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
[Back to Top]
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.
 Algorithms for optimization with risk management
 Uncertainty modeling
 Applications, especially to transportation and energy.
Background: (or [Back to Top])
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 highfare paying customers by
closing lowerfare 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 "worstcase 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 2^{n}, 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.
In many situations, one desires the find the solution that gives the best
value on the average. Oftentimes, however, it is very important to measure
and control the risk of the decision
being made. There are many ways to model risk, and there has been
considerable activity in the research community to develop optimization
models that can take risk into account. One class of such models is defined
by problems where the constraints are modeled using the notion of stochastic
dominance, which conveys the preferences of an arbitrary decisionmaker who
is riskaverse. One advantage of such formulation is that it does not require
the knowledge of the decision maker’s utility function, which is a common
approach to incorporate risk management into optimization. The concepts of
stochastic dominance have been used for many years, particularly in
Economics, but recently they have been incorporated into optimization.
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. I am
particularly interested in the use of alternative sampling approaches – for
example, the socalled QuasiMonte Carlo methods – in that context. More recently I have been focusing on the
development of theory and algorithms for optimization problems with
stochastic dominance constraints. Another topic I have been working on deals,
the issue of modeling uncertainty, through the study of learning algorithms
that can be used when estimation and optimization occur simultaneously.
Finally, I work on application problems where such methods can be used, such
as in transportation and energy. I have recently developed some interest in
working on uncertainty models related to sustainability, and plan to increase
my involvement in that area in the near future.
[Back
to Top]
TEACHING
 Foundation of Operations Management (undergraduate course)
[Back
to Top]
GRANTS
 Project: "Optimization Algorithms for Problems with
Stochastic Dominance Constraints"
CoPI: 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"
CoPIs: William Cooper (University of Minnesota) and Anton Kleywegt
(Georgia Tech)
Funding source: National Science Foundation
Date: June, 2007, through June, 2010
 Project: "Improved Operations at Coyote Logistics: Solving
the Network"
CoPI: Karen Smilowitz (Northwestern)
Funding source: Coyote Logistics
Date: April, 2008, through March, 2009
 Project: "Yield Management Opportunities at Carry
Transit"
CoPIs: Mark Daskin and Karen Smilowitz (Northwestern)
Funding source: Superior Bulk Logistics
Date: January, 2007, through December, 2008
 Project: "Yield Management Opportunities at Carry
Transit"
CoPIs: 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"
CoPI: 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
[Back to Top]
UNIVERSITY
COLLABORATORS
Alexander Shapiro, Georgia
Institute of Technology (PhD advisor)
Bernardo Pagnoncelli, Universidad Adolfo Ibanez
Lijian Chen, University of Louisville
William Cooper, University of Minnesota
Mark Daskin, Northwestern University
Jian Hu, Northwestern University
Anton Kleywegt, Georgia Institute of Technology
Jane Lin, University of Illinois at Chicago
Jeff Linderoth, University of Wisconsin
Sanjay Mehrotra, Northwestern University
Marco Nie, Northwestern University
Reuven Rubinstein, Technion,
Israel
Karen Smilowitz, Northwestern University
Leilei Zhang, Iowa State University
[Back to Top]
PUBLICATIONS
Click here for a list.
[Back
to Top]
AWARDS
 INFORMS
Revenue Management and Pricing Section Prize for Best Paper (shared with
coauthors 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), 19931998.
[Back to Top]
LINKS
Societies:
Stochastic Programming pages:
Revenue Management pages:
Other sites:
PERSONAL LINKS
[Back
to Top]
