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A parametric simplex algorithm for biobjective piecewise linear programming problems
An fptas for the weighted number of tardy jobs minimization on a single machine with deteriorating jobs
School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, Liaoning 110034, China |
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).
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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. |
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