Scheduling chains of operations on a batching machine with disjoint sets of operation compatibility

Nadia Brauner (1) , Guyslain Naves (2)

1 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
2 G-SCOP_OC - Optimisation Combinatoire

We consider a scheduling problem that arises from an industrial application in chemical experimentations, where a single machine can process a fixed number of compatible jobs simultaneously. The precedence graph is restricted to be a disjoint union of chains, and the compatibility constraints are given by a partition of the tasks. Nevertheless, with these restrictions we prove the NP-completeness of the problem when the machine has a capacity of two, implying the difficulties for greater capacities. We also present a short proof for an infinite capacity. Our results also show the NP-completeness of the D-Supersequence problem, even when there are only two kinds of strings. We show polynomiality results when the number of chains in the precedence graph is fixed or when each chain has only two jobs.

Mots clés: scheduling; batching machine; supersequence

Domaines: Recherche opérationnelle [math.OC]; Mathématique discrète [cs.DM]

Nadia Brauner, Guyslain Naves. Scheduling chains of operations on a batching machine with disjoint sets of operation compatibility. 2008. ⟨hal-00264402⟩