Volume 47, Number 1, January-March 2013
|Page(s)||33 - 46|
|Published online||11 February 2013|
Minimizing the number of tardy jobs for the single machine scheduling problem: MIP-based lower and upper bounds
1 CNRS, LAAS,
7 avenue du colonel Roche,
2 Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, 31077 Toulouse, France
3 CDTA, lotissement du 20 août 1956, Baba Hassen, Alger, Algeria.
Accepted: 13 December 2012
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.
Mathematics Subject Classification: 90B35 / 90C11
Key words: Single machine scheduling / tardy jobs / dominance conditions / mixed-integer programming
© EDP Sciences, ROADEF, SMAI, 2013
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