Single-machine scheduling with coupled task and rejection

Fanyu Kong; Cuixia Miao; Yujia Huo; Jiaxin Song

doi:10.3934/mfc.2023008

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2024, Volume 7, Issue 3: 328-335. Doi: 10.3934/mfc.2023008

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Single-machine scheduling with coupled task and rejection

School of Mathematical Sciences, Qufu Normal University, Qufu Shandong 273165, China

^*Corresponding author: Cuixia Miao
^*Corresponding author: Cuixia Miao

Received: June 2022

Revised: December 2022

Early access: February 2023

Published: August 2024

This research was supported by the Province Natural Science Foundation of Shandong [ZR2022MA019] and the National Natural Science Foundation of China [12271295, 12001313].

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Abstract

We consider the single-machine scheduling with coupled task and rejection, in which each coupled task is either accepted and processed on a single machine or rejected with a certain rejection penalty. Each accepted coupled task $J_{j}$ is made of two tasks with processing times $a_j$ and $b_j$ , respectively, and a fixed exactly time interval $L_j$ between the two tasks is required. The objective is to minimize the makespan of the accepted coupled task and the total penalty of the rejected coupled task. We present $3$ -approximation algorithm for the cases of $a_{j} = L_{j} = p$ and $b_j = L_j = p$ , respectively, and prove that the problems with common $b_j$ or common $a_j$ is polynomially solvable. Furthermore, when $a_{j} = b_{j} = p$ , we provide a $2$ -approximation algorithm for $L_{j}>p$ and show that the problem with for $L_{j}\leq p$ can be solved in polynomial time.

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Mathematics Subject Classification: Primary: 90B35; Secondary: 90C27.

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[1]	A. Azadeh, M. H. Farahani, S. Torabzadeh and M. Baghersad, Scheduling prioritized patients in emergency department laboratories, Computer Methods and Programs in Biomedicine, 117 (2014), 61-70. doi: 10.1016/j.cmpb.2014.08.006.
[2]	Y. Bartal, S. Leonardi, A. Marchetti-Spaccamela, J. Sgall and L. Stougie, Multiprocessor scheduling with rejection, SIAM Journal on Discrete Mathematics, 13 (2000), 64-78. doi: 10.1137/S0895480196300522.
[3]	B. Chen and X. Zhang, Scheduling coupled tasks with exact delays for minimum total job completion time, Journal of Scheduling, 24 (2021), 209-221. doi: 10.1007/s10951-020-00668-1.
[4]	A. Condotta and N. V. Shakhlevich, Scheduling coupled-operation jobs with exact time-lags, Discrete Applied Mathematics, 160 (2012), 2370-2388. doi: 10.1016/j.dam.2012.05.026.
[5]	M. Elshafei, H. D. Sherali and J. C. Smith, Radar pulse interleaving for multitarget tracking, Naval Research Logistics, 51 (2004), 72-94. doi: 10.1002/nav.10103.
[6]	J. Gao, J. Zou and X. X. Cheng, Machine scheduling with job rejection and DeJong's learning effect, Mathematical Foundations of Computing, 6 (2023), 253-267. doi: 10.3934/mfc.2022024.
[7]	R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey, Annals of Operations Research, 5 (1979), 287-326. doi: 10.1016/S0167-5060(08)70356-X.
[8]	F. J. Hwang and B. M. T. Lin, Coupled-task scheduling on a single machine subject to a fixed-job-sequence, Computers and Industrial Engineering, 60 (2011), 690-698. doi: 10.1016/j.cie.2011.01.002.
[9]	D. W. Li and X. W. Lu, Two-agent parallel-machine scheduling with rejection, Theoretical Computer Science, 703 (2017), 66-75. doi: 10.1016/j.tcs.2017.09.004.
[10]	L. F. Lu, L. Q. Zhang and J. J. Yuan, The unbounded parallel batch machine scheduling with release dates and rejection to minimize makespan, Theoretical Computer Science, 396 (2008), 283-289. doi: 10.1016/j.tcs.2008.02.015.
[11]	J. C. Moskop and K. V. Iserson, Triage in medicine, Part Ⅱ: Underlying values and principles, Annals of Emergency Medicine, 49 (2007), 51-60. doi: 10.1016/j.annemergmed.2006.07.012.
[12]	A. J. Orman and C. N. Potts, On the complexity of coupled-task scheduling, Discrete Applied Mathematics, 72 (1997), 141-154. doi: 10.1016/S0166-218X(96)00041-8.
[13]	D. Shabtay, N. Gaspar and M. Kaspi, A survey on offline scheduling with rejection, Journal of Scheduling, 16 (2013), 3-28. doi: 10.1007/s10951-012-0303-z.
[14]	R. D. Shapiro, Scheduling coupled tasks, Naval Research Logistics Quarterly, 28 (1980), 489-498. doi: 10.1002/nav.3800270312.
[15]	M. I. Skolnik, Introduction to Radar Systems, New York, 1980.
[16]	Z. H. Yang, Y. M. Ying and Q. L. Min, Online optimization for residential PV-ESS energy system scheduling, Mathematical Foundations of Computing, 2 (2019), 55-71. doi: 10.3934/mfc.2019005.
[17]	W. Yu, H. Hoogeveen and J. K. Lenstra, Minimizing makespan in a two-machine flow shop with delays and unit-time operations is NP-hard, Journal of Scheduling, 7 (2004), 333-348. doi: 10.1023/B:JOSH.0000036858.59787.c2.
[18]	L. Q. Zhang, L. F. Lu and J. J. Yuan, Single machine scheduling with release dates and rejection, European Journal of Operational Research, 198 (2009), 975-978. doi: 10.1016/j.ejor.2008.10.006.