Robust Optimization Strategies for Total Cost Control in Project Management

We describe robust optimization procedures for controlling total completion time penalty plus crashing cost in projects with uncertain activity times. These activity times arise from an unspecified distribution within a family of distributions with known support, mean and covariance. We develop linear and linear-based decision rules for making decisions about activity start times and the crashing of activity times. These rules identify decisions that perform well against all possible scenarios of activity time uncertainty. The resulting crashing strategies are implemented in both static and rolling horizon modes. Whereas the traditional planning methodology PERT does not consider correlation between past and future performance within or between activities, our methodology models both types of correlation. We compare our procedures against PERT, and also against the alternative approach of Monte Carlo simulation which assumes more information. Extensive computational results show that our crashing strategies provide over 99% probability of meeting the overall project budget, compared to less than 45% for the previous approaches that use the same information. Expected budget overruns are similarly improved from over 25% to less than 0.1%. The relative advantages of the static and rolling horizon implementations are also discussed. We identify several managerial insights from our results.