New algorithms for minimizing the weighted number of tardy jobs on a single machine
In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or is taken as a parameter in the sense of parameterized comp...
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| Published in: | Annals of operations research Vol. 298; no. 1-2; pp. 271 - 287 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01.03.2021
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| ISSN: | 0254-5330, 1572-9338 |
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| Abstract | In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or is taken as a parameter in the sense of parameterized complexity. These three parameters are the number of different due dates, processing times, and weights in our set of input jobs. We show that the problem belongs to the class of fixed parameter tractable (FPT) problems when combining any two of these three parameters. We also show that the problem is polynomial-time solvable when either one of the latter two parameters are constant, complementing Karp’s result who showed that the problem is NP-hard already for a single due date. |
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| AbstractList | In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or is taken as a parameter in the sense of parameterized complexity. These three parameters are the number of different due dates, processing times, and weights in our set of input jobs. We show that the problem belongs to the class of fixed parameter tractable (FPT) problems when combining any two of these three parameters. We also show that the problem is polynomial-time solvable when either one of the latter two parameters are constant, complementing Karp’s result who showed that the problem is NP-hard already for a single due date. |
| Audience | Academic |
| Author | Karhi, Shlomo Hermelin, Danny Pinedo, Michael Shabtay, Dvir |
| Author_xml | – sequence: 1 givenname: Danny surname: Hermelin fullname: Hermelin, Danny organization: Department of Industrial Engineering and Management, Ben-Gurion University – sequence: 2 givenname: Shlomo surname: Karhi fullname: Karhi, Shlomo organization: Department of Management, Bar-Ilan University – sequence: 3 givenname: Michael surname: Pinedo fullname: Pinedo, Michael organization: Stern School of Business, New York University – sequence: 4 givenname: Dvir orcidid: 0000-0002-2709-599X surname: Shabtay fullname: Shabtay, Dvir email: dvirs@bgu.ac.il organization: Department of Industrial Engineering and Management, Ben-Gurion University |
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| Cites_doi | 10.1007/s10107-014-0830-9 10.1016/0167-6377(95)00031-9 10.1007/BF02216825 10.1023/B:JOSH.0000046073.05827.15 10.1016/j.tcs.2013.05.023 10.1007/s10951-016-0478-9 10.1016/S0304-3975(02)00811-3 10.3934/jimo.2014.10.219 10.1145/321921.321934 10.1016/0305-0548(94)00090-U 10.1007/s10852-005-9011-4 10.1007/1-4020-8141-3_18 10.1287/moor.8.4.538 10.1007/978-1-4612-0515-9 10.1007/s10951-017-0550-0 10.1016/S0377-2217(02)00180-7 10.1287/mnsc.16.1.77 10.1016/S0167-5060(08)70356-X 10.1287/mnsc.15.1.102 10.1093/acprof:oso/9780198566076.001.0001 10.1007/978-3-319-21275-3 10.1109/SCT.1992.215379 10.1109/FOCS.2011.31 10.1145/1806689.1806739 10.1007/978-3-319-34171-2_6 10.1007/978-1-4684-2001-2_9 10.1007/978-3-319-44914-2_9 |
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| DOI | 10.1007/s10479-018-2852-9 |
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| Keywords | Weighted number of tardy jobs NP-hard Fixed parametrized tractability Single machine scheduling Polynomial time algorithms |
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| Snippet | In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis... |
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| SubjectTerms | Algorithms Business and Management Case studies Combinatorics Complexity theory Context switching Dynamic programming Intelligent devices Job shops Knapsack problem Management Moving averages Operations research Operations Research/Decision Theory Parameters Polynomials Production scheduling S.I.: CoDIT2017-Combinatorial Optimization Scheduling Simulated annealing (Mathematics) Studies Theory of Computation |
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| Title | New algorithms for minimizing the weighted number of tardy jobs on a single machine |
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