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My current research interests revolve around the development and applications of optimization and economic models for service operations and organizations. In addition, I have continuing interests in complementarity theory. In particular, I am interested in:
Below are a sample of my current research projects.
I am currently a co-principal investigator on a project to study the concept of customer efficiency: the process of aligning operations to enhance the ability of customers to serve themselves. This work is supported by the National Science Foundation, the Marketing Science Institute as well as the Wharton e-Business Initiative.
The goals of this project are:
In order to accomplish these goals, we have undertaken a very large study of customer behavior in retail banking, including detailed data on customers across various delivery channels and across several firms.
My collaborators and Ph.D. on this project include:
Computable equilibrium models play a vital role in the analysis of economic and physical systems, such as general equilibrium models and complementarity models of frictional contacts. However, we must be intellectually honest when undertaking a computational equilibrium study. Simply setting parameters to their mean and computing a solution can lead to very misleading or simply incorrect solutions. Most of these parameters are drawn from some distribution or generated via expert opinion. Given the practical importance attached to the results of computable equilibrium models, it is crucial that algorithms generate meaningful numerical results beyond simple point predictions.
The standard approach to overcome the above mentioned problems with computable equilibrium models subject to data uncertainty is to undertake a Monte Carlo simulation study. Unfortunately, these analyses are currently prohibitive in terms of their computational complexity. The purpose of the research proposed herein is to overcome these computational problems in order to make such analyses feasible and accessible to scholars and analysts.
In order to arrive at a practical tool for the analysis of stochastic equilibrium models, a three year project is proposed to develop, implement and test a solution methodology for stochastic variational inequalities, a very general framework for equilibrium modelling. By "solution", we mean the distribution of the equilibria for a model subject to uncertainty in the problem data. The proposed tasks will lead to the development of a state-of-the-art solution method for the deterministic variational inequality problem coupled with a major extension to traditional Monte Carlo simulation methods to exploit the analytical gradients that are available through the use of sensivitity/ perturbation analysis for this class of problems. These two analytical tools will then be combined in a very efficient simulation system to compute mean values for the solution variables and/or other measures of interest. The end result will be a state-of-the-art stochastic variational inequality system that will be implemented as a GAMS solver for use by the wider academic and industrial/ government community. Several new applications will be used to test and illustrate this new methodology.
