Diffusion Activity Networks

Abstract

An activity network (nodes and so that an arc always leads from a smaller numbered node to a higher numberednode. The graph has only one node with no incident arcs, which is calledthe starting node and numbered is the only nodewith no emanating arcs and is named the terminal node. An arc representsan activity and a node the start or the culmination of that activity. Theterminal node represents the end of the project. These kinds of graphsare also referred to as Activity on Arc () representation of.

In DiAN the process represented by the arcs is a diffusion process,the state of which is identified with the remaining work content (rwc).The process starts at time '0' at rwc = 1 with a negative drift coefficient.An absorbing barrier is placed at rwc = 0 to identify with the end of theprocess. The completion time of an activity is thus the first passage timeof such a diffusion process.

The paradigm of DiAN, while offering an enhanced modeling concept, raisesmany questions regarding computational challenges, definition of projectmanagement metrics and applicability of such a tool in areas beyond projectmanagement. The thesis primarily focuses on understanding such foundationalissues. These issues are as follows.

Development of a conceptual framework to model the projects using DiANtechniques. A related issue was to develop a framework to translate thecommon managerial knowledge to the parameters of the DiAN model.Computational aspects of various performance metrics under the paradigmof DiAN. We focus mainly on calculation of completion time of a projectto show the computational feasibility of this technique.Controlling an activity that has deviated substantially from its intendedcourse of execution. We propose and evaluate multiple strategies from bothplanning and execution point of view.Generation of the test sets of a given complexity index to evaluate theeffectiveness of this technique in an objective manner.Finally, some generalizations, extensions, and variants of DiAN are presentedto stimulate future research on this topic.

The work presented here reflects the development of a new paradigm.In so, it offers more questions than answers. We have focused on the developmentof the framework along with enough analysis to validate its practical applicability.