Criticality Analysis of Activity Networks under Interval Uncertainty

Dedicated to the memory of Professor Stefan Chanas - The extended abstract version of this paper has appeared in Proceedings of 11th International Conference on Principles and Practice of Constraint Programming (CP2005) ("Interval Analysis in Scheduling", Fortin et al. 2005)International audienceThis paper reconsiders the Project Evaluation and Review Technique (PERT) scheduling problem when information about task duration is incomplete. We model uncertainty on task durations by intervals. With this problem formulation, our goal is to assert possible and necessary criticality of the different tasks and to compute their possible earliest starting dates, latest starting dates, and floats. This paper combines various results and provides a complete solution to the problem. We present the complexity results of all considered subproblems and efficient algorithms to solve them