Minimizing a Makespan Under Uncertainty

This paper reconsiders the most basic scheduling problem, that of minimizing the makespan of a partially ordered set of activities, in the context of incomplete knowledge. After positioning this paper in the scope of temporal networks under uncertainty, we provide a complete solution to the problem of finding floats of activities, and of locating surely critical ones, as they are often isolated. The minimal float problem is NP-hard while the maximal float problem is polynomial. New complexity results and efficient algorithms are provided for the interval-valued makespan minimization problem.