Mixed integer formulations using natural variables for single machine scheduling around a common due date - Cnam - Conservatoire national des arts et métiers Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Mixed integer formulations using natural variables for single machine scheduling around a common due date

Anne-Elisabeth Falq
Pierre Fouilhoux

Résumé

While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims at minimizing the weighted sum of earliness tardiness penalties around a common due-date. Using natural variables, we provide one compact formulation for the unrestrictive case and, for the general case, a non-compact formulation based on non-overlapping inequalities. We show that the separation problem related to the latter formulation is solved polynomially. In this formulation, solutions are only encoded by extreme points. We establish a theoretical framework to show the validity of such a formulation using non-overlapping inequalities, which could be used for other scheduling problems. A Branch-and-Cut algorithm together with an experimental analysis are proposed to assess the practical relevance of this mixed integer programming based methods.
Fichier principal
Vignette du fichier
1901.06880.pdf (477.21 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02074488 , version 1 (26-03-2019)
hal-02074488 , version 2 (15-02-2021)

Identifiants

Citer

Anne-Elisabeth Falq, Pierre Fouilhoux, Safia Kedad-Sidhoum. Mixed integer formulations using natural variables for single machine scheduling around a common due date. 2019. ⟨hal-02074488v1⟩
274 Consultations
65 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More