Approximation Schemes for Scheduling Jobs with Common Due Date on Parallel Machines to Minimize Total Tardiness
The problem of scheduling n nonpreemptive jobs having a common due date d on m, m > or = 2, parallel identical machines to minimize total tardiness is studied. Approximability issues are discussed and two families of algorithms {A[varepsilon]} and {B[varepsilon]} are presented such that (T0 - T*)...
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| Published in | Journal of heuristics Vol. 8; no. 4; pp. 415 - 428 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer Nature B.V
01.07.2002
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1381-1231 1572-9397 |
| DOI | 10.1023/A:1015487829051 |
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| Abstract | The problem of scheduling n nonpreemptive jobs having a common due date d on m, m > or = 2, parallel identical machines to minimize total tardiness is studied. Approximability issues are discussed and two families of algorithms {A[varepsilon]} and {B[varepsilon]} are presented such that (T0 - T*)/(T* + d) < or = [varepsilon] holds for any problem instance and any given [varepsilon] > 0, where T* is the optimal solution value and T0 is the value of the solution delivered by A[varepsilon] or B[varepsilon]. Algorithms A[varepsilon] and B[varepsilon] run in O(n2m/[varepsilon]m-1) and O(nm+1/[varepsilon]m) time, respectively, if m is a constant. For m = 2, algorithm A[varepsilon] can be improved to run in O(n3/[varepsilon]) time. |
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| AbstractList | The problem of scheduling n nonpreemptive jobs having a common due date d on m, m > or = 2, parallel identical machines to minimize total tardiness is studied. Approximability issues are discussed and two families of algorithms {A[varepsilon]} and {B[varepsilon]} are presented such that (T0 - T*)/(T* + d) < or = [varepsilon] holds for any problem instance and any given [varepsilon] > 0, where T* is the optimal solution value and T0 is the value of the solution delivered by A[varepsilon] or B[varepsilon]. Algorithms A[varepsilon] and B[varepsilon] run in O(n2m/[varepsilon]m-1) and O(nm+1/[varepsilon]m) time, respectively, if m is a constant. For m = 2, algorithm A[varepsilon] can be improved to run in O(n3/[varepsilon]) time. |
| Author | Kovalyov, Mikhail Y. Werner, Frank |
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| Cites_doi | 10.1145/321906.321909 10.1016/0041-5553(86)90072-8 10.1287/mnsc.11.3.460 10.1145/321941.321951 10.1145/321921.321934 10.1023/A:1009626427432 10.1016/S0167-5060(08)70356-X 10.1016/B978-0-12-468662-5.50020-3 10.1287/opre.25.6.920 |
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| References_xml | – volume: 22 start-page: 463 year: 1975 ident: 407837_CR6 publication-title: Journal of the ACM doi: 10.1145/321906.321909 – volume: 26 start-page: 30 year: 1986 ident: 407837_CR9 publication-title: U.S.S.R. Comput. Maths. Math. Phys doi: 10.1016/0041-5553(86)90072-8 – volume: 11 start-page: 460 year: 1965 ident: 407837_CR10 publication-title: Management Science doi: 10.1287/mnsc.11.3.460 – ident: 407837_CR13 – volume-title: Computers and Intractability: A Guide to the Theory of NP-Completeness year: 1979 ident: 407837_CR1 – volume: 23 start-page: 317 year: 1976 ident: 407837_CR5 publication-title: Journal of the ACM doi: 10.1145/321941.321951 – volume: 23 start-page: 116 year: 1976 ident: 407837_CR11 publication-title: Journal ACM doi: 10.1145/321921.321934 – start-page: 41 volume-title: Algorithms and Complexity. New Directions and Recent Results.–Proc. Symp. year: 1976 ident: 407837_CR2 – volume-title: “Efficient Approximate Algorithms for Combinatorial Problems year: 1981 ident: 407837_CR3 – volume: 3 start-page: 287 year: 1998 ident: 407837_CR8 publication-title: Journal of Heuristics doi: 10.1023/A:1009626427432 – volume: 5 start-page: 287 year: 1979 ident: 407837_CR4 publication-title: Annals of Discrete Mathematics doi: 10.1016/S0167-5060(08)70356-X – ident: 407837_CR7 doi: 10.1016/B978-0-12-468662-5.50020-3 – volume: 25 start-page: 920 year: 1977 ident: 407837_CR12 publication-title: Operations Research doi: 10.1287/opre.25.6.920 |
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| SubjectTerms | Algorithms Approximation Graphs Heuristic Job shops Parallel processing Scheduling Studies |
| Title | Approximation Schemes for Scheduling Jobs with Common Due Date on Parallel Machines to Minimize Total Tardiness |
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