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

Chuanli Zhao

doi:10.3934/jimo.2016033

Article Contents

2017, Volume 13, Issue 2: 587-593. Doi: 10.3934/jimo.2016033

This issue Previous Article A parametric simplex algorithm for biobjective piecewise linear programming problems Next Article A scaled conjugate gradient method with moving asymptotes for unconstrained optimization problems

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
* Corresponding author

Received: September 2015

Revised: December 2015

Published: August 2017

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

Abstract / Introduction Full Text(HTML) Related Papers Cited by

Abstract

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:

Mathematics Subject Classification: Primary: 90B35; Secondary: 90C26.

Citation:

Full Text(HTML)

Related Papers

Cited by

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.