American Institute of Mathematical Sciences

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April  2015, 11(2): 685-700. doi: 10.3934/jimo.2015.11.685

Two-machine scheduling with periodic availability constraints to minimize makespan

Ganggang Li 1, and  Xiwen Lu 1,

1. 

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

Received  November 2013 Revised  May 2014 Published  September 2014

A two-machine scheduling problem where one machine has periodic availability constraints has been studied. The objective is to minimize makepan. For the nonresumable version, we give a better approximation algorithm with performance ratio of $4/3$. For the resumable version, we provide an offline $4/3$-approximation algorithm and an optimal online algorithm, respectively.
Keywords: availability constraint, nonresumable, Scheduling, resumable, algorithm..
Mathematics Subject Classification: Primary: 90B3.
Citation: Ganggang Li, Xiwen Lu. Two-machine scheduling with periodic availability constraints to minimize makespan. Journal of Industrial & Management Optimization, 2015, 11 (2) : 685-700. doi: 10.3934/jimo.2015.11.685
References:
[1]

T. C. E. Cheng and G. Wang, An improved heuristic for two-machine flowshop scheduling with an availability constraint, Operation Research Letters, 26 (2000), 223-229. doi: 10.1016/S0167-6377(00)00033-X.  Google Scholar

[2]

R. L. Graham, Bounds on multiprocessing timing anomalies, SIAM Journal on Applied Mathematics, 17 (1969), 416-429. doi: 10.1137/0117039.  Google Scholar

[3]

M. Ji, Y. He and T. C. E. Cheng, Single-machine scheduling with periodic maintenance to minimize makespan, Computer & Operations Research, 34 (2007), 1764-1770. doi: 10.1016/j.cor.2005.05.034.  Google Scholar

[4]

C. J. Liao, D. L. Shyur and C. H. Lin, Makespan minimization for two parallel machines with an availability constraint, European journal of operational Research, 160 (2005), 445-456. doi: 10.1016/j.ejor.2003.08.034.  Google Scholar

[5]

C. J. Liao and W. J. Chen, Single-machine scheduling with periodic maintenance and nonresumable jobs, Computers & operations Research, 30 (2003), 1335-1347. doi: 10.1016/S0305-0548(02)00074-6.  Google Scholar

[6]

C. Y. Lee, Machine scheduling with an availability constraint, Journal of Global optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681.  Google Scholar

[7]

W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs, Journal of Industrial and Management Optimization, 8 (2012), 271-283. doi: 10.3934/jimo.2012.8.271.  Google Scholar

[8]

G. Wang and T. C. E. Cheng, Heuristics for two-machine no-wait flowshop scheduling with an availability constraint, Information Processing Letters, 80 (2001), 305-309. doi: 10.1016/S0020-0190(01)00181-8.  Google Scholar

[9]

D. H. Xu, Z. M. Cheng, Y. Q. Yin and H. X. Li, Makespan minimization for two parallel machines scheduling with a periodic availability constraint, Computer & Operations Research, 36 (2009), 1809-1812. doi: 10.1016/j.cor.2008.05.001.  Google Scholar

[10]

M. Y. Yue, A simple proof of the inequality $FFD(L)\leq \frac{11}{9}OPT(L)+1,\forall L$ for the FFD Bin-Packing algorithm, Acta Mathematics Application Sinica, 7 (1991), 321-331. doi: 10.1007/BF02009683.  Google Scholar

show all references

References:
[1]

T. C. E. Cheng and G. Wang, An improved heuristic for two-machine flowshop scheduling with an availability constraint, Operation Research Letters, 26 (2000), 223-229. doi: 10.1016/S0167-6377(00)00033-X.  Google Scholar

[2]

R. L. Graham, Bounds on multiprocessing timing anomalies, SIAM Journal on Applied Mathematics, 17 (1969), 416-429. doi: 10.1137/0117039.  Google Scholar

[3]

M. Ji, Y. He and T. C. E. Cheng, Single-machine scheduling with periodic maintenance to minimize makespan, Computer & Operations Research, 34 (2007), 1764-1770. doi: 10.1016/j.cor.2005.05.034.  Google Scholar

[4]

C. J. Liao, D. L. Shyur and C. H. Lin, Makespan minimization for two parallel machines with an availability constraint, European journal of operational Research, 160 (2005), 445-456. doi: 10.1016/j.ejor.2003.08.034.  Google Scholar

[5]

C. J. Liao and W. J. Chen, Single-machine scheduling with periodic maintenance and nonresumable jobs, Computers & operations Research, 30 (2003), 1335-1347. doi: 10.1016/S0305-0548(02)00074-6.  Google Scholar

[6]

C. Y. Lee, Machine scheduling with an availability constraint, Journal of Global optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681.  Google Scholar

[7]

W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs, Journal of Industrial and Management Optimization, 8 (2012), 271-283. doi: 10.3934/jimo.2012.8.271.  Google Scholar

[8]

G. Wang and T. C. E. Cheng, Heuristics for two-machine no-wait flowshop scheduling with an availability constraint, Information Processing Letters, 80 (2001), 305-309. doi: 10.1016/S0020-0190(01)00181-8.  Google Scholar

[9]

D. H. Xu, Z. M. Cheng, Y. Q. Yin and H. X. Li, Makespan minimization for two parallel machines scheduling with a periodic availability constraint, Computer & Operations Research, 36 (2009), 1809-1812. doi: 10.1016/j.cor.2008.05.001.  Google Scholar

[10]

M. Y. Yue, A simple proof of the inequality $FFD(L)\leq \frac{11}{9}OPT(L)+1,\forall L$ for the FFD Bin-Packing algorithm, Acta Mathematics Application Sinica, 7 (1991), 321-331. doi: 10.1007/BF02009683.  Google Scholar

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