New valid inequalities for a multi-echelon multi-item lot-sizing problem with returns and lost sales

Franco Quezada (1) , Céline Gicquel (2) , Safia Kedad-Sidhoum (3, 4)

1 RO - Recherche Opérationnelle
2 ROCS - Réseaux & Optimisation Combinatoire et Stochastique - LISN
3 CNAM - Conservatoire National des Arts et Métiers [CNAM]
4 CEDRIC - Centre d'études et de recherche en informatique et communications

This work studies a multi-echelon multi-item lot-sizing problem with remanufacturing and lost sales. The problem is formulated as a mixed-integer linear program. A new family of valid inequalities taking advantage of the problem structure is introduced and used in a customized branch-and-cut algorithm. The provided numerical results show that the proposed algorithm outperforms both the generic branch-andcut algorithm embedded in a standard-alone mathematical solver and a previously published customized branch-and-cut algorithm.

Mots clés: Production planning; Lot-sizing; Remanufacturing; Mixed-integer linear programming; Valid inequalities

Domaines: Recherche opérationnelle [math.OC]

Franco Quezada, Céline Gicquel, Safia Kedad-Sidhoum. New valid inequalities for a multi-echelon multi-item lot-sizing problem with returns and lost sales. ICCL 2021: International Conference on Computational Logistics, Sep 2021, Enschede (online), Netherlands. pp.192-207, ⟨10.1007/978-3-030-87672-2_13⟩. ⟨hal-03351045⟩