Project Reliability Interval for a Stochastic Project Network Subject to Time and Budget Constraints

Abstract

Completion time and cost in a project are affected by uncertainties, such as weather, human resources availability, equipment efficiency, etc. The activity durations of the project, thus, should be regarded as stochastic. Such a project is usually modeled as a stochastic project network (SPN). The SPN can be represented in the form of an activity-on-arc diagram, in which each activity has several possible durations and different costs. Every activity duration possesses a corresponding cost and probability. Based on the concept of minimal paths, two algorithms are utilized to find the upper and lower duration vectors under both time and budget constraints. For an SPN, the project reliability is defined as the probability that the project can be completed under both time and budget thresholds. Theoretically, it is difficult to compute project reliability using the upper and lower duration vectors directly because of the domination property among the duration vectors. Therefore, this paper proposes the derivation of project reliability interval depending on the relationships among the upper and lower duration vectors. The exact project reliability is proved to be contained within the interval. Two examples, including a practical case of disaster recovery system construction, are presented to demonstrate the scalability and practicability of the proposed solution procedure.