Fast minimum float computation in activity networks under interval uncertainty

This paper considers the following basic problem in scheduling under uncertainty: given an activity-on-node network where each activity has an uncertain duration represented by an interval, compute the minimum float of each activity over all duration scenarios. For solving this NP-hard problem, Dubois et al. [5] and Fortin et al. [7] have recently proposed an algorithm based on path enumeration. In this paper, we establish structural properties of optimal solutions and a new lower bound allowing us to design an efficient branch-and-bound procedure. We also propose two mixed integer programming formulations. The methods are compared experimentally on a large variety of randomly generated problem instances. The results show that the proposed branch-and-bound procedure is very fast and consistently outperforms the MIP formulations and the path enumeration algorithm.