Amir Azaron - is with the Department of Industrial Engineering, University of Bu-Ali-Sina, Hamadan
S.M.T. Fatemi Ghomi - is with the Department of Industrial Engineering, Amirkabir University of Technology

In this paper, we apply the stochastic dynamic programming to approximate the mean project completion time in dynamic Markov PERT networks. It is assumed that the activity durations are independent random variables with exponential distributions, but some social and economical problems influence the mean of activity durations. It is also assumed that the social problems evolve in accordance with the independent semi-Markov processes over the planning horizon. By using the stochastic dynamic programming, we find a dynamic path with maximum expected length from the source node to the sink node of the stochastic dynamic network. The expected value of such path can be considered as an approximation for the mean project completion time in the original dynamic PERT network.

Dynamic Programming, Stochastic Processes, Longest Path, Graph Theory