Evaluating flexible solutions in single machine scheduling via objective function maximization: the study of computational complexity

Mohamed Ali Aloulou; Mikhail Y. Kovalyov; Marie-Claude Portmann

RAIRO - Operations Research (2007)

  • Volume: 41, Issue: 1, page 1-18
  • ISSN: 0399-0559

Abstract

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We study a deterministic problem of evaluating the worst case performance of flexible solutions in the single machine scheduling. A flexible solution is a set of schedules following a given structure determined by a partial order of jobs and a type of the schedules. In this paper, the schedules of active and non-delay type are considered. A flexible solution can be used on-line to absorb the impact of data disturbances related to, for example, job arrival, tool availability or machine breakdowns. The performance of a flexible solution includes the best case and the worst case performances. The best case performance is an ideal performance that can be achieved only if the on-line conditions allow to implement the best schedule of the set of schedules characterizing the flexible solution. In contrast, the worst case performance indicates how poorly the flexible solution may perform when following the given structure in the on-line circumstances. The best-case and the worst-case performances are usually evaluated by the minimum and maximum values of the considered objective function, respectively. We present algorithmic and computational complexity results for some maximization scheduling problems. In these problems, the jobs to be scheduled have different release dates and precedence constraints may be given on the set of jobs.

How to cite

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Aloulou, Mohamed Ali, Kovalyov, Mikhail Y., and Portmann, Marie-Claude. "Evaluating flexible solutions in single machine scheduling via objective function maximization: the study of computational complexity ." RAIRO - Operations Research 41.1 (2007): 1-18. <http://eudml.org/doc/250110>.

@article{Aloulou2007,
abstract = { We study a deterministic problem of evaluating the worst case performance of flexible solutions in the single machine scheduling. A flexible solution is a set of schedules following a given structure determined by a partial order of jobs and a type of the schedules. In this paper, the schedules of active and non-delay type are considered. A flexible solution can be used on-line to absorb the impact of data disturbances related to, for example, job arrival, tool availability or machine breakdowns. The performance of a flexible solution includes the best case and the worst case performances. The best case performance is an ideal performance that can be achieved only if the on-line conditions allow to implement the best schedule of the set of schedules characterizing the flexible solution. In contrast, the worst case performance indicates how poorly the flexible solution may perform when following the given structure in the on-line circumstances. The best-case and the worst-case performances are usually evaluated by the minimum and maximum values of the considered objective function, respectively. We present algorithmic and computational complexity results for some maximization scheduling problems. In these problems, the jobs to be scheduled have different release dates and precedence constraints may be given on the set of jobs. },
author = {Aloulou, Mohamed Ali, Kovalyov, Mikhail Y., Portmann, Marie-Claude},
journal = {RAIRO - Operations Research},
keywords = {Scheduling; single machine; schedule flexibility; maximization problems; active and non-delay schedules.},
language = {eng},
month = {6},
number = {1},
pages = {1-18},
publisher = {EDP Sciences},
title = {Evaluating flexible solutions in single machine scheduling via objective function maximization: the study of computational complexity },
url = {http://eudml.org/doc/250110},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Aloulou, Mohamed Ali
AU - Kovalyov, Mikhail Y.
AU - Portmann, Marie-Claude
TI - Evaluating flexible solutions in single machine scheduling via objective function maximization: the study of computational complexity
JO - RAIRO - Operations Research
DA - 2007/6//
PB - EDP Sciences
VL - 41
IS - 1
SP - 1
EP - 18
AB - We study a deterministic problem of evaluating the worst case performance of flexible solutions in the single machine scheduling. A flexible solution is a set of schedules following a given structure determined by a partial order of jobs and a type of the schedules. In this paper, the schedules of active and non-delay type are considered. A flexible solution can be used on-line to absorb the impact of data disturbances related to, for example, job arrival, tool availability or machine breakdowns. The performance of a flexible solution includes the best case and the worst case performances. The best case performance is an ideal performance that can be achieved only if the on-line conditions allow to implement the best schedule of the set of schedules characterizing the flexible solution. In contrast, the worst case performance indicates how poorly the flexible solution may perform when following the given structure in the on-line circumstances. The best-case and the worst-case performances are usually evaluated by the minimum and maximum values of the considered objective function, respectively. We present algorithmic and computational complexity results for some maximization scheduling problems. In these problems, the jobs to be scheduled have different release dates and precedence constraints may be given on the set of jobs.
LA - eng
KW - Scheduling; single machine; schedule flexibility; maximization problems; active and non-delay schedules.
UR - http://eudml.org/doc/250110
ER -

References

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