带有固定区间的单机双代理可中断总误工问题

doi:10.15960/j.cnki.issn.1007-6093.2019.01.007

运筹学学报 ›› 2019, Vol. 23 ›› Issue (1): 61-71.doi: 10.15960/j.cnki.issn.1007-6093.2019.01.007

带有固定区间的单机双代理可中断总误工问题

陈秋宏, 张新功^*

重庆师范大学数学科学学院, 重庆 401331

收稿日期:2017-10-11 出版日期:2019-03-15 发布日期:2019-03-15
通讯作者: 张新功 E-mail:zxg7980@163.com
基金资助:
国家自然科学基金（Nos.11571321，715610007），贵州省教育厅项目（No.14zd007），重庆市科委自然科学基金（No.cstc2018jcyjAX0631）

Two-agent preemptive scheduling of jobs with fixed time windows problem about total tardiness on a single machine

CHEN Qiuhong, ZHANG Xingong^*

College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

Received:2017-10-11 Online:2019-03-15 Published:2019-03-15

摘要/Abstract

摘要：

研究带有固定区间的两个代理单机排序问题.第一个代理工件可中断，且工件到达时间与工期满足一致关系，目标函数为最小化总误工.第二个代理工件被安排在固定时间窗口.目标是寻找一个排序，使得满足第二个代理目标可行情况下，第一个代理目标函数值最小.在固定区间等于加工时间的情况下，利用分块原则，提出了一个伪多项式时间动态规划算法，并给出了固定区间大于加工时间情况下的时间复杂度分析.

关键词: 单台机器, 两个代理, 总误工, 固定时间窗口

Abstract:

This paper considers two agent scheduling problems with fixed time windows on a single machine. The jobs of the first agent might be preemptive. There exists agreeable condition with release time and due data. The objective function is to minimize the total tardiness. The focus is to find an optimal sequence that minimizes the objective of the first agent, while keeping all jobs of the second agent schedule within fixed time windows. By block principle, we present a pseudo-polynomial time dynamic programming algorithm when fixed time window equals the processing time. If the fixed time windows is larger than the processing time, we give the time complexity of the proposed problem.

Key words: single scheduling, two-agent, total tardiness, fixed time windows

中图分类号:

O223

陈秋宏, 张新功. 带有固定区间的单机双代理可中断总误工问题[J]. 运筹学学报, 2019, 23(1): 61-71.

CHEN Qiuhong, ZHANG Xingong. Two-agent preemptive scheduling of jobs with fixed time windows problem about total tardiness on a single machine[J]. Operations Research Transactions, 2019, 23(1): 61-71.

参考文献

[1] Agnetis A, Mirchandani P B, Pacciarelli D, et al. Scheduling problems with two competing agents[J]. Operations Research, 2004, 52(2):229-242.
[2] Agnetis A, Pacciarelli D, Pacifici A. Multi-agent single machine scheduling[J]. Annals of Operations Research, 2007, 150(1):3-15.
[3] Cheng T C E, Ng C T, Yuan J J. Multi-agent scheduling on a single machine with max-form criteria[J]. European Journal of Operational Research, 2008, 188(2):603-609.
[4] Leung J Y T, Pinedo M, Wan G H. Competitive two-agent scheduling and its applications[J]. Operations Research, 2010, 58(2):458-469.
[5] Perez-Gonzalez P, Framinan J M. A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs:Multi-agent scheduling problems[J]. European Journal of Operational Research, 2014, 235(1):1-16.
[6] 马露, 张新功. 关于总误工损失的两个代理单机排序问题[J]. 运筹学学报, 2017, 21(1):13-22.
[7] Lawler E L. A pseudopolynomial algorithm for sequencing jobs to minimize total tardiness[J]. Annals of Discrete Mathematics, 1977, 1:331-342.
[8] Koulamas C, Kyparisis G J. Single machine scheduling with release times, deadlines and tardiness objectives[J]. European Journal of Operational Research, 2001, 133(2):447-453.
[9] Tian Z J, Ng C T, Cheng T C E. An O(n²) algorithm for scheduling equal-length preemptive jobs on a single machine to minimize total tardiness[J]. Journal of Scheduling, 2006, 9(4):343-364.
[10] Tian Z J, Ng C T, Cheng T C E. Preemptive scheduling of jobs with agreeable due dates on a single machine to minimize total tardiness[J]. Operations Research Letters, 2009, 37(5):368-374.
[11] Graham R L, Lawler E L, Lenstra J K, et al. Optimization and approximation in deterministic machine scheduling:a survey[J]. Annals of Discrete Mathematics, 1979, 5:287-326.
[12] Pinedo M L. Scheduling:Theory, Algorithms, and Systems[M]. New Jersey:Prentice Hall, 1955.
[13] Baker K R, Lawler E L, Lenstra J K, et al. Preemptive scheduling of a single machine to minimize maximum cost subject to release dates and precedence constraints[J]. Operations Research, 1983, 31(2):381-386.
[14] Brucker P. Scheduling Algorithms[M]. Berlin:Springer-Verlag, 2007.

带有固定区间的单机双代理可中断总误工问题

Two-agent preemptive scheduling of jobs with fixed time windows problem about total tardiness on a single machine

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