DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

synchronizability of a scale-free dynamical network is robust against random removal of nodes,
but is fragile to specific removal of the most highly connected nodes.
The scale free property and high degree of clustering (the small world effect) however are not
exclusive for a large number of real networks. Yet most models proposed to describe the topology
of complex networks have the difficulty capturing simultaneously these two features. It has been
shown in (Ravasz and Barabasi, 2003) that these two features are the consequence of a
hierarchical organization present in the networks. This argument also agrees with that proposed
by Herbert Simon (Simon 1997) who argues: “we could expect complex systems to be hierarchies
in a world in which complexity has to evolve from simplicity. In their dynamics, hierarchies have
a property, near decomposability, that greatly simplifies their behavior. Near decomposability
also simplifies the description of complex systems and makes it easier to understand how the
information needed for the development of the system can be stored in reasonable compass”.
Indeed many networks are fundamentally modular: one can easily identify groups of nodes that
are highly interconnected with each other, but have only a few or no links to nodes outside of the
group to which they belong. This clearly identifiable modular organization is at the origin of high
degree of clustering coefficient. On the other hand these modules can be organized in a
hierarchical fashion into increasingly large groups, giving rise to “hierarchical networks”, while
still maintaining the scale-free topology. Thus modularity, scale-free character and high degree of
clustering can be achieved under a common roof. Moreover, in hierarchical networks the degree
of clustering characterizing the different groups follows a strict scaling law, which can be used to
identify the presence of hierarchical structure in real networks.
The mathematical theory of graphs with arbitrary degree distributions known as “generalized
random graphs” can be found in (Newman et al. 2001) and (Newman 2003). Using the
“generating function formulation”, the authors have been able to solve the percolation problem
(i.e. have found conditions for predicting the appearance of a giant component), have obtained
formulae for calculating clustering coefficient and average path length for generalized random
graphs. The authors have proposed and studied models of propagation of diseases, failures, fads
and synchronization on such graphs and have extended their results for bipartite and directed
graphs.
Network dynamics though in its infancy promises a formal framework to characterize the
organizational and functional aspects in supply chains. With the changing trends in supply chains,
many new issues have become critical like: organizational resistance to change, inter-functional
or inter-organizational conflicts, relationship management, and consumer and market behavior.
Such problems are ill structured and behavioral and cannot be commonly addressed by analytical
tools such as mathematical programming. Successful supply chain integration depends on the
supply chain partners’ ability to synchronize and share real-time information. The establishment
of collaborative relationship among supply chain partners is a pre-requisite to information
sharing. As a result successful supply chain management relies on systematically studying
questions like 1) what are the robust architectures for collaboration and what are the coordination
strategies that lead to such architectures, 2) if different entities make decisions on whether or not
to cooperate on the basis of imperfect information about the group activity, and incorporate
expectations on how their decision will affect other entities, can overall cooperation be sustained
for long periods of time 3) how do the expectations, group size, and diversity affect coordination
and cooperation and 4) which kinds of organizations are most able to sustain ongoing collective
action, and how might such organizations evolve over time. Network dynamics addresses many
of such questions and should be explored in context of supply chains.
8. Conclusions and Future Work
The idea of managing the whole supply chain and transform them into a highly autonomous,
dynamic, agile, adaptive and reconfigurable network certainly provides an appealing vision for
managers. The infrastructure provided by Information technology has made this vision partially