Thursday, October 5, 2017

Doing Scholarly Operations Research with Undergraduates

Usually when faculty at a Research 1 university, such as UMass Amherst, conduct research they involve doctoral students, since doctoral students need to do research for their dissertation and, upon receiving the PhD, may continue onwards to do research, as faculty at other institutions or perhaps as practitioners. I have supervised the PhD dissertations of 20 PhD students and  I continue to collaborate with quite a few of them, even working with doctoral students of my doctoral students (nice to see the academic genealogy tree growing).

In the last several years, because of the growing prominence of the Commonwealth Honors College at UMass Amherst and also the Isenberg School of Management, under great leadership, we have been attracting truly outstanding undergraduate students and, my personal bias, is towards the Operations and Information Management (OIM) students, since they are in the department in which I teach at the Isenberg School.

I have had the pleasure of co-chairing two honors theses of OIM majors: Emilio Alvarez Flores, who graduated in May 2016, and Karen Li, who graduated in 2017. Emilio now works for Cisco and Karen for Brigham and Women's Hospital.

Emilio's thesis was entitled: Optimizing Non-Governmental Organizations' Operations and Fundraising: A Game-Theoretical Supply Chain Approach. He defended his dissertation at the Undergraduate Research Conference at UMass on April 22, 2016. A paper that we wrote, together with Professor Ceren Soylu of the Economics Department at UMass, was based on his thesis:  A Generalized Nash Equilibrium Network Model for Post-Disaster Humanitarian Relief, Anna Nagurney, Emilio Alvarez Flores, and Ceren Soylu, Transportation Research E 95: (2016), pp 1-18. I have continued to work with Emilio (below is a photo of us with my great collaborator Professor Patrizia Daniele of the University of Catania in Italy at the Dynamics of Disasters conference that I co-organized and which took place last summer in Greece).
At the conference in Greece, we presented the paper: A Variational Equilibrium Network Framework for Humanitarian Organizations in Disaster Relief: Effective Product Delivery Under Competition for Financial Funds, Anna Nagurney, Patrizia Daniele, Emilio Alvarez Flores, and Valeria Caruso.

The title of Karen Li's thesis was: Hospital Competition in Prices and Quality: A Variational Inequality Framework and she successfully defended it at the Undergraduate Research Conference on April 28, 2017. Her thesis is 100 pages. Below is a photo from the conference and defense - Professor Chaitra Gopalappa, the co-chair came, as well as many of Karen's friends and even family members!
And today we received some wonderful news: Our paper, with the same title as her thesis, was accepted for publication in the journal Operations Research for Health Care! In this paper, we construct a game theory model to capture competition among hospitals for patients for their medical procedures. The utility functions of the hospitals contain a revenue component and a component due to altruism benefit. The hospitals compete in prices charged to paying patients as well as in the quality levels of their procedures. Both prices and quality levels are subject to lower and upper bounds. We state the governing Nash equilibrium conditions and provide the variational inequality formulation. We establish existence of an equilibrium price and quality pattern and also present a Lagrange analysis of the equilibrium solutions. An algorithm is proposed and then applied to numerical examples comprising a case study focusing on four major hospitals in Massachusetts.

What I found especially gratifying in working with these exceptional students was their energy, intelligence, passion for doing good, incredible work ethic, and, frankly, "fearlessness."  We were going to solve these challenging problems, no matter what, and they permeated our dreams, obsessed us, and we did it! Perhaps it is better to have time constraints on the research in terms of a deadline in the form of graduation but, then again, you need the right students, as well as the fascinating problems. And this morning, as part of an email message from Karen, she said: "oh, how much I miss your lectures!!" Karen is the only student that I have ever had who took all the classes that I teach. Can you top the life and joy of being an academic?!