Scheduling Problems with Equipment Health Index

Louise Penz (1, 2) , Stéphane Dauzere-Peres (3) , Margaux Nattaf (4, 5)

1 LITIS - Laboratoire d'Informatique, du Traitement de l'Information et des Systèmes
2 RI2C - LITIS - Equipe Réseaux d'interactions et Intelligence Collective
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
4 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
5 G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production

Our problem considers a single machine with a health index on which jobs of different families are scheduled to minimize the sum of completion times and maintenance operations are scheduled to restore the health of the machine. The health of the machine decreases when jobs are processed. Moreover, to be scheduled, each job requires the machine to have a minimum health index which depends on the job family. Two cases are studied: (1) The daily case with a single flexible maintenance operation, and (2) The weekly case with two flexible maintenance operations. The second case is shown to be NP-complete. Two Mixed Integer Linear Programming models are presented for each case. The first model uses ``classical'' positional variables, while the second model improves the first model by using the notion of master sequence. Different valid inequalities are also proposed. Computational experiments show that the second model is much more efficient than the first model when solved with a standard solver, and the impact of the valid inequalities is discussed.

Mots clés: Mathematical programming; Master sequence; Single; machine scheduling; Flexible maintenance; Machine health index

Domaines: Recherche opérationnelle [math.OC]; Combinatoire [math.CO]

Louise Penz, Stéphane Dauzere-Peres, Margaux Nattaf. Scheduling Problems with Equipment Health Index. 23ème congrès annuel de la Société Française de Recherche Opérationnelle et d'Aide à la Décision, INSA Lyon, Feb 2022, Villeurbanne - Lyon, France. ⟨hal-03595411⟩