Parallel-machine scheduling with potential disruption and positional-dependent processing times

1.
Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
2.
Business School, Hunan University, Changsha, Hunan 410082, China
3.
Department of Business Administration, Fu Jen Catholic University, New Taipei City, Taiwan

* Corresponding author: Mengqi Liu
* Corresponding author: Mengqi Liu

Received: September 30, 2015

Revised: December 31, 2015

Published: August 2017

This paper was supported in part by the National Natural Science Foundation of China (71301022,71471057); and in part by the Personnel Training Fund of Kunming University of Science and Technology (KKSY201407098).

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Abstract

In this paper, we address the scheduling problem with positional-dependent processing times in a disruptive environment, in which there is a possibility that some of the machines become unavailable for a certain period of time with a certain probability due to a disruption at a particular time. By positional-dependent processing times, we mean that the actual processing time of a job depends on its processing position on a machine. Since some machines may be unavailable for a certain period of time, both non-resumable and resumable cases are considered. The objective is to minimize the expected total completion time. For various cases, we provide the complexity results and present efficient pseudo-polynomial time algorithms for the corresponding problems.

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Mathematics Subject Classification: Primary: 90B3E; Secondary: 90C59.

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