Diffusion Activity Networks

An activity network (AN) is a directed acyclic graph with n nodes and A arcs. The nodes are numbered from 1 to n so that an arc always leads from a smaller numbered node to a higher numbered node. The graph has only one node with no incident arcs, which is called the starting node and numbered 1. Node n is the only node with no emanating arcs and is named the terminal node. An arc represents an activity and a node the start or the culmination of that activity. The terminal node represents the end of the project. These kinds of graphs are also referred to as Activity on Arc (AoA) representation of AN. 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 the process. The completion time of an activity is thus the first passage time of such a diffusion process. The paradigm of DiAN, while offering an enhanced modeling concept, raises many questions regarding computational challenges, definition of project management metrics and applicability of such a tool in areas beyond project management. The thesis primarily focuses on understanding such foundational issues. These issues are as follows. • Development of a conceptual framework to model the projects using DiAN techniques. A related issue was to develop a framework to translate the common managerial knowledge to the parameters of the DiAN model. • Computational aspects of various performance metrics under the paradigm of DiAN. We focus mainly on calculation of completion time of a project to show the computational feasibility of this technique. • Controlling an activity that has deviated substantially from its intended course of execution. We propose and evaluate multiple strategies from both planning and execution point of view. • Generation of the test sets of a given complexity index to evaluate the effectiveness of this technique in an objective manner. • Finally, some generalizations, extensions, and variants of DiAN are presented to 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 development of the framework along with enough analysis to …