Criticality analysis of activity networks under interval uncertainty

Authors:
Jérôme Fortin;Paweł Zieliński;Didier Dubois;Hélène Fargier
Affiliations:
LIRMM, Université Montpellier 2 and CNRS, Montpellier Cedex 5, France 34392;Institute of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland 50-370;I.R.I.T., Université Paul Sabatier, Toulouse Cedex 4, France 31062;I.R.I.T., Université Paul Sabatier, Toulouse Cedex 4, France 31062
Venue:
Journal of Scheduling
Year:
2010

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Abstract

This 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.