Order constraints for single machine scheduling with non-linear cost

Christoph Dürr (1) , Oscar Carlos Vasquez Perez (1, 2)

1 RO - Recherche Opérationnelle
2 Industrial Engineering Department

Typically in a scheduling problem we are given jobs of different processing times $p_j$ and different priority weights $w_j$, and need to schedule them on a single machine in order to minimize a specific cost function. In this paper we consider the non-linear objective function $\sum w_j C_j^\beta$, where $C_j$ is the completion time of job $j$ and $\beta>0$ is some arbitrary real constant. Except for $\beta=1$ the complexity status of this problem is open. Past research mainly focused on the quadratic case ($\beta=2$) and proposed different techniques to speed up exact algorithms. This paper proposes new pruning rules and generalizations of existing rules to non-integral $\beta$. An experimental study evaluates the impact of the proposed rules on the exact algorithm A*.

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

Christoph Dürr, Oscar Carlos Vasquez Perez. Order constraints for single machine scheduling with non-linear cost. 16th Workshop on Algorithm Engineering and Experiments (ALENEX 2014), Jan 2014, Portland, United States. pp.98-111, ⟨10.1137/1.9781611973198.10⟩. ⟨hal-00908203⟩