Fuzzy PERT in series-prallel graphs

Hélène Fargier (1, 2) , Vincent Galvagnon (3) , Didier Dubois (1, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 ONERA - The French Aerospace Lab [Toulouse]

This paper deals with the fuzzy project scheduling approach, where fuzzy intervals model uncertain durations of tasks. While it is easy to compute fuzzy earliest starting dates of tasks in the critical path method, the problem of determining latest starting dates and slack times is much more tricky and has never been solved in a fully satisfactory manner in the past. Here, we propose a rigorous treatment of this problem in series-parallel graphs, in the framework of possibility theory. The main difficulty lies in the fact that the variation of latest starting dates and slack times, as a function of task durations, is not straightforward to predict for general graph topologies. However, it is easier in the case of series-parallel graphs. The case of interval-valued durations is first addressed, and then extended to fuzzy intervals.

Mots clés: Stochastic processes; Delay effects; Processor scheduling; Possibility theory; Topology; Project management; Random variables; Probability; Calculus

Domaines: Intelligence artificielle [cs.AI]

Hélène Fargier, Vincent Galvagnon, Didier Dubois. Fuzzy PERT in series-prallel graphs. 9th IEEE International Conference on Fuzzy Systems (FUZZ- IEEE 2000), IEEE Neural Networks Council, May 2000, San Antonio (Texas), United States. pp.717-722, ⟨10.1109/FUZZY.2000.839120⟩. ⟨hal-03463136⟩