American Institute of Mathematical Sciences

Advanced
April  2010, 6(2): 269-282. doi: 10.3934/jimo.2010.6.269

A semi-online algorithm and its competitive analysis for a single machine scheduling problem with bounded processing times

Jiping Tao 1, , Zhijun Chao 1, and  Yugeng Xi 1,

1. 

Department of Automation, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, China, China, China

Received  April 2009 Revised  October 2009 Published  March 2010

The single machine semi-online scheduling problem with the objective of minimizing total completion time is investigated with the assumption that the ratio of the longest to the shortest processing time is not greater than a constant $\gamma$. A semi-online algorithm is designed and its competitive ratio is proven to be $1+ \frac{\gamma - 1}{1 + \sqrt {1 + \gamma (\gamma - 1)}}$. The competitive analysis method is as following: it starts from an arbitrary instance and modifies the instance towards the possible structure of the worst-case instance with respect to the given online algorithm. The modification guarantees that the performance ratio does not decrease. Eventually, it comes up with a relatively simple instance with a special structure, whose performance ratio can be directly analyzed and serves as an upper bound on the competitive ratio.
Keywords: online algorithms, single machine scheduling, competitive analysis..
Mathematics Subject Classification: Primary: 90B35; Secondary: 68Q2.
Citation: Jiping Tao, Zhijun Chao, Yugeng Xi. A semi-online algorithm and its competitive analysis for a single machine scheduling problem with bounded processing times. Journal of Industrial and Management Optimization, 2010, 6 (2) : 269-282. doi: 10.3934/jimo.2010.6.269
[1]

Hua-Ping Wu, Min Huang, W. H. Ip, Qun-Lin Fan. Algorithms for single-machine scheduling problem with deterioration depending on a novel model. Journal of Industrial and Management Optimization, 2017, 13 (2) : 681-695. doi: 10.3934/jimo.2016040
[2]

Jiping Tao, Ronghuan Huang, Tundong Liu. A $2.28$-competitive algorithm for online scheduling on identical machines. Journal of Industrial and Management Optimization, 2015, 11 (1) : 185-198. doi: 10.3934/jimo.2015.11.185
[3]

Xianzhao Zhang, Dachuan Xu, Donglei Du, Cuixia Miao. Approximate algorithms for unrelated machine scheduling to minimize makespan. Journal of Industrial and Management Optimization, 2016, 12 (2) : 771-779. doi: 10.3934/jimo.2016.12.771
[4]

Güvenç Şahin, Ravindra K. Ahuja. Single-machine scheduling with stepwise tardiness costs and release times. Journal of Industrial and Management Optimization, 2011, 7 (4) : 825-848. doi: 10.3934/jimo.2011.7.825
[5]

Jiayu Shen, Yuanguo Zhu. An uncertain programming model for single machine scheduling problem with batch delivery. Journal of Industrial and Management Optimization, 2019, 15 (2) : 577-593. doi: 10.3934/jimo.2018058
[6]

Ganggang Li, Xiwen Lu, Peihai Liu. The coordination of single-machine scheduling with availability constraints and delivery. Journal of Industrial and Management Optimization, 2016, 12 (2) : 757-770. doi: 10.3934/jimo.2016.12.757
[7]

Muminu O. Adamu, Aderemi O. Adewumi. A survey of single machine scheduling to minimize weighted number of tardy jobs. Journal of Industrial and Management Optimization, 2014, 10 (1) : 219-241. doi: 10.3934/jimo.2014.10.219
[8]

Ran Ma, Jiping Tao. An improved 2.11-competitive algorithm for online scheduling on parallel machines to minimize total weighted completion time. Journal of Industrial and Management Optimization, 2018, 14 (2) : 497-510. doi: 10.3934/jimo.2017057
[9]

Ping Yan, Ji-Bo Wang, Li-Qiang Zhao. Single-machine bi-criterion scheduling with release times and exponentially time-dependent learning effects. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1117-1131. doi: 10.3934/jimo.2018088
[10]

Hongwei Li, Yuvraj Gajpal, C. R. Bector. A survey of due-date related single-machine with two-agent scheduling problem. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1329-1347. doi: 10.3934/jimo.2019005
[11]

Chengxin Luo. Single machine batch scheduling problem to minimize makespan with controllable setup and jobs processing times. Numerical Algebra, Control and Optimization, 2015, 5 (1) : 71-77. doi: 10.3934/naco.2015.5.71
[12]

Chuanli Zhao, Yunqiang Yin, T. C. E. Cheng, Chin-Chia Wu. Single-machine scheduling and due date assignment with rejection and position-dependent processing times. Journal of Industrial and Management Optimization, 2014, 10 (3) : 691-700. doi: 10.3934/jimo.2014.10.691
[13]

Xingong Zhang. Single machine and flowshop scheduling problems with sum-of-processing time based learning phenomenon. Journal of Industrial and Management Optimization, 2020, 16 (1) : 231-244. doi: 10.3934/jimo.2018148
[14]

Yunqiang Yin, T. C. E. Cheng, Jianyou Xu, Shuenn-Ren Cheng, Chin-Chia Wu. Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration. Journal of Industrial and Management Optimization, 2013, 9 (2) : 323-339. doi: 10.3934/jimo.2013.9.323
[15]

Peng Guo, Wenming Cheng, Yi Wang. A general variable neighborhood search for single-machine total tardiness scheduling problem with step-deteriorating jobs. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1071-1090. doi: 10.3934/jimo.2014.10.1071
[16]

Shuen Guo, Zhichao Geng, Jinjiang Yuan. Single-machine Pareto-scheduling with multiple weighting vectors for minimizing the total weighted late works. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021192
[17]

Lili Ding, Xinmin Liu, Yinfeng Xu. Competitive risk management for online Bahncard problem. Journal of Industrial and Management Optimization, 2010, 6 (1) : 1-14. doi: 10.3934/jimo.2010.6.1
[18]

Ruinian Li, Yinhao Xiao, Cheng Zhang, Tianyi Song, Chunqiang Hu. Cryptographic algorithms for privacy-preserving online applications. Mathematical Foundations of Computing, 2018, 1 (4) : 311-330. doi: 10.3934/mfc.2018015
[19]

Leiyang Wang, Zhaohui Liu. Heuristics for parallel machine scheduling with batch delivery consideration. Journal of Industrial and Management Optimization, 2014, 10 (1) : 259-273. doi: 10.3934/jimo.2014.10.259
[20]

Min Ji, Xinna Ye, Fangyao Qian, T.C.E. Cheng, Yiwei Jiang. Parallel-machine scheduling in shared manufacturing. Journal of Industrial and Management Optimization, 2022, 18 (1) : 681-691. doi: 10.3934/jimo.2020174

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (139)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy