This past Tuesday, while teaching my Transportation and Logistics class at the Isenberg School of Management, a class that I love to teach, we were discussing the importance of identifying conditions that guarantee uniqueness of equilibria. I had presented an extended model of transportation network equilibria and we were analyzing it qualitatively.
In order to emphasize to the students the importance of uniqueness (I was focusing on link flows), I related to the students a wonderful workshop that I had spoken at, which took place at Stanford University. The workshop was entitled: Applied General Equilibrium Workshop and it took place March 11-12, 1988. My presentation was (I checked on my cv): "Variational inequalities and the computation of large-scale equilibria."
I mentioned to my students how exciting it was for me to see George Dantzig there, Curtis Eaves, the Nobel laureate Kenneth Arrow, and also Herbert Scarf. My dissertation advisor at Brown University, Stella Dafermos, was also there and we were the only two females that had been invited to take part. Strangely enough, I even recall now, although the workshop took place back in 1988, what Kenneth Arrow was wearing (one of his favorite plaid shirts), and Herb Scarf's shoes, which, for some reason, impressed me because they were stylish and looked so comfortable. I recall them as being beige Rockport shoes. The audience, when I spoke about Wardrop's two principles of travel behavior, thought I had said "Wardrobe equilibrium", which Stella and I thought was very funny.
At the workshop we also discussed conditions for uniqueness, which was judged to be a very important property for policy makers when it came to equilibrium problems and a Harvard economics professor was especially avid on this point. The workshop was an intellectual delight and one of the last times that I was with my advisor at a conference since she passed away in 1990.
On Tuesday, when I was reminiscing and sharing the above in my class, I had no idea until I got back to my office and then saw the news, that Professor Herbert E. Scarf had passed away and only two days ago!
INFORMS produced a fine tribute to Scarf and the INFORMS President, Ed Kaplan of Yale, recently shared the sad news with all of us. I told my students today of Scarf's passing.
Scarf I remember as being very stately, pleasant, and elegant and had a very warm and welcoming way about him. I was in awe of him because of his book, "Computation of Economic Equilibria," with T. Hansen, which was published by Yale University Press in 1973. Scarf was an economist and also a great contributor to operations research.
In my first book, "Network Economics: A Variational Inequality Approach", which was published in 1993 as the first book in the series: Advances in Computational Economics, I cite Scarf's book in chapter 7, which is on Walrasian Price Equilibrium. That book is my most highly cited publication according to Google Scholar.
Scarf was a true visionary and realized the importance of algorithmic tools to solve complex equilibrium problems. We have much to thank him for and he will be missed.
Showing posts with label equilibrium. Show all posts
Showing posts with label equilibrium. Show all posts
Thursday, November 19, 2015
Saturday, September 12, 2015
Human Migration Networks, the Refugee Crisis, and Operations Research
The refugee crisis in the Middle East, especially from Syria, and Europe has been a top news story for many weeks now. The coverage has been extensive and the below graphic is compliments of USA Today.
The migrant crisis has been escalating especially the past several weeks with refugees, thousands from Syria, arriving in Greece, usually now by boat from Turkey, and then following land routes, sometimes with the assistance of various governments, to their ultimate destinations. Some have specific country preferences because they may have friends or relatives in certain locations or they have heard good things about a particular country. Germany, for example, has been identified as a final point for many because of its prosperity and also the welcome that Angela Merkel has been extending.
There have also been news articles that have included interviews with refugees who do not want to go to specific countries.
This crisis with the suffering children and families risking their lives and giving up their countries in order to escape war and strife resonates with everyone and it has become also a humanitarian crisis because of the extraordinary numbers of refugees. The crisis has been called by some Europeans as the biggest one since World War II.
In reading about the crisis and also taking to many European friends and researchers as well as practitioners about it I could not help but go back to some of my earlier work on human migration networks.
Many of my doctoral students come from different countries and, ultimately, they settle somewhere as either academics or industry professionals. My second doctoral student, Jie Pan, whose dissertation I co-supervised with Professor Alexander Eydeland, was from China and he was brilliant. In fact, his English was so good that he ended up teaching math courses at Amherst College. His dissertation was titled: "Variational inequalities in the modeling and computation of spatial economic equilibria: Structural reformulations and the method of multipliers," Department of Mathematics and Statistics, University of Massachusetts Amherst, 1992. We published papers in Operations Research, Operations Research Letters, and the European Journal of Operational Research.
Together we also did a lot of work on human migration networks. My first paper on the topic was published in Economic Letters. Since I was always fascinated by transportation and networks, studying migration was a natural application for me (and I was born in Canada so I am also a migrant, in a sense). In that paper, however, there were no costs associated with migration, which is actually a huge issue especially now in terms of the refugee crisis. I followed up with several papers in which migration costs were introduced as well as class transformations.
With Jie Pan, we wrote a paper that modeled migration as a chaining phenomenon and also integrated Markov chains and variational inequalities. In essence, humans can continue to migrate, which we expect to see in the migration crisis in the future. If those who locate in a certain location are not happy, then they will eventually move if the costs associated with migration are not too high relative to the utility gain. Humans compare the utilities of where they are at with the utility of another destination and include also the "transportation" or translocation cost in making their decisions. Our paper, "Using Markov chains to model human migration in a network equilibrium framework," was published in Mathematical and Computer Modelling and, propitiously, today, I found out that the journal has made the paper available online for free, which is great.
We established in this paper that a stable population distribution is shown to exist under certain assumptions.
Other operations researchers, who have a passion and inquisitiveness as to how people move in the long-term and where they settle, have also used our variational inequality framework to build other human migration network models.
Sadly, Jie Pan died at age 36. He had been diagnosed with lupus and traveled for treatment to China where he passed away. He had achieved promotion and tenure at St. Joseph's University in Philadelphia. I also co-authored a paper with him (posthumously) while I was a Fellow at Radcliffe on evolution variational inequalities, projected dynamical systems, and human migration. The world lost a brilliant operations researcher, husband, and father.
Amazingly, the work that we did on human migration networks is now being used also in ecology especially in the case of the migration of fish!
There have also been news articles that have included interviews with refugees who do not want to go to specific countries.
This crisis with the suffering children and families risking their lives and giving up their countries in order to escape war and strife resonates with everyone and it has become also a humanitarian crisis because of the extraordinary numbers of refugees. The crisis has been called by some Europeans as the biggest one since World War II.
In reading about the crisis and also taking to many European friends and researchers as well as practitioners about it I could not help but go back to some of my earlier work on human migration networks.
Many of my doctoral students come from different countries and, ultimately, they settle somewhere as either academics or industry professionals. My second doctoral student, Jie Pan, whose dissertation I co-supervised with Professor Alexander Eydeland, was from China and he was brilliant. In fact, his English was so good that he ended up teaching math courses at Amherst College. His dissertation was titled: "Variational inequalities in the modeling and computation of spatial economic equilibria: Structural reformulations and the method of multipliers," Department of Mathematics and Statistics, University of Massachusetts Amherst, 1992. We published papers in Operations Research, Operations Research Letters, and the European Journal of Operational Research.
Together we also did a lot of work on human migration networks. My first paper on the topic was published in Economic Letters. Since I was always fascinated by transportation and networks, studying migration was a natural application for me (and I was born in Canada so I am also a migrant, in a sense). In that paper, however, there were no costs associated with migration, which is actually a huge issue especially now in terms of the refugee crisis. I followed up with several papers in which migration costs were introduced as well as class transformations.
With Jie Pan, we wrote a paper that modeled migration as a chaining phenomenon and also integrated Markov chains and variational inequalities. In essence, humans can continue to migrate, which we expect to see in the migration crisis in the future. If those who locate in a certain location are not happy, then they will eventually move if the costs associated with migration are not too high relative to the utility gain. Humans compare the utilities of where they are at with the utility of another destination and include also the "transportation" or translocation cost in making their decisions. Our paper, "Using Markov chains to model human migration in a network equilibrium framework," was published in Mathematical and Computer Modelling and, propitiously, today, I found out that the journal has made the paper available online for free, which is great.
We established in this paper that a stable population distribution is shown to exist under certain assumptions.
Other operations researchers, who have a passion and inquisitiveness as to how people move in the long-term and where they settle, have also used our variational inequality framework to build other human migration network models.
Sadly, Jie Pan died at age 36. He had been diagnosed with lupus and traveled for treatment to China where he passed away. He had achieved promotion and tenure at St. Joseph's University in Philadelphia. I also co-authored a paper with him (posthumously) while I was a Fellow at Radcliffe on evolution variational inequalities, projected dynamical systems, and human migration. The world lost a brilliant operations researcher, husband, and father.
Amazingly, the work that we did on human migration networks is now being used also in ecology especially in the case of the migration of fish!
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