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EDUCATION
Ph.D: Industrial and Systems
Engineering, Georgia Institute of Technology, 1998
M.S.: Applied Mathematics, Georgia Institute of Technology, 1995, and University of Sao Paulo, Brazil, 1992
B.S.: Computer Science, University of Sao Paulo, Brazil, 1987
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A BRIEF STATEMENT ABOUT MY RESEARCH
My research focuses
mostly on optimization of systems when there is uncertainty involved.
It includes:
- Theory and algorithms for
stochastic optimization, particularly using sampling methods.
- Uncertainty modeling
- Applications of stochastic
optimization, especially to transportation and revenue management.
- Simulation methodology
(especially estimation of derivatives and probability of rare events in
stochastic systems).
Background: (or [Back to
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My research interests lie
in a broad area consisting of problems where the goal is to optimize a
process while taking into account underlying uncertainty (in short, optimization
under uncertainty). The presence of uncertainty arises from various
sources - e.g., future information, noisy measurements, unexpected events,
etc. Problems of such type are ubiquitous, arising in a variety of areas such
as production planning, finance, engineering design, and service logistics,
to name a few. A realistic example occurs in the airline industry, where a
company must decide which ticket classes (at different prices) will be on
sale at each point in time during the booking process. This is a difficult
problem, especially because customers who are willing to pay more (e.g.,
those traveling on business) usually do not book early. Thus, on one hand the
airline wants to reserve some seats for those high-fare paying customers by
closing lower-fare classes, but on the other hand it does not know how many
of those customers will actually book a ticket. The airline wants then to optimize
its revenue but needs to deal with the uncertainty of demand.
The uncertainties in a problem are usually modeled by random variables, with
each combination of values taken by such variables - sometimes called a
scenario - corresponding to a possible
outcome. Of course, one cannot expect to make a decision that will be optimal
regardless of the outcome; rather, it is desirable to make a decision that
optimizes some sensible performance measure. For example, the goal may be to
protect oneself against a "worst-case scenario.'' Another possibility is
to find a solution that is optimal "on the average.'' Risk - often
measured by
variance or statistical percentiles - is another common measure.
Optimization problems under uncertainty (also called stochastic
optimization problems) have been studied since the 1950's; however, it
was not until recently that computer power allowed for the solution of
realistic problems in reasonable time. Since then, many models and
corresponding solution techniques have been developed, with applications in a
variety of subjects. Despite all the advances in the area, many issues remain
to be addressed. One such issue concerns the development of numerical methods
that can be implemented to solve practical problems. In particular, the
introduction of more uncertainty factors to make the models more realistic
poses obvious computational difficulties, as the number of possible scenarios
grows. As a very simple example, consider a model with n independent
random variables, each with two possible alternatives; the total number of
scenarios is thus 2n, and so even for moderate values of n
it becomes impractical to take all possible outcomes into account. In such
cases, sampling techniques are a natural tool to be used. However,
since sampling only provides an approximation, it is necessary to study the
impact of its use and to develop optimization methods that can incorporate
sampling in an appropriate way.
Another fundamental issue concerns the representation of uncertainty itself
in the optimization problem. Many of the models found in the literature
assume that the uncertain quantities
follow some probability distributions, and solutions methods - such as the
sampling-based methods discussed above - are derived based on knowledge of
those distributions. In practice, however,
one must estimate the distributions, typically from available data. Such an
estimation procedure is oftentimes conducted simultaneously with the
optimization; that is, data are collected, a distribution is estimated, the
optimization problem is solved (and the solution is implemented), more data
are collected, and so forth. In other words, a learning procedure
takes place. This interplay between learning and optimization, however, has
not been well studied, and recent research we have conducted with
collaborators shows that some unexpected situations may arise in that
context.
The core of my research lies in the development of theory and algorithms for
optimization problems under uncertainty. Sampling and simulation techniques
play a central role in my studies, and more recently I have been focusing on
the issue of modeling uncertainty as well. At the same time, I work on
application problems where such methods can be used, such as in
transportation and revenue management.
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TEACHING
- IE 315 Stochastic Models and
Simulation
- IE 317 Discrete Event Systems
Simulation
- IE 460-1 Stochastic Models
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GRANTS
- Project: "Optimization
Algorithms for Problems with Stochastic Dominance Constraints"
Co-PI: Sanjay Mehrotra (Northwestern)
Funding source: National Science Foundation
Date: September, 2007, through August, 2010
- Project: "Model Accuracy
and Learning in Revenue Management and Dynamic Pricing"
Co-PIs: William Cooper (University of Minnesota) and Anton Kleywegt (Georgia Tech)
Funding source: National Science Foundation
Date: June, 2007, through June, 2010
- Project: "Yield
Management Opportunities at Carry Transit"
Co-PIs: Mark Daskin and Karen Smilowitz (Northwestern)
Funding source: Superior Bulk Logistics, Inc.
Date: January, 2007, through December, 2008
- Project: "Yield
Management Opportunities at Carry Transit"
Co-PIs: Mark Daskin and Karen Smilowitz (Northwestern)
Funding source: Seed Grant award, provided by the Transportation Center at Northwestern
Date: June, 2007, through September, 2007
- Project: "Stochastic
Optimization for Revenue Management"
Co-PI: William Cooper (University of Minnesota)
Funding source: National Science Foundation
Date: October, 2001, through September, 2005
- Project: "Periodic
Transportation Scheduling under Uncertainty"
Funding source: Seed Grant award, provided by The Ohio State University
Date: January, 1999, through December, 1999
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UNIVERSITY COLLABORATORS
Alexander Shapiro,
Georgia Institute of
Technology (PhD advisor)
Fabian Bustamante, Northwestern University
William Cooper, University of Minnesota
Mark Daskin, Northwestern University
Anton Kleywegt, Georgia Institute of Technology
Jeff Linderoth, University of Wisconsin
Sanjay Mehrotra, Northwestern University
Reuven Rubinstein, Technion,
Israel
Karen Smilowitz, Northwestern University
Stephen Wright, University of Wisconsin
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PUBLICATIONS
Click here
for a list.
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AWARDS
- INFORMS Revenue Management and Pricing Section Prize for Best
Paper (shared with co-authors William L. Cooper and Anton Kleywegt), 2007.
- Meritorious Service Award, awarded by
the journal Operations Research, 2005.
- Meritorious Service Award, awarded by
the journal Operations Research, 2004.
- Winner of the 1998 George Nicholson Student Paper Competition
(organized by INFORMS).
- Outstanding Ph.D. student award, Georgia Institute of Technology,
1998.
- Doctoral scholarship from CNPq
(Brazilian government science agency), 1993-1998.
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LINKS
Societies:
Stochastic
Programming pages:
Revenue Management pages:
Other
sites:
PERSONAL LINKS
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