American Institute of Mathematical Sciences

Advanced
January  2009, 5(1): 95-102. doi: 10.3934/jimo.2009.5.95

Online scheduling of two uniform machines to minimize total completion times

P. Liu 1, and  Xiwen Lu 1,

1. 

Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China, China

Received  January 2008 Revised  September 2008 Published  December 2008

In this paper, we study the online scheduling problem on two uniform machines with speeds 1 and $s \geq 1$, in which jobs are arriving over time. We consider both the preemptive and the non-preemptive machine environments. We first present a 2.618-competitive algorithm for the non-preemptive setting with the objective to minimize the total completion times. In the preemptive setting with the objective to minimize the total weighted completion times, we give an online algorithm which has a competitive ratio of 2.
Keywords: Scheduling; Uniform machine; Online algorithm; Competitive ratio..
Mathematics Subject Classification: 90B35, 90C2.
Citation: P. Liu, Xiwen Lu. Online scheduling of two uniform machines to minimize total completion times. Journal of Industrial and Management Optimization, 2009, 5 (1) : 95-102. doi: 10.3934/jimo.2009.5.95
[1]

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
[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]

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
[4]

Ran Ma, Lu Zhang, Yuzhong Zhang. A best possible algorithm for an online scheduling problem with position-based learning effect. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021144
[5]

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
[6]

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
[7]

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
[8]

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
[9]

Donglei Du, Xiaoyue Jiang, Guochuan Zhang. Optimal preemptive online scheduling to minimize lp norm on two processors. Journal of Industrial and Management Optimization, 2005, 1 (3) : 345-351. doi: 10.3934/jimo.2005.1.345
[10]

Zhenhuan Yang, Yiming Ying, Qilong Min. Online optimization for residential PV-ESS energy system scheduling. Mathematical Foundations of Computing, 2019, 2 (1) : 55-71. doi: 10.3934/mfc.2019005
[11]

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
[12]

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
[13]

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
[14]

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
[15]

Ganggang Li, Xiwen Lu. Two-machine scheduling with periodic availability constraints to minimize makespan. Journal of Industrial and Management Optimization, 2015, 11 (2) : 685-700. doi: 10.3934/jimo.2015.11.685
[16]

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
[17]

Hongtruong Pham, Xiwen Lu. The inverse parallel machine scheduling problem with minimum total completion time. Journal of Industrial and Management Optimization, 2014, 10 (2) : 613-620. doi: 10.3934/jimo.2014.10.613
[18]

Chaoming Hu, Xiaofei Qian, Shaojun Lu, Xinbao Liu, Panos M Pardalos. Coordinated optimization of production scheduling and maintenance activities with machine reliability deterioration. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021142
[19]

Alireza Goli, Taha Keshavarz. Just-in-time scheduling in identical parallel machine sequence-dependent group scheduling problem. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021124
[20]

Aude Hofleitner, Tarek Rabbani, Mohammad Rafiee, Laurent El Ghaoui, Alex Bayen. Learning and estimation applications of an online homotopy algorithm for a generalization of the LASSO. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 503-523. doi: 10.3934/dcdss.2014.7.503

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (95)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy