数学季刊 ›› 2022, Vol. 37 ›› Issue (4): 331-342.doi: 10.13371/j.cnki.chin.q.j.m.2022.04.001

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关于工件具有多个维护区间最小化总误工量的可中断排序的一个注记

  

  1. 1. School of Management Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450046, China; 2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China; 3. School of Sciences, Henan University of Technology, Zhengzhou 450001, China
  • 收稿日期:2022-11-14 出版日期:2022-12-30 发布日期:2022-12-14
  • 通讯作者: HE Ru-yan (1991-), female, native of Zhengzhou, Henan, lecturer of Zhengzhou University of Aeronautics, engages in scheduling theory; E-mail:heruyan219@163.com
  • 作者简介:HE Ru-yan (1991-), female, native of Zhengzhou, Henan, lecturer of Zhengzhou University of Aeronautics, engages in scheduling theory; YUAN Jin-jiang (1965-), male, native of Zhengzhou, Henan, professor of Zhengzhou University, engages in scheduling theory; ZHANG Yuan (1990-), female, native of Zhengzhou, Henan, lecturer of Henan University of Technology, engages in scheduling theory.
  • 基金资助:
     Supported by National Natural Science Foundation of China (Grant Nos. 12071442, 12201186).

A Note on Preemptive Scheduling with Multiple Maintenance Activities to Minimize the Total Late Work

  1. 1. School of Management Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450046, China; 2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China; 3. School of Sciences, Henan University of Technology, Zhengzhou 450001, China
  • Received:2022-11-14 Online:2022-12-30 Published:2022-12-14
  • Contact: HE Ru-yan (1991-), female, native of Zhengzhou, Henan, lecturer of Zhengzhou University of Aeronautics, engages in scheduling theory; E-mail:heruyan219@163.com
  • About author:HE Ru-yan (1991-), female, native of Zhengzhou, Henan, lecturer of Zhengzhou University of Aeronautics, engages in scheduling theory; YUAN Jin-jiang (1965-), male, native of Zhengzhou, Henan, professor of Zhengzhou University, engages in scheduling theory; ZHANG Yuan (1990-), female, native of Zhengzhou, Henan, lecturer of Henan University of Technology, engages in scheduling theory.
  • Supported by:
     Supported by National Natural Science Foundation of China (Grant Nos. 12071442, 12201186).

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摘要： We study the single-machine preemptive scheduling problem with multiple maintenance activities to minimize the total late work, in which the jobs must be processed in the time space not occupied by the maintenance intervals. For this problem, we present a polynomial algorithm to determine the optimal schedule and establish a formula expression to the optimal value. Moreover, our result is used to correct some minor errors in the literature related to the single-machine (preemptive or non-preemptive) scheduling with one maintenance activity to minimize the total late work. 

关键词: Scheduling, Late work, Maintenance intervals 

Abstract: We study the single-machine preemptive scheduling problem with multiple maintenance activities to minimize the total late work, in which the jobs must be processed in the time space not occupied by the maintenance intervals. For this problem, we present a polynomial algorithm to determine the optimal schedule and establish a formula expression to the optimal value. Moreover, our result is used to correct some minor errors in the literature related to the single-machine (preemptive or non-preemptive) scheduling with one maintenance activity to minimize the total late work. 

Key words: Scheduling, Late work, Maintenance intervals 

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