A Note on a Fully Polynomial-Time Approximation Scheme for Minimizing Makespan of Deteriorating Jobs
In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan. They presented a fully polynomial-time approximation scheme which is based on a dynamic programming. Unfortunately, their dynamic programming is incorrect. So the fully pol...
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| Veröffentlicht in: | Mathematical problems in engineering Jg. 2013; H. 2013; S. 1 - 7 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cairo, Egypt
Hindawi Publishing Corporation
01.01.2013
John Wiley & Sons, Inc |
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| ISSN: | 1024-123X, 1563-5147 |
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| Abstract | In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan. They presented a fully polynomial-time approximation scheme which is based on a dynamic programming. Unfortunately, their dynamic programming is incorrect. So the fully polynomial-time approximation scheme is also invalid. In this paper, we construct an instance to show how their dynamic programming does not work and provide a correct dynamic programming, based on which a new fully polynomial-time approximation scheme is derived. |
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| AbstractList | In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan. They presented a fully polynomial-time approximation scheme which is based on a dynamic programming. Unfortunately, their dynamic programming is incorrect. So the fully polynomial-time approximation scheme is also invalid. In this paper, we construct an instance to show how their dynamic programming does not work and provide a correct dynamic programming, based on which a new fully polynomial-time approximation scheme is derived. |
| Author | Wan, Long |
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| Cites_doi | 10.1002/nav.3800030106 10.1016/j.tcs.2006.06.006 10.1016/0377-2217(90)90089-T 10.1016/S0020-0190(03)00262-X 10.1016/j.tcs.2010.09.017 10.1142/S0217595912500194 10.1016/0166-218X(96)00102-3 10.1016/j.tcs.2009.04.018 |
| ContentType | Journal Article |
| Copyright | Copyright © 2013 Long Wan. Copyright © 2013 Long Wan.; This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| DOI | 10.1155/2013/957494 |
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| References | (1) 1990; 38 (5) 2009; 410 (12) 1956; 3 (3) 1994; 21 (6) 2003; 87 (2) 1990; 47 (8) 2006; 362 (10) 1998; 45 (7) 2011; 412 (4) 1996; 70 (11) 1998; 3 (9) 2012; 29 (10) 1994; 21 11 12 2 3 4 5 (7) 1998; 45 8 9 (6) 1998; 3 |
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| SubjectTerms | Approximation Construction Deterioration Dynamic programming Job shops Mathematical analysis Mathematical problems Polynomials Production scheduling Scheduling |
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| Title | A Note on a Fully Polynomial-Time Approximation Scheme for Minimizing Makespan of Deteriorating Jobs |
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