Recent Developments In Stochastic Activity Networks

Abstract

This paper surveys recent results for project planning, controlling, and scheduling by means of stochastic activity networks. Stochastic activity networks allow for handling projects with stochastic evolution structure and feedback. We focus upon analytical methods for so-called GERT networks, which have six different node types whose arc weights represent the execution probabilities and (stochastic) durations of the respective activities of the project, and which generally contain cycles.First, we discuss structural questions and stochastic processes associated with GERT networks. Some of those results can be exploited for developing methods for evaluating different classes of GERT networks (in the sense of time planning). For example, the temporal analysis of the special STEOR networks follows from computing the renewal functions of the Markov renewal processes associated with those networks, and more general GERT networks can often be reduced to simpler structures. Finding optimal time-cost trade-offs for STEOR networks leads to stochastic dynamic programming or optimal control problems. There is also a growing interest in stochastic scheduling problems with precedence constraints given by GERT networks. Moreover, decision activity networks, which generalize the model of decision CPM, are briefly studied. Finally, we list some applications of stochastic activity networks. After some introductory remarks, the paper begins with a brief summary of basic concepts, so that it is essentially self-contained.