The prize-collecting single machine scheduling with bounds and penalties
Abstract
This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of n jobs and a single machine are considered, where each job has a processing time , a profit and a rejection penalty . The upper bound on the processing number is U. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold U while the total profit of the accepted jobs does not fall below a specified profit bound . We first demonstrate that this problem is NP-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms.
References
[1]
Abedinnia H, Clock CH, Grosse EH, and Schneider M Machine scheduling problems in production: a tertiary study Comput Ind Eng 2017 111 403-416
[2]
Alon N, Azar Y, Woeginger GJ, and Yadid T Approximation schemes for scheduling on parallel machines J Sched 1998 1 1 55-66
[3]
Bartal Y, Leonardi S, Marchetti-Spaccamela A, Sgall J, and Stougie L Multiprocessor scheduling with rejection SIAM Discret Math 2000 13 1 64-78
[4]
Bold M and Goerigk M Investigating the recoverable robust single machine scheduling problem under interval uncertainty Discret Appl Math 2022 313 99-114
[5]
de Weerdt M, Baart R, He L (2021) Single-machine scheduling with release times, deadlines, setup times, and rejection. Eur J Oper Res 291(2):629–639.
[6]
Fan J, Lu XW, and Liu PH Integrated scheduling of production and delivery on a single machine with availability constraint Theoret Comput Sci 2015 562 581-589
[7]
Garey MR and Johnson DS Computers and intractability: a guide to the theory of NP-completeness 1979 New York City W.H Freeman and Company
[8]
Gerstl E and Mosheiov G Single machine scheduling problems with generalised due-dates and job-rejection Int J Prod Res 2017 55 11 3164-3172
[9]
Graham RL Bounds for certain multiprocessing anomalies Bell Syst Tech J 1966 45 9 1563-1581
[10]
Graham RL, Lawler EL, Lenstra JK, and Rinnooy Kan AHG Optimization and approximation in deterministic sequencing and scheduling: a survey Ann Discret Math 1979 5 287-326
[11]
Guo JS, Liu W, and Hou B An approximation algorithm for P-prize-collecting set cover problem J Oper Res Soc China 2023 11 1 207-217
[12]
Guo SN, Ma R, Sun YF, Zhang XY, and Zhang Y Online scheduling with deterioration and unexpected processor breakdown Theor Comput Sci 2023 972 114058
[13]
He C, Leung JYT, Lee K, and Pinedo ML Improved algorithms for single machine scheduling with release dates and rejections 4OR 2016 14 1 41-55
[14]
Hochbaum DS and Shmoys DB Using dual approximation algorithms for scheduling problems theoretical and practical results J ACM 1987 34 1 144-162
[15]
Hoogeveen H Multicriteria scheduling Eur J Oper Res 2005 167 3 592-623
[16]
Jansen K An EPTAS for scheduling jobs on uniform processors: using an MILP relaxation with a constant number of integral variables SIAM Discret Math 2010 24 2 457-485
[17]
Jansen K, Klein KM, and Verschae J Closing the gap for makespan scheduling via sparsification techniques Math Oper Res 2020 45 4 1371-1392
[18]
Kellerer H and Strusevich V Fast approximation schemes for Boolean programming and scheduling problems related to positive convex half-product Eur J Oper Res 2013 228 1 24-32
[19]
Kones I and Levin A A unified framework for designing EPTAS for load balancing on parallel machines Algorithmica 2019 81 7 3025-3046
[20]
Kong M, Liu XB, Pei J, Zhou ZP, and Pardalos PM Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine Optim Lett 2020 14 4 857-871
[21]
Li WD and Cui QN Vector scheduling with rejection on a single machine 4OR 2018 16 1 95-104
[22]
Li WD, Li JP, Zhang XJ, and Chen ZB Penalty cost constrained identical parallel machine scheduling problem Theor Comput Sci 2015 607 part 2 181-192
[23]
Liu XF, Xiao M, Li WD, Zhu YY, and Ma L Algorithms for single machine scheduling problem with release dates and submodular penalties J Comb Optim 2023 45 4 105
[24]
Lu LF, Ng CT, and Zhang LQ Optimal algorithms for single-machine scheduling with rejection to minimize the makespan Int J Prod Econ 2011 130 2 153-158
[25]
Mor B and Shapira D Scheduling with regular performance measures and optional job rejection on a single machine J Oper Res Soc 2020 71 8 1315-1325
[26]
Ou JW, Zhong XL, and Wang GQ An improved heuristic for parallel machine scheduling with rejection Eur J Oper Res 2015 241 3 653-661
[27]
Shabtay D, Gaspar N, and Kaspi M A survey on offline scheduling with rejection J Sched 2013 16 1 3-28
[28]
Sun RQ, Deng B (2023) W-prize-collecting scheduling problem on a single machine. In: Proceedings of the 2022 6th international conference on computer science and artificial intelligence (CSAI ’22). Association for computing machinery, New York, USA, pp 237–242.
[29]
Zhang LQ, Lu LF, and Yuan JJ Single machine scheduling with release dates and rejection Eur J Oper Res 2009 198 3 975-978
[30]
Zheng HY, Gao SG, Liu W, Wu WL, Du DZ, and Hou B Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties J Comb Optim 2022 44 1 343-353
Index Terms
- The prize-collecting single machine scheduling with bounds and penalties
Index terms have been assigned to the content through auto-classification.
Recommendations
Scheduling a single machine with parallel batching to minimize makespan and total rejection cost
We consider the problem of scheduling a set of n jobs on a single machine with parallel batching and with rejection being allowed. Two bi-criteria problems are considered: (a) minimize the makespan subject to the constraint that the total rejection cost ...
Scheduling a single server in a two-machine flow shop
We study the problem of scheduling a single server that processes n jobs in a two-machine flow shop environment. A machine dependent setup time is needed whenever the server switches from one machine to the other. The problem with a given job sequence ...
Approximation Scheme for Single-Machine Rescheduling with Job Delay and Rejection
Algorithmic Aspects in Information and ManagementAbstractIn this paper, we consider the single-machine rescheduling with job delay and rejection. In this problem, we are given a set of jobs and a single machine, where each job has a processing time and weight. We can get an original scheduling with the ...
Comments
Information & Contributors
Information
Published In
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 16 August 2024
Accepted: 01 August 2024
Author Tags
Author Tags
Qualifiers
- Research-article
Funding Sources
- Project of Yunnan Province Caiyun Postdoctoral
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 05 Jan 2025