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Minimizing the number of late jobs on parallel machines with alpha time windows

Vincent Jeauneau 1 Philippe Chrétienne 1
1 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We consider the problem of minimization the number of late jobs on parallel machines in presence of alpha time windows (di = ri + pi + alpha for all jobs). We prove the NPcompleteness of this problem even when m = 2 and di = d for all jobs. We develop a lower bound by solving a minimum cost flow problem associated to a relaxation of the problem. A set of heuristics are presented to minimize the number of late jobs based on a job-focused and machine-focused approach. A simulation experiment is realized to test the effectiveness of heuristics regarding the lower bound. This simulation has been computed for 1; 2; 5; 10; 15 and 20 machines and it shows that the best heuristic has an average deviation to the bound of 4.88%, 6.35%, 7.38%, 7.5%, 7.87% and 7.64% respectively.
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Contributor : Vincent Jeauneau <>
Submitted on : Monday, December 23, 2013 - 3:07:00 PM
Last modification on : Thursday, March 21, 2019 - 2:32:23 PM
Document(s) archivé(s) le : Monday, March 24, 2014 - 1:15:08 AM


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  • HAL Id : hal-00922087, version 1


Vincent Jeauneau, Philippe Chrétienne. Minimizing the number of late jobs on parallel machines with alpha time windows. 6th Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA 2013), Aug 2013, Gent, Belgium. ⟨hal-00922087⟩



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