The Nobel Prize in Economic Sciences 2012 and Matching Theory
Tinaz Ekim, Bogaziçi University, Turkey
Graph Mining by Vertex Dismantlings
Bertrand Jouve, CNRS, France
Hierarchical Games for Dynamic Supply Chains with Cost Learning
Suresh P. Sethi, The University of Texas at Dallas, United States
The Nobel Prize in Economic Sciences 2012 and Matching Theory
Tinaz Ekim
Bogaziçi University
Turkey
Brief Bio
Tinaz Ekim is an associate professor in the Department of Industrial Engineering at Bogaziçi University, Turkey. She completed her Ms degree at the Université Paris Dauphine in the Computer Science and Mathematics Department. She obtained her PhD in 2006 in Operations Research from Ecole Polytechnique Fédérale de Lausanne (EPFL), supervised by Dominique de Werra. Her research focuses on Structural and Algorithmic Graph Theory, Combinatorial Optimization and Complexity Theory. She was the director of three bilateral research grants with France and Slovenia, and director of two other national research grants. She is also the recipient of the Young Scientist Award 2016 given by the Turkish Academy of Sciences. She was a Fulbright Visiting Scholar during the academic year 2017-2018 at the University of Oregon. More information available at http://www.ie.boun.edu.tr/~tinaz
Abstract
The Nobel Prize in Economic Sciences 2012 was awarded jointly to A. E. Roth and L. S. Shapley "for the theory of stable allocations and the practice of market design." The reason why it was awarded to A. E. Roth and L. S. Shapley is two-fold: their extremely valuable efforts in applying scientific findings in very important real life problems such as kidney exchange and student placement problems, and their contribution to the theory of stable matchings.
In this talk, we will present the theory of stable matchings starting from the basics such as the Gale-Shapley Algorithm, discussing more advanced topics such as manipulation and existence of stable matchings under various conditions. Two important applications, namely kidney exchange and student placement problems will be given special consideration. In the second part of the talk, the role of graph theory in stable matchings will be discussed in more depth. In particular, the links between stable matchings and the problem of finding an inclusion-wise maximal matching of minimum size will be explored. As a natural consequence of this link, the need for studying various graph classes will be emphasized.
Graph Mining by Vertex Dismantlings
Bertrand Jouve
CNRS
France
Brief Bio
Bertrand Jouve is a mathematics senior researcher at the French National Centre for Scientific Research (CNRS). His work mainly focuses on the construction of mathematical models of graph theory to be used for the analysis of large-scale interaction networks. A part of his work is interdisciplinary. After working at the frontier of neuroscience, he has been working for about fifteen years in the field of social networks. In recent years, his work was oriented towards the use of local topology properties to improve complex network models.
Bertrand Jouve was a Scientific Deputy Director for 5 years at the CNRS Institute of Social Sciences and Humanities and was President of the french National Network of Social Science and Humanity Centers until last year.
Abstract
When considering the topology of complex networks, an important question is how local topological constraints impact the overall topology of the network. This issue is addressed from a mathematical perspective by examining some particular families of graphs. For these graphs, the results of an exploration of the vertices in an order determined by the properties of their neighbourhood may lead to the conclusion that global properties exist. We review classic results and some more recent generalizations that use simplicial geometry. These families of graphs can be used as models for the construction of large networks whose topology can be controlled by local actions.
Hierarchical Games for Dynamic Supply Chains with Cost Learning
Suresh P. Sethi
The University of Texas at Dallas
United States
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Brief Bio
Suresh P. Sethiis Eugene McDermott Professor of Operations Management and Director of the Center for Intelligent Supply Networks at The University of Texas at Dallas. He has written 7 books and published over 400 research papers in the fields of manufacturing and operations management, finance and economics, marketing, and optimization theory. He teaches a course on optimal control theory/applications and organizes a seminar series on operations management topics. He initiated and developed the doctoral programs in operations management at both University of Texas at Dallas and University of Toronto. He serves on the editorial boards of several journals including Production and Operations Management and SIAM Journal on Control and Optimization. He was named a Fellow of The Royal Society of Canada in 1994. Two conferences were organized and two books edited in his honor in 2005-6. Other honors include: IEEE Fellow (2001), INFORMS Fellow (2003), AAAS Fellow (2003), POMS Fellow (2005), IITB Distinguished Alum (2008), SIAM Fellow (2009), POMS President (2012), INFORMS Fellows Selection Committee (2014-16), Alumni Achievement Award, Tepper School of Business, Carnegie Mellon University (2015).
Abstract
We consider a decentralized two-period supply chain in which a manufacturer produces a product with benefits of cost learning, and sells it through a retailer facing a price-dependent demand. The manufacturer’s second-period production cost declines linearly in the first-period production, but with a random learning rate. The manufacturer may or may not have the inventory carryover option. We formulate the resulting problems as two-period Stackelberg games and obtain their feedback equilibrium solutions explicitly. We then examine the impact of mean learning rate and learning rate variability on the pricing strategies of the channel members, on the manufacturer’s production decisions, and on the retailer’s procurement decisions. We show that as the mean learning rate or the learning rate variability increases, the traditional double marginalization problem becomes more severe, leading to greater efficiency loss in the channel. We obtain revenue sharing contracts that can coordinate the dynamic supply chain. In particular, when the manufacturer may hold inventory, we identify two major drivers for inventory carryover: market growth and learning rate variability. Finally, we demonstrate the robustness of our results by examining a model in which cost learning takes place continuously.