Robust optimization for generalized project networks

Abstract

Completion time estimation is a key component for project management. In addition to uncertain task times, uncertain task outcomes also have a significant impact on the evaluation of completion time. For example, due to some uncontrolled factors in a project, certain task may have a probability of failure, which will result in full repetition or partial rework of the task. Introduction of new task or change of precedence relationships may occur during project execution as a contingency measure. Another example is probabilistic branching, i.e., after the project reaches a milestone, it may be necessary to choose among alternative plans by that time. However, these uncertainties are often ignored in standard approaches, e.g., the program evaluation and review technique (PERT). In this thesis, we introduce the generalized project network to capture all the uncertainties in both task durations and task outcomes. A distributionally robust optimization model is developed to estimate the project completion time as well as the target-based measure of tardiness. We develop an efficient algorithm to solve the distributionally robust optimization model. The performance of the estimates obtained through distributionally robust optimization is evaluated through numerical studies. Numerical studies show that our model is practical and general to capture all the uncertainties in both task durations and task outcomes in completion time estimation problems. The proposed algorithm demonstrates exceptional efficiency, allowing us to solve one large size project instance, solved by the simulation method in the literature, in 98.2 seconds.