An exact method for the bi-objective one-machine problem with maximum lateness and unit family setup cost objectives

Christian Artigues (1) , Nicolas Jozefowiez (1) , Mohamed Ali Aloulou (2)

1 LAAS-MOGISA
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

This paper deals with an NP-hard bi-objective one-machine problem with ready times involving maximum lateness and unit family setup cost objectives. Considering separately both objectives, the maximum lateness one-machine problem is also NP-hard but efficiently solved by Carlier's algorithm while the unit family setup cost one machine-problem with two families can be solved in polynomial time by Darte's algorithm, even when precedence constraints are considered. Under the epsilon-constraint framework we propose a branch-and-bound method to minimize the first objective with a given upper bound on the second.

Domaines: Recherche opérationnelle [math.OC]

Christian Artigues, Nicolas Jozefowiez, Mohamed Ali Aloulou. An exact method for the bi-objective one-machine problem with maximum lateness and unit family setup cost objectives. International Symposium on Combinatorial Optimization (ISCO 2010), Mar 2010, Hammamet, Tunisia. pp.1233-1240. ⟨hal-00492202⟩