Sequential estimation and decision-making in project management: A Bayesian way and heuristic approaches

In spite of their wide application since the development of the Critical Path Method (CPM) and the Program Evaluation and Review Technique (PERT), these methods contain serious theoretical weaknesses in modeling uncertainty. These methods have a static view of project progression, inevitably leading to decisions about scheduling and activity crashing that may be used only once. By visualizing decision-making problems using influence diagrams and sequential diagrams, in addition to precedence diagrams, we gain in-depth insight into a project by allowing dependence among activity durations and including the sequential nature of activity crashing decisions. We propose two estimation models by which to predict the conditional duration of a succeeding activity given the observed duration or resources of a preceding activity. First, the Linear Bayesian Model updates the mean and variance of the duration of the succeeding activity by combining its prior mean and variance with the observed duration or resources of the preceding activity. Second, the Heuristic Model estimates the duration of the upcoming activity using the approximation equation. One important feature of the Heuristic Model is that it can reflect partial information in estimating the duration of an upcoming activity. In Order to determine the optimal level of crashing for each activity, we introduce the Dynamic Decision-Making Model. An optimal crashing decision is actually implemented on the most immediate activities, while the crashing decision for other non-immediate activities is updated repeatedly based on observation Of completed activities; this continues as each activity becomes the most immediate one, until the project is complete. We compare our model, which features dependent estimation and dynamic decision-making with a traditional model, which relies on independent estimation and static decision-making. Using some example Projects, we demonstrate that the simulated average project cost using our model is lower than that using the traditional model. Sensitivity analysis shows that as the degree of dependence among activity durations increases, the expected relative benefit of our model increases. Also, as a way to reflect risk-averse behavior, we include a concave utility function with respect to project cost and then illustrate the decision-making processes and the result.