An approximation to the completion time distribution for a probabilistic activity network with the time-schedule constraints

Time constraints and uncertainty of activity network have attracted much research interest in recent years, because they can be applied to represent a large amount of real situations. In this paper, we propose a general approach for obtaining the completion time distribution for a probabilistic activity network with time-schedule constraints. The procedure introduce in this paper have been developed by combing and adjusting two algorithms in the scientific literature. The former, proposed by J.J.Mattin, can be used for transforming a parallel subnet consisting of n paths to a single equivalent arc. The latter, proposed by F. Guerriero and L.Talarico in 2009 can be applied in activity networks with all the three kinds of time-constraints. The method, developed in this paper, can be utilized to obtain the completion time distribution in most practical situations.