Models for accurate computation of earliest and latest start times and optimal compression in project networks

Operations research techniques, especially linear and integer programming, have been suggested for use in project management. Most frequently these techniques are applied to finding critical path(s) in project networks and for compressing activities for an early project completion. The simplest of these models are usually found in introductory operations research/management science textbooks and they often suffer from a common deficiency: when they employ earliest start times (ES) as variables in the model, ES of activities that are not on the critical path may be computed incorrectly. This may lead to inefficient resource reallocation and leveling. Furthermore, activities outside the critical path may be compressed unnecessarily, as will be demonstrated in this paper. We present a zero-one mixed integer programming model to correctly compute earliest and latest start times of all activities and determine the optimal compression schedule. Several extensions to the model are offered to provide different perspectives of the project and enable a project manager to answer "what if" type questions. A small example is used to demonstrate the effectiveness of the models.