| dc.contributor.author | Aissi, Hassene | |
| dc.contributor.author | Aloulou, Mohamed Ali | |
| dc.contributor.author | Kovalyov, Mikhail Y. | |
| dc.date.accessioned | 2010-06-30T13:38:05Z | |
| dc.date.available | 2010-06-30T13:38:05Z | |
| dc.date.issued | 2011 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/4508 | |
| dc.language.iso | en | en |
| dc.subject | Scheduling | en |
| dc.subject | Assignment | en |
| dc.subject | Robustness | en |
| dc.subject | Min-max approach | en |
| dc.subject | Scenarios | en |
| dc.subject | Uncertainty | en |
| dc.subject | Single machine | en |
| dc.subject.ddc | 003 | en |
| dc.title | Minimizing the number of late jobs on a single machine under due date uncertainty | en |
| dc.type | Article accepté pour publication ou publié | |
| dc.description.abstracten | We study the problem of minimizing the number of late jobs on a single machine where job processing times are known precisely and due dates are uncertain. The uncertainty is captured through a set of scenarios. In this environment, an appropriate criterion to select a schedule is to find one with the best worst-case performance, which minimizes the maximum number of late jobs over all scenarios. For a variable number of scenarios and two distinct due dates over all scenarios, the problem is proved NP-hard in the strong sense and non-approximable in pseudo-polynomial time with approximation ratio less than 2. It is polynomially solvable if the number s of scenarios and the number v of distinct due dates over all scenarios are given constants. An O(nlog n) time s-approximation algorithm is suggested for the general case, where n is the number of jobs, and a polynomial 3-approximation algorithm is suggested for the case of unit-time jobs and a constant number of scenarios. Furthermore, an O(n s+v−2/(v−1) v−2) time dynamic programming algorithm is presented for the case of unit-time jobs. The problem with unit-time jobs and the number of late jobs not exceeding a given constant value is solvable in polynomial time by an enumeration algorithm. The obtained results are related to a min-max assignment problem, an exact assignment problem and a multi-agent scheduling problem. | en |
| dc.relation.isversionofjnlname | Journal of Scheduling | |
| dc.relation.isversionofjnlvol | 14 | |
| dc.relation.isversionofjnlissue | 4 | |
| dc.relation.isversionofjnldate | 2011 | |
| dc.relation.isversionofjnlpages | 351-360 | |
| dc.relation.isversionofdoi | http://dx.doi.org/10.1007/s10951-010-0183-z | en |
| dc.description.sponsorshipprivate | oui | en |
| dc.relation.isversionofjnlpublisher | Springer | en |
| dc.subject.ddclabel | Recherche opérationnelle | en |
