Tuesday, February 21, 2012

Networks and Operations Research, Patterns and Big Data -- So How Does Money and Traffic Flow?

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We've heard about the new geography -- now we are hearing about the new mathematics and at the prestigious Goldman Sachs technology conference that took place recently in San Francisco.

There, as noted by Quentin Hardy, writing for The New York Times, Steve Mills, IBM's senior vice president for software and systems was quoted as saying that when it comes to algorithms, "If I can do a power grid, I can do water supply..." Even traffic, which like water and electricity has value when it flows effectively. Moreover, Mills is quoted as saying in terms of cross-pollination and finding commonalities and patterns with the help of big data and algorithms that we are now: "leveraging the cost structure of new mathematics."

When I read about flows and especially in the context of transportation, electric power grids, natural resources, and finance, of course, networks and operations research and even economics immediately come to my mind since I have been researching and writing about the topic for many years.

I have always been fascinated by the commonality among problems and find that networks and the associated methodologies, such as optimization theory, game theory, variational inequality theory, and projected dynamical systems, provide a captivating medium for visualization, analysis, and computation and a way of bridging disciplines.

In our research and publications, we were able to answer several open questions, raised over a half a century ago:

1. How does money flow -- does it flow like water or electricity (raised by Cohen in 1952).

2. How are electric power generations and distribution networks like transportation networks (raised by Beckmann, McGuire, and Winsten in their classic 1956 book, Studies in the Economics of Transportation).

You can see the answers to the above questions in our papers in Computational Management Science and Naval Research Logistics, respectively.

In addition, we established, through a supernetwork formalism, how supply chain network equilibrium problems could be reformulated and solved as transportation network equilibrium problems -- thereby, constructing a common conceptual, modeling, and algorithmic framework for these two important classes of problems. That paper, On the Relationship Between Supply Chain and Transportation Network Equilibria: A Supernetwork Equivalence with Computations, was published in Transportation Research E 42: (2006) pp 293-316.

I also have a synthesis of the above equivalences in my Supply Chain Network Economic: Dynamics of Prices, Flows, and Profits book, which was published in 2006 and written that glorious year when I was a Science Fellow at the Radcliffe Institute for Advanced Study at Harvard University.

For those of you who are interested in the history of networks, with a focus on financial networks, and which includes a reference to Cohen above, please see my presentation on Financial Networks delivered at the Workshop on Measuring Systemic Risk, courtesy of the Federal Reserve Bank of Chicago and the University of Chicago in December 2010.

What seems like new mathematics (as was the case also with the new geography) to some is that now a wider circle is coming to realize the importance of research that has been going on for quite a long time, with major innovations over decades (frankly, centuries). Yes, I think it is really cool when an algorithm I implemented for predicting urban traffic flows can also be used to predict product flows on supply chain networks or financial transactions. Even major corporations are starting to notice.