Program Evaluation and Review Technique (Pert) Scheduling with Resource Constraints Using Qualitative Simulation Graphs (Qsg)

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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 uncertainty in their event timings, and the model characterizes all possible

outcomes of the decision making process with respect to a project schedule as long as

interval delay times are used and are not violated. There are two versions of the QSGM

model available involving activity time delays: deterministic delay time version, interval

time delay version. The deterministic delay time version could pose technical and schedule

risks since it uses expected time delays and was not designed to find optimal schedules. To

mitigate both technical and schedule risk, the interval time delay version is used in place of

the deterministic delay time version. Applying the interval time delay version, when two

(2) resources are allocated to competing activities, the time delay is in interval format. A

scheduling risk may be present since optimal scheduling algorithms actual delay times

often vary from the inputs. The scheduler is unsure if the timing of the activity impacts the

project’s optimal schedule significantly, and the only way to verify the impact is to rerun

the simulation with the latest schedule information. If the sequence of the optimal schedule

becomes invalid due to actual delay time changes, the remaining activities must be

rescheduled. To mitigate the schedule risk for competing resources, the coverage property

of the QSGM is a necessary function, so the simulation will not have to be rerun. The

conversion from PERT to the QSGM model generates the possibility of supreme

scheduling decisions without recompiling the schedule when actual activity durations differ

from estimated activity durations, mitigating technical, cost, and schedule risks. This

particular model does not miss schedule outcomes that a sampling-based approach might

miss with a finite sample size. The output from...
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