Total Cost Control in Project Management via Satisficing

We consider projects with uncertain activity times and the possibility of expediting, or crashing, them. Activity times come from a partially specified distribution within a family of distributions. This family is described by one or more of the following details about the uncertainties: support, mean, and covariance. We allow correlation between past and future activity time performance across activities. Our objective considers total completion time penalty plus crashing and overhead costs. We develop a robust optimization model that uses a conditional value-at-risk satisficing measure. We develop linear and piecewise-linear decision rules for activity start time and crashing decisions. These rules are designed to perform robustly against all possible scenarios of activity time uncertainty, when implemented in either static or rolling horizon mode. We compare our procedures against the previously available Program Evaluation and Review Technique and Monte Carlo simulation procedures. Our computational studies show that, relative to previous approaches, our crashing policies provide both a higher level of performance, i.e., higher success rates and lower budget overruns, and substantial robustness to activity time distributions. The relative advantages and information requirements of the static and rolling horizon implementations are discussed. This paper was accepted by Dimitris Bertsimas, optimization.