带有退化效应和序列相关运输时间的排序问题

doi:10.15960/j.cnki.issn.1007-6093.2016.04.007

运筹学学报

带有退化效应和序列相关运输时间的排序问题

苗翠霞^1,*邹娟¹

1. 曲阜师范大学数学科学学院，山东曲阜 273165

收稿日期:2016-02-28 出版日期:2016-12-15 发布日期:2016-12-15
通讯作者: 苗翠霞 miaocuixia@126.com
基金资助:
国家自然科学基金(No. 11201259), 教育部博士点基金(Nos. 20123705120001, 20123705110003), 山东省自然科学基金(Nos. ZR2014AM012, BS2013SF016), 曲阜师范大学科研奖励基金(No. xkj201516)

Scheduling with simple deterioration and past-sequence-dependent delivery times

MIAO Cuixia^1,*ZOU Juan¹

1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China

Received:2016-02-28 Online:2016-12-15 Published:2016-12-15

摘要/Abstract

摘要：

考虑带有退化效应和序列相关运输时间的单机排序问题. 工件的加工时间是其开工时间的简单线性增加函数. 当机器单个加工工件时, 极小化最大完工时间、(加权)总完工时间和总延迟问题被证明是多项式可解的, EDD序对于极小化最大延迟问题不是最优排序, 另外, 就交货期和退化率一致情形给出了一最优算法. 当机器可分批加工工件时, 分别就极小化最大完工时间和加权总完工时间问题提出了多项式时间最优算法.

关键词: 排序, 并行分批, 退化效应, 序列相关运输时间

Abstract:

In this paper, the single-machine scheduling problem with simple deterioration and past-sequence-dependent (p-s-d) job delivery times is considered, in which the processing time of each job is a simple linear increasing function of its starting time. When the machine can process only one job at a time, firstly, the makespan, the total (weighted) completion time and the total lateness minimization problems are solvable in polynomial, the EDD rule is not an optimal solution to the maximum lateness minimization problem, and an optimal solution to the case where jobs have agreeable due dates and deteriorating rates is proposed. When the machine can process up to $b$ jobs simultaneously as a batch, i.e., the parallel-batch scheduling problems, two polynomial time optimal algorithms for the makespan minimization problem and the total weighted completion time minimization problem are presented, respectively.

Key words: scheduling, parallel-batch, deterioration, past-sequence-dependent delivery times

苗翠霞, 邹娟. 带有退化效应和序列相关运输时间的排序问题[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2016.04.007.

MIAO Cuixia, ZOU Juan. Scheduling with simple deterioration and past-sequence-dependent delivery times[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.04.007.

参考文献

[1] Gupta G N D, Gupta S K. Single facility scheduling with nonlinear processing times [J]. Computer and Industrial Engineering, 1988, 14: 387-393.

[2] Browne S, Yechiali U. Scheduling deteriorating jobs on a single processor [J]. Operations Research, 1990, 28: 495-498.

[3] Mosheiov G. Scheduling jobs under simple linear deterioration [J]. Computers and Operations Research, 1994, 21: 653-659.

[4] Cheng T C E, Ding Q, Lin B M T. A concise survey of scheduling with time-dependent processing times [J]. European Journal of Operational Research, 2004, 152: 1-13.

[5] Gawiejnowicz S. Time-Dependent Scheduling [M]. Berlin: Springer-Verlag, 2008.

[6] Cheng T C E, Yang S J, Yang D L. Common due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity [J]. International Journal of Production Economics, 2012, 135: 154-161.

[7] Wang J B, Wang M Z. Single-machine scheduling with nonlinear deterioration [J]. Optimization Letters, 2012, 6: 87-98.

[8] Wang J B, Wang J J. Single-machine scheduling problems with precedence constraints and simple linear deterioration [J]. Applied Mathematical Modelling, 2015, 39: 1172-1182.

[9] Brucker P, Gladky A, Hoogeveen H, et al. Scheduling a batching machine [J]. Journal of Scheduling, 1998, 1: 31-54.

[10] Potts C N, Kovalyov M Y. Scheduling with batching: a review [J]. European Journal of Operational Research, 2000, 120: 228-249.

[11] Yuan J J, Qi X L, Lu L F, et al. Single machine unbounded parallel-batch scheduling [J]. European Journal of Operational Research, 2008, 186: 112-117.

[12] Li S S, Chen R X. Scheduling a bounded parallel-batching machine with incompatible job families and rejection [J]. Journal of the Operations Research Society of China, 2014, 2(4): 499-510.

[13] Wang C F, Zhang Y Z. On-line batch scheduling with known information in advance [J]. Operations Research Transactions, 2016, 20(1): 84-90.

[14] Koulamas C, Kyparisis G J. Single-machine scheduling problems with past-sequence-dependent delivery times [J]. International Journal of Production Economics, 2010, 126: 264-266.

[15] Liu M, Zheng F F, Chu C B, et al. New results on single-machine scheduling with past-sequence-dependent delivery times [J]. Theoretical Computer Science, 2012, 438: 55-61.

[16] Liu M, Zheng F F, Chu C B, et al. Single-machine scheduling with past-sequence-dependent delivery times and release times [J]. Information Processing Letters, 2012, 112: 835-838.

[17] Cheng T C E, Lee W C, Wu C C. Single-machine scheduling with deteriorating jobs and past-sequence-dependent setup times [J]. Applied Mathematical Modelling, 2011, 35: 1861-1867.

[18] Liu M, Zheng F F, Wang S J, et al. Scheduling deteriorating jobs with past-sequence-dependent delivery times [J]. International Journal of Production Economics, 2013, 44: 418-421.

[19] Shen L X, Wu Y B. Single machine past-sequence-dependent delivery times scheduling with general position-dependent and time-dependent learning effects [J]. Applied Mathematical Modelling, 2013, 37: 5444-5451.

[20] Zhao C L, Tang H Y. Single machine scheduling problems with general position-dependent processing times and past-sequence-dependent delivery times [J]. Journal of Applied Mathematics Computer, 2014, 45: 259-274.

[21] Yin Y Q, Cheng T C E, Xu J Y, et al. Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration [J]. Journal of Industral and Management Optimization, 2013, 9(2): 323-339.

[22] Graham R L, Lawler E L, Lenstra J K, et al. Optimization and approximation in deterministic sequencing and scheduling: a survey [J]. Annals of Discrete Mathematics, 1979, 5: 287-326.

带有退化效应和序列相关运输时间的排序问题

Scheduling with simple deterioration and past-sequence-dependent delivery times

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	张玉忠. 工件可拒绝排序问题综述[J]. 运筹学学报, 2020, 24(2): 111-130.
[2]	陈如冰, 原晋江. 工件具有加工位置上限最小化加权总误工量的单机排序问题[J]. 运筹学学报, 2020, 24(2): 131-144.
[3]	刘晓霞, 余山杉, 罗文昌. 工作有到达时间且拒绝工件总个数受限的单机平行分批排序问题的近似算法[J]. 运筹学学报, 2020, 24(1): 131-139.
[4]	苟燕, 戴秦, 张新功. 具有时间与位置相关的两类平行机排序问题[J]. 运筹学学报, 2019, 23(4): 86-94.
[5]	李刚刚, 鲁习文. 目标为最小化工件运输时间和的单台机器带一个维修时间段的排序问题的一个改进算法[J]. 运筹学学报, 2019, 23(4): 95-104.
[6]	李文华, 翟威娜, 柴幸, 高超. 具有两个不相容工件族单位工件的有界分批在线排序问题[J]. 运筹学学报, 2019, 23(4): 105-110.
[7]	张国川, 陈林. 负载均衡问题[J]. 运筹学学报, 2019, 23(3): 1-14.
[8]	仲维亚, 杨若瑶. 工件具有子工件工期的排序问题[J]. 运筹学学报, 2019, 23(2): 67-74.
[9]	彭南南, 张玉忠, 柏庆国, 王成飞. 工件满足一致性的同类机在线分批排序问题[J]. 运筹学学报, 2019, 23(1): 111-118.
[10]	赵晓成, 李大刚. 机器和工人都有加工资质约束的平行机排序问题研究[J]. 运筹学学报, 2018, 22(3): 99-108.
[11]	何程, 韩鑫鑫. 同时最小化最大费用和最大完工时间的双代理无界平行分批排序[J]. 运筹学学报, 2018, 22(3): 109-116.
[12]	闵啸，朱俊蕾，刘静. 两台带服务等级的可拒绝同型机排序问题的在线算法[J]. 运筹学学报, 2018, 22(3): 117-124.
[13]	酒明珠, 高园, 原晋江. 工件可自由下线最小化总完工时间的平行分批排序问题[J]. 运筹学学报, 2018, 22(1): 32-41.
[14]	张龙, 张玉忠, 柏庆国. 一类博弈排序问题的纳什均衡存在性证明 [J]. 运筹学学报, 2018, 22(1): 87-96.
[15]	王磊, 张玉忠, 邢伟, 任建峰. 具有可变配送费用和固定配送时刻的单机排序问题[J]. 运筹学学报, 2017, 21(3): 14-22.