Dependence Modeling for Large-scale Project Cost and Time Risk Assessment: Additive Risk Factor Approaches

High-dimensional dependence modeling remains a crucial challenge in quantitative project cost and time risk analysis. Building a complete and mathematically consistent correlation matrix becomes unrealistically restrictive as the number of uncertain performance units in a project (i.e., activity times and costs) increases, regardless of using empirical data or with subjective judgment. This article presents a pair of additive factor dependence models that provide analytic solutions to the generation of a complete and mathematically consistent correlation matrix. The additive risk factor (ARF) models account for multiple risk factors in two classes (i.e., extra-marginal and intramarginal) while providing additional flexibility for a strategic tradeoff between the accuracy and the scalability to high-dimensional project risks. We extend the ARF models to present an analytic solution to the program evaluation and review technique (PERT) problem with correlated activity times. Numerical examples demonstrate the accuracy and computational efficiency of the ARF approaches. The ARF approaches and the ARF-PERT would serve as a quick and sensible alternative to large-scale Monte Carlo simulation, in particular during the early stage of the project life-cycle.