Branching Probabilities Planning of Stochastic Network for Project Duration Planning

Projects such as new product development have the similar uncertainty about the job sequence/duration of the project. In order to complete the project by the desired date with a certain confidence, the variable times or branching probabilities should be designed appropriately. In this paper, we will propose a new planning method for the branching probabilities to realize the desired project duration. We usually represent project processes as stochastic networks, such as GERT. In realistic projects, we must analyze generalized complex GERT networks. In this case, analytical treatment is difficult because of the network complexity. Monte Carlo simulation is a practical technique for complex GERT networks. The project duration is determined based on the variable-time and the branching-probability for each arrow. By our former method, we can estimate the project duration efficiently by analyzing the times and probabilities by the combination use of Monte Carlo simulation and probability theory. However, the reverse problems are difficult to be solved; that is, it is difficult for us to find branching probabilities that can realize the desired project duration. We propose a planning method for branching probabilities to realize the desired project duration using genetic algorithm technique supported by Monte Carlo simulation. By our method, we can plan the set of branching-probabilities to finish the project by the desired date. Also, we can show the sensitivity of each arrow for the better project management.