Impact of activity time stochasticity on critical paths and their completion probabilities in construction projects

Accurate planning and project control activities are essential in ensuring the timely completion of construction projects. Even though the classical scheduling techniques like Gantt charts, critical path method (CPM), program evaluation and review technique (PERT), etc., are well-designed and can effectively support construction scheduling functions, they do not account for the variability in activity times arising out of the random/stochastic nature of the activities involved. The study utilizes a simulation-based approach to identify the impact of variability in activity time durations on critical paths and on the probability of timely completion of construction projects. The effectiveness of four different probability distribution functions, namely uniform, triangular, bound exponential, and unbound exponential, in capturing the stochasticity of activity times in construction projects was also evaluated as part of the study. A MATLAB-based simulation framework was developed to sample random durations of project activities and compute various project scheduling parameters based on PERT assumptions. Activity time variability was introduced in the network by extending pessimistic time (tp) by up to 50%. Observation in the study suggests that for projects that experience delays during execution, allocating additional resources to the preassigned critical path may not always be effective in addressing these delays. Instead, dynamic corrective measures (time extensions, resource allocation, etc.) that consider all possible scenarios of project completion and can account for any possible changes in critical path due to the incurred delay may be adopted to ensure a higher probability of project completion within the revised schedule. Exponential bounded distribution was found to provide a more realistic estimate of project completion time with a high probability of timely completion of construction projects. The study also suggests exponential unbound distribution to be effective in simulating worst-case scenarios encountered in construction projects. Future research could validate this approach on real projects and use machine learning to automate scheduling adjustments for delays.