Find all longer and shorter boundary duration vectors under project time and budget constraints

Abstract

A large-scale project can be modeled as a project network in AOA form (arrows denote the activities and nodes denote the events). We study the case that activity durations are integer random variables. Given the project time (the deadline required to complete the project) constraint and budget constraint, we use some techniques in network analysis to develop two algorithms in order to generate all longer boundary duration vectors and shorter boundary duration vectors, respectively. Each feasible duration vector is between such longer and shorter boundary vectors. Whenever accidents happening in the project duration, the project manager can update the activity durations according to the longer and shorter boundary duration vectors without contradicting project time and budget constraints.