American Institute of Mathematical Sciences

Advanced
April  2017, 13(2): 587-593. doi: 10.3934/jimo.2016033

An fptas for the weighted number of tardy jobs minimization on a single machine with deteriorating jobs

Chuanli Zhao ,

School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, Liaoning 110034, China

* Corresponding author

Received  September 2015 Revised  December 2015 Published  May 2016

Fund Project: This paper was supported by Science and Research Project Foundation of Liaoning Province Education Department (L2014433).

We consider a single machine scheduling problem in which the processing time of a job is a nondecreasing function of its starting time. The jobs have a common due date. The objective is to minimize the weighted number of tardy jobs. The problem is NP-hard. We present a pseudo-polynomial dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS).

Keywords: Scheduling, single machine, deteriorating jobs, FPTAS.
Mathematics Subject Classification: Primary: 90B35; Secondary: 90C26.
Citation: Chuanli Zhao. An fptas for the weighted number of tardy jobs minimization on a single machine with deteriorating jobs. Journal of Industrial and Management Optimization, 2017, 13 (2) : 587-593. doi: 10.3934/jimo.2016033
References:
[1]

G. I. B. Alidaee and N. K. Womer, Scheduling with time dependent processing times: Review and extensions, Journal of the Operational Research Society, 50 (1999), 711-720. 

[2]

A. Bachman and A. Janiak, Minimizing maximum lateness under linear deterioration, European Journal of Operational Research, 126 (2000), 557-566.  doi: 10.1016/S0377-2217(99)00310-0.

[3]

A. Bachman, A. Janiak and M. Y. Kovalyov, Minimizing the total weighted completion time of deteriorating jobs, Information Processing Letters, 81 (2002), 81-84.  doi: 10.1016/S0020-0190(01)00196-X.

[4]

S. Browne and U. Yechiali, Scheduling deteriorating jobs on a single processor, Operations Research, 38 (1990), 495-498.  doi: 10.1287/opre.38.3.495.

[5]

Z.-L. Chen, A note on single-processor scheduling with time-dependent execution times, Operations Research Letters, 17 (1995), 127-129.  doi: 10.1016/0167-6377(94)00058-E.

[6]

T. C. E. Cheng, Q. Ding and B. M. T. Lin, A concise survey of scheduling with time-dependent processing times, European Journal of Operational Research, 152 (2004), 1-13.  doi: 10.1016/S0377-2217(02)00909-8.

[7]

S. Gawiejnowicz, Time-Dependent Scheduling, Springer-Verlag Berlin Heidelberg, 2008.

[8]

J. N. D. Gupta and S. K. Gupta, Single facility scheduling with nonlinear processing times, Computers and Industrial Engineering, 14 (1998), 387-393. 

[9]

A. Kononov, Scheduling problems with linear increasing processing times, in Operations Research Proceedings 1996 (eds. U. Zimmermann et al.), Berlin-Heidelberg, Springer, (1997), 208–212.

[10]

A. Kononov and S. Gawiejnowicz, NP-hard cases in scheduling deteriorating jobs on dedicated machines, Journal of the Operational Research Society, 52 (2001), 708-717.  doi: 10.1057/palgrave.jors.2601117.

[11]

M. Y. Kovalyov and W. Kubiak, A fully polynomial approximation scheme for minimizing makespan of deteriorating jobs, Journal of Heuristics, 3 (1998), 287-297. 

[12]

M. Y. Kovalyov and W. Kubiak, A fully polynomial approximation scheme for the weighted earliness-tardiness problem, Operations Research, 47 (1999), 757-761.  doi: 10.1287/opre.47.5.757.

[13]

M. Pinedo, Theory, Algorithms, and Systems, Prentice-Hall, Upper Saddle River, 2008.

[14]

G. J. Woeginger, Scheduling with time-dependent execution times, Information Processing Letters, 54 (1995), 155-156.  doi: 10.1016/0020-0190(95)00011-Z.

[15]

C. L. Zhao, C.-J. Hsu, S.-R. Cheng, Y. Q. Yin and C.-C. Wu, Due date assignment and single machine scheduling with deteriorating jobs to minimize the weighted number of tardy jobs, Applied Mathematics and Computation, 248 (2014), 503-510.  doi: 10.1016/j.amc.2014.09.095.

show all references

References:
[1]

G. I. B. Alidaee and N. K. Womer, Scheduling with time dependent processing times: Review and extensions, Journal of the Operational Research Society, 50 (1999), 711-720. 

[2]

A. Bachman and A. Janiak, Minimizing maximum lateness under linear deterioration, European Journal of Operational Research, 126 (2000), 557-566.  doi: 10.1016/S0377-2217(99)00310-0.

[3]

A. Bachman, A. Janiak and M. Y. Kovalyov, Minimizing the total weighted completion time of deteriorating jobs, Information Processing Letters, 81 (2002), 81-84.  doi: 10.1016/S0020-0190(01)00196-X.

[4]

S. Browne and U. Yechiali, Scheduling deteriorating jobs on a single processor, Operations Research, 38 (1990), 495-498.  doi: 10.1287/opre.38.3.495.

[5]

Z.-L. Chen, A note on single-processor scheduling with time-dependent execution times, Operations Research Letters, 17 (1995), 127-129.  doi: 10.1016/0167-6377(94)00058-E.

[6]

T. C. E. Cheng, Q. Ding and B. M. T. Lin, A concise survey of scheduling with time-dependent processing times, European Journal of Operational Research, 152 (2004), 1-13.  doi: 10.1016/S0377-2217(02)00909-8.

[7]

S. Gawiejnowicz, Time-Dependent Scheduling, Springer-Verlag Berlin Heidelberg, 2008.

[8]

J. N. D. Gupta and S. K. Gupta, Single facility scheduling with nonlinear processing times, Computers and Industrial Engineering, 14 (1998), 387-393. 

[9]

A. Kononov, Scheduling problems with linear increasing processing times, in Operations Research Proceedings 1996 (eds. U. Zimmermann et al.), Berlin-Heidelberg, Springer, (1997), 208–212.

[10]

A. Kononov and S. Gawiejnowicz, NP-hard cases in scheduling deteriorating jobs on dedicated machines, Journal of the Operational Research Society, 52 (2001), 708-717.  doi: 10.1057/palgrave.jors.2601117.

[11]

M. Y. Kovalyov and W. Kubiak, A fully polynomial approximation scheme for minimizing makespan of deteriorating jobs, Journal of Heuristics, 3 (1998), 287-297. 

[12]

M. Y. Kovalyov and W. Kubiak, A fully polynomial approximation scheme for the weighted earliness-tardiness problem, Operations Research, 47 (1999), 757-761.  doi: 10.1287/opre.47.5.757.

[13]

M. Pinedo, Theory, Algorithms, and Systems, Prentice-Hall, Upper Saddle River, 2008.

[14]

G. J. Woeginger, Scheduling with time-dependent execution times, Information Processing Letters, 54 (1995), 155-156.  doi: 10.1016/0020-0190(95)00011-Z.

[15]

C. L. Zhao, C.-J. Hsu, S.-R. Cheng, Y. Q. Yin and C.-C. Wu, Due date assignment and single machine scheduling with deteriorating jobs to minimize the weighted number of tardy jobs, Applied Mathematics and Computation, 248 (2014), 503-510.  doi: 10.1016/j.amc.2014.09.095.

[1]

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
[2]

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
[3]

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
[4]

Cuixia Miao, Yuzhong Zhang. Scheduling with step-deteriorating jobs to minimize the makespan. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1955-1964. doi: 10.3934/jimo.2018131
[5]

Wenchang Luo, Lin Chen. Approximation schemes for scheduling a maintenance and linear deteriorating jobs. Journal of Industrial and Management Optimization, 2012, 8 (2) : 271-283. doi: 10.3934/jimo.2012.8.271
[6]

Imed Kacem, Eugene Levner. An improved approximation scheme for scheduling a maintenance and proportional deteriorating jobs. Journal of Industrial and Management Optimization, 2016, 12 (3) : 811-817. doi: 10.3934/jimo.2016.12.811
[7]

Ji-Bo Wang, Dan-Yang Lv, Shi-Yun Wang, Chong Jiang. Resource allocation scheduling with deteriorating jobs and position-dependent workloads. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022011
[8]

Chunlai Liu, Yanpeng Fan, Chuanli Zhao, Jianjun Wang. Multiple common due-dates assignment and optimal maintenance activity scheduling with linear deteriorating jobs. Journal of Industrial and Management Optimization, 2017, 13 (2) : 713-720. doi: 10.3934/jimo.2016042
[9]

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
[10]

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
[11]

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
[12]

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
[13]

Zhichao Geng, Jinjiang Yuan. Scheduling family jobs on an unbounded parallel-batch machine to minimize makespan and maximum flow time. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1479-1500. doi: 10.3934/jimo.2018017
[14]

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
[15]

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
[16]

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
[17]

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
[18]

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
[19]

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
[20]

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

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (217)
  • HTML views (378)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy