Polynomial time algorithms for constant capacitated single-item lot sizing problem with stepwise production cost

Ayse Akbalik (1) , Christophe Rapine (1)

1 LGIPM - Laboratoire de Génie Industriel, de Production et de Maintenance

This paper presents two polynomial time algorithms for the constant capacitated lot sizing problem with a batch production. We give several optimality properties for the general problem. Assuming constant production capacity, constant batch size and Wagner-Whitin cost structure, we derive O(T^4) and O(T^6) time algorithms respectively for the case with production capacity multiple of the batch size and for the case with arbitrary fixed capacities.% the general case.

Mots clés: Single-item; capacitated lot sizing problem; stepwise costs; polynomial time algorithm; dynamic programming

Domaines: Recherche opérationnelle [math.OC]

Ayse Akbalik, Christophe Rapine. Polynomial time algorithms for constant capacitated single-item lot sizing problem with stepwise production cost. Operations Research Letters, 2012, 40, pp.390-397. ⟨10.1016/j.orl.2012.05.003⟩. ⟨hal-00766771⟩