Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals

Valery S. Gordon; F. Werner; O. A. Yanushkevich

RAIRO - Operations Research - Recherche Opérationnelle (2001)

  • Volume: 35, Issue: 1, page 71-83
  • ISSN: 0399-0559

Abstract

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This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e., their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e., no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an O ( n log n ) algorithm (where n is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.

How to cite

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Gordon, Valery S., Werner, F., and Yanushkevich, O. A.. "Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals." RAIRO - Operations Research - Recherche Opérationnelle 35.1 (2001): 71-83. <http://eudml.org/doc/105238>.

@article{Gordon2001,
abstract = {This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e., their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e., no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an $O(n \log n)$ algorithm (where $n$ is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.},
author = {Gordon, Valery S., Werner, F., Yanushkevich, O. A.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {single machine scheduling; release and due dates; deadlines; number of late jobs},
language = {eng},
number = {1},
pages = {71-83},
publisher = {EDP-Sciences},
title = {Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals},
url = {http://eudml.org/doc/105238},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Gordon, Valery S.
AU - Werner, F.
AU - Yanushkevich, O. A.
TI - Single machine preemptive scheduling to minimize the weighted number of late jobs with deadlines and nested release/due date intervals
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 1
SP - 71
EP - 83
AB - This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e., their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e., no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an $O(n \log n)$ algorithm (where $n$ is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.
LA - eng
KW - single machine scheduling; release and due dates; deadlines; number of late jobs
UR - http://eudml.org/doc/105238
ER -

References

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  2. [2] V.S. Gordon and V.S. Tanaev, Single machine deterministic scheduling with step functions of penalties, in: Computers in Engineering. Minsk (1971) 3-8 (in Russian). 
  3. [3] 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. Ann. Discrete Math. 5 (1979) 287-326. Zbl0411.90044MR558574
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  9. [9] E.L. Lawler, Knapsack-like scheduling problems, the Moore–Hodgson algorithm and the “tower of sets” property. Math. Comput. Modelling 20 (1994) 91-106. Zbl0810.90070
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  11. [11] E.L. Lawler and J.M. Moore, A functional equation and its application to resource allocation and sequencing problems. Management Sci. 16 (1969) 77-84. Zbl0184.23303
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  13. [13] J.K. Lenstra, A.H.G. Rinnooy Kan and P. Brucker, Complexity of machine scheduling problems. Ann. Discrete Math. 1 (1977) 343-362. Zbl0353.68067MR456421
  14. [14] C.L. Monma, Linear-time algorithms for scheduling on parallel processors. Oper. Res. 30 (1980) 116-124. Zbl0481.90048
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  16. [16] J.B. Sidney, An extension of Moore’s due date algorithm, edited by S.E. Elmaghraby, Symposium on the Theory of Scheduling and its Applications. Springer, Berlin, Lecture Notes in Econom. and Math. Systems 86 (1973) 393-398. Zbl0273.90032
  17. [17] V.S. Tanaev and V.S. Gordon, On scheduling to minimize the weighted number of late jobs. Vestsi Akad. Navuk Belarus Ser. Fizi.-Mat. Navuk 6 (1983) 3-9 (in Russian). Zbl0534.90045MR714131
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