Program Evaluation and Review Technique (PERT) Scheduling with Resource Constraints Using Qualitative Simulation Graphs (QSG)
Prepared by: Susan H. Davenport
July 6th, 2009
This report assesses the risk in the application of the Qualitative Simulation Graph Methodology (QSGM) model that addresses Program Evaluation and Review
Technique (PERT) scheduling-with-resources problem. PERT scheduling is a network
Analysis technique based on mathematical equations known as Runge-Kutta that
establishes and weights best and worst-case scenarios against the most likely set of
occurrences, but PERT does not factor in the most likely estimates that could leave the
project manager with a programmatic risk.
The QSGM model, used to mitigate the possible programmatic risk, is a general purpose
Qualitative Discrete-Event Simulation (QDES) framework that can be used for any type of
Discrete-Event Simulation (DES) problem. QSGM adds a coverage property that consists
of every possible scenario known to a scheduling problem, including both best and worst-
case scenarios. The QSGM’s coverage property defines any possible sequence of events
with all possible sequence of events with specific timing. Due to the technical risk of the
large number of possible scenarios generated from ASGM, the application is more reliable
when applied to a fixed time horizon or problems analyzed at a strategic level. Since the
activity-on-arc PERT network fits the fixed time horizon and more strategic class of
problems, the QSGM model addresses the known coverage property shortcoming with
PERT (best and worst-case scenarios). The QSGM model generates an opportunity event
since the model generates all possible scenarios in the project schedule and the
corresponding