English

运筹学学报 >

2016 , Vol. 20 >Issue 4: 61 - 68

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.04.007

运筹学

带有退化效应和序列相关运输时间的排序问题

展开
  • 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

  网络出版日期: 2016-12-15

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)

收起

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

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

Received date: 2016-02-28

  Online published: 2016-12-15

Fold

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

本文引用格式

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, 2016 , 20(4) : 61 -68 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.04.007

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

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.
Options
文章导航

/

〈 〉