This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible job sequence that minimizes the number of tardy jobs. On the basis of an original mathematical integer programming formulation, this paper shows how good-quality lower and upper bounds can be computed. Numerical experiments are provided for assessing the proposed approach.
Keywords: single machine scheduling, tardy jobs, dominance conditions, mixed-integer programming
@article{RO_2013__47_1_33_0,
author = {Briand, Cyril and Ourari, Samia},
title = {Minimizing the number of tardy jobs for the single machine scheduling problem: {MIP-based} lower and upper bounds},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {33--46},
year = {2013},
publisher = {EDP Sciences},
volume = {47},
number = {1},
doi = {10.1051/ro/2013025},
mrnumber = {3031098},
zbl = {1282.90065},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2013025/}
}
TY - JOUR AU - Briand, Cyril AU - Ourari, Samia TI - Minimizing the number of tardy jobs for the single machine scheduling problem: MIP-based lower and upper bounds JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2013 SP - 33 EP - 46 VL - 47 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2013025/ DO - 10.1051/ro/2013025 LA - en ID - RO_2013__47_1_33_0 ER -
%0 Journal Article %A Briand, Cyril %A Ourari, Samia %T Minimizing the number of tardy jobs for the single machine scheduling problem: MIP-based lower and upper bounds %J RAIRO - Operations Research - Recherche Opérationnelle %D 2013 %P 33-46 %V 47 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2013025/ %R 10.1051/ro/2013025 %G en %F RO_2013__47_1_33_0
Briand, Cyril; Ourari, Samia. Minimizing the number of tardy jobs for the single machine scheduling problem: MIP-based lower and upper bounds. RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 1, pp. 33-46. doi: 10.1051/ro/2013025
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