Our current research involves developing a modeling
framework for enterprise networks. A simple definition of an enterprise
network is a collection of one or more business units interacting
in order to produce one or more products or services. The simplified
problem is to be able to provide the solution to a load-balancing
problem between the various business units, in which the profit
for the overall network is maximized.
By representing enterprise networks as graphs, topological
properties can be utilized. Graphs of enterprise networks consist
of five different parts: activity flows, individual flows of material
throughout the network, terminals, through which material can flow
into and out of the network, manufacturing units, which alter the
quality of the material, routers, where decisions must be made to
split/join flows, and storage units, in which material can be stored.
The difference in costs between two nodes of the graph is the change
in value of the material, and represents a potential for flow. Constitutive
equations can then be introduced which relate the value added to
the flow rate through an activity. These are developed from relating
flow rates to the total activity costs.
By exploiting analogies to previously well-developed
electric circuit and thermodynamic theory, certain classes of networks
can be shown to be self-optimized; hence the name "Adaptive
Enterprise Networks." Analogies to certain important developments
from circuit theory have been developed. Kirchhoff-like laws provide
conservation equations for flow and value. A lemma similar to Tellegen’s
Theorem represents the balance of the overall inlet-outlet of flow
with internal flows and respective changes in value. Finally, a
theorem similar to Maxwell’s Theory of Minimum Heat Dissipation,
provides the conditions for which the solution to the network provides
minimum activity costs. Currently, however, only a certain class
of problems (ones in which the cost-flow constitutive relationships
are monotonically positive) can be handled by the framework.
Also, we look to show that by connecting individual
networks at the proper terminals, larger networks can be created.
These networks could then potentially be controlled in a decentralized
fashion, allowing for more rapid response to deviations in flows
Furthermore, by using passivity theory, the network
solution has been shown to be stable; again, however, for only a
certain class of problems.
Most recently, a simple case study of a silicon
production facility has been explored. One of the key challenges
is to be able to incorporate multi-component flows into the framework,
and to produce the maximum profit solution.
In addition to the multi-component problem, many
other issues need to be resolved for further, successful development
of the modeling framework. The primary issue is that it should be
able to work for a wider ranging class of problems. Such examples
would be to consider situations with fixed costs (i.e. to consider
the economic feasibility of purchasing new pieces of equipment).
These situations would require cost-flow relationships to be both
non-monotonic, but also negative. Also, the feasibility of introducing
discrete planning and multi-product units should be examined. Furthermore,
the question of whether or not the expressions used for storage
units provide the optimal solution needs to be answered.