John Nash's Last Book and the Operations Research Connections via Greece

Our terrific Dynamics of Disasters conference, which took place in Kalamata, Greece, in now over. It was such a pleasure working on this conference with my fellow co-organizers, Professor Panos M. Pardalos and Professor Ilias Kotsireas.

While there, I learned of some quite surprising news,which further supports the small world hypothesis (at least when it comes to our terrfic operations research community).

While at one of our nice get-togethers at the conference (I have posted many photos on the blog in previous posts), we reinisced about John Nash, the Nobel laureate, who tragically died in a taxi crash in New Jersey, along with his wife, after returning from Oslo, Norway, where he was honored with the Abel Prize. I wrote about receiving this shocking news while in Gothenburg, Sweden. 

John Nash greatly influenced so much of my work in competitive supply chains and game theory and he is also referenced many times in the book that I am presently writing.

Professor Panos M. Pardalos of the University of Florida, who is renowned in operations research, told me at one of our get-togethers in Kalamata that he commissioned John Nash's last book for Springer.

The book, "Open Problems in Mathematics," is co-edited by Michael Rassias and John Nash. In fact, Princeton University, in its many tributes to Nash, mentioned the book and this article contains a photo of Rassias with Nash.  Rassias speaks eloquently of the kindness of Nash and how he plans to emulate him. Rassias and Nash had just completed the foreword to their book before Nash left for Oslo. According to the Princeton tribute:

They agreed upon a quote from Albert Einstein that resonated with Nash (although Nash pointed out that Einstein was a physicist, not a mathematician, Rassias said): "Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning."

Professor Ilias Kotsireas of Wilfrid Laurier University in Canada (who worked tirelessly in making our conference a success) shared with me  the photo below of him with John Nash and with Professor Stephen M. Watt, currently the Dean of Mathematics at the University of Waterloo in Canada.

Nash was one of 4 invited speakers at the ECCAD 2008 conference at Shepherd University, Shepherdstown, WV., at which the above photo was taken.

Keeping with the small world theme of this post, Michael Rassias, who is a postdoc fellow at Princeton University, is the son of Professor Themistocles M. Rassias, who was a co-organizer of the conference in Athens, Greece, in the summer of 2013 on Network Models in Economics and Finance at which I was a plenary speaker.

That conference banquet took place at the magnificent "new" Acropolis museum, with a view of the Parthenon; see photo below. Pardalos was also a co-organizer of that conference.

Our paper, "A Supply Chain Game Theory Framework for Cybersecurity Investments Under Network Vulnerability," A. Nagurney, L.S. Nagurney, and S. Shukla, will appear in the volume, Computation, Cryptography, and Network Security, which is co-edited by N. J. Daras and  M. Th. Rassias, and is in press with Springer.

And, would you believe, that a contributor to the volume of Nash's last book is Professor Stephen Miller of Williams College,  who is married to my Marketing colleague at the Isenberg School of Management, Professor Liz Miller!

A Stunning Infographic via a Tweet - Nash, Braess, Sadik-Khan, and Me Thanks to Dewan Karim

It's always enjoyable to get a pleasant message whether through email, a phone call, in person, or even via a tweet.

I have been mourning the tragic death of John Nash while in Sweden since he influenced so much of my work and was such an extraordinary individual.

Last week, via Twitter, I received a message from Dewan Karim who tweeted the above infographic, which I thought was stunning. Obviously, it had taken him time to prepare  so I contacted him to thank him  and asked him for permission to post it in this blogpost, which he granted. Dewan tweets under Complete Mobility @DewanMKarim. He is a professional engineer and is a transportation planner in the greater Toronto area.

Not only did he include John Nash, but also Dietrich Braess, of Braess paradox fame, whom I also admire so much, and had the pleasure of hosting at the Isenberg School back in 2006.

Dewan told me that he attended the Traffic panel that I was a panelist on at the World Science Festival in NYC, which I wrote a post on.  He became very interested in the Braess paradox which I spoke on and, in particular, relative to Mayor Bloomberg shutting Broadway from 42nd to 47th Street to vehicular traffic and converting it to a pedestrian plaza.  This decision was made in conjunction with Dr. Janette Sadik-Khan.


Interestingly, I last saw Dr. Sadik-Khan, of whom I am also a big fan, when she and I were panelists together on the Transport and Traffic at The New York Times Energy for Tomorrow Conference, also in NYC, in  2013.

I like the above ninfographic so much that I will show it to my students in my Transportation and Logistics class at the Isenberg School next Fall.

In any event, it is so nice to be on the same page with researchers and a practitioner I so much admire.

Thank you, Dewan Karim!

Rest in Peace, John F. Nash, INFORMS Fellow and Nobel Laureate in Economic Sciences

I just heard the shocking news that John F. Nash, an INFORMS Fellow, in the inaugural class of 2002,  and 1994 Nobel laureate in Economic Sciences,  was killed in a taxi crash on the New Jersey turnpike.  He was traveling with his wife of many years, Alice Nash, who also died in the crash.

Just last week, John Nash had been in Norway to receive the Abel Prize for his contributions to mathematics.

Here I am in Sweden writing another book and in almost every chapter I am citing the work of John Nash, specifically, his contributions to noncooperative game theory.

It is such a horrible shame that he and his wife died in this way.

He had a Brilliant Mind.

He had  lectured at UMass Amherst in October 2002 on Ideal Money and Asymptotically Ideal Money. The below photo is courtesy of UMass Amherst.

I have written about John Nash and his influence on my work and that of others several times on this blog and I leave you with the link to a previous post.

Rest in Peace, John Nash, and your wife, as well! Many, many thanks for your incredible contributions to mathematics, operations research, and economics!

Supply Chain Network Design and Redesign, Game Theory, and Nash Equilibria

There is a wonderful interview (but too short) by Ron Howard, the Director of the Academy Award winning movie, "A Beautiful Mind," with John F. Nash Jr., the 1994 Nobel laureate in Economic Sciences, in a trailer that accompanies the DVD of this movie. I had the pleasure of recently seeing both.

As John Nash walks away at the end of the interview, bundled up in a warm overcoat and knit cap, he ruefully comments that he has lost so many years and he needs to get back to research since that is what matters.

John Nash's contributions to game theory earned him the Nobel Prize. His work has influenced numerous disciplines, in addition to economics, notably, operations research and management science, political science, applied mathematics, and computer science.

I cite Nash's classical (1950) and (1951) papers in many of my papers that deal with competition.

For example, in a paper, "Supply Chain Network Design Under Profit Maximization and Oligopolistic Competition," which was published recently in the journal, Transportation Research E (2010), I devised a model in which firms seek to determine their optimal supply chain network designs in terms of manufacturing, storage, and shipment capacities, as well as product flows so as to maximize profits. The governing concept is that of a Nash - Cournot equilibrium. This model extends my earlier model in which a firm seeks to design (or redesign) its supply chain network so as to minimize its total costs associated with capacity enhancements (even from scratch) as well as the operational costs. In the latter, no competition was assumed. That study, "Optimal Supply Chain Network Design and Redesign at Minimal Total Cost with Demand Satisfaction," is in press in the International Journal of Production Economics.

High tech companies, including Samsung, Hewlett Packard, and IBM, as well as apparel companies from Benetton to Zara well understand the competitive advantages of careful cost control in supply chains. In addition, more and more companies, including Frito-Lay, Tesco, P&G, and Colgate are being recognized for their supply chain performance.

The analytical challenges of identifying not only the optimal capacities associated with various supply chain network activities, coupled with the optimal production quantities, storage volumes, as well as shipments are tremendous, since the possibilities of where to site manufacturing plants and distribution centers, for example, and at which capacities, may be great. Furthermore, the determination of the optimal supply chain network design (or redesign if a supply chain network already exists with some capacities) needs to be done in a rigorous manner that captures the system-wide nature of the problem.

I've also recently made use of the Nash equilibrium concept in devising a model to capture the gains of possible mergers and acquisitions of firms which are competitors. That paper, "Formulation and Analysis of Horizontal Mergers Among Oligopolistic Firms with Insights into the Merger Paradox: A Supply Chain Network Perspective," is in press in the journal Computational Management Science.

The algorithms that can be applied to determine the optimal designs of supply chain networks, operating either in a centralized manner or in a competitive, decentralized manner, are also reported in the above papers.

I agree with Nash that it is imperative to carve out the necessary time to do research.