Education History

Adaptive Enterprise Networks

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 or costs.

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.