Lower bound for the mean project completion time in dynamic PERT networks

We apply the stochastic dynamic programming to obtain a lower bound for the mean project completion time in a PERT network, where the activity durations are exponentially distributed random variables. Moreover, these random variables are non-static in that the distributions themselves vary according to some randomness in society like strike or inflation. This social randomness is modelled as a function of a separate continuous-time Markov process over the time horizon. The results are verified by simulation.