Tito Homem-de-Mello
Professor

School of Business

Universidad Adolfo Ibanez

 

Email: tito.hmello <at> uai <dot> cl

 

AREAS OF INTEREST

  • Optimization under uncertainty
  • Risk management
  • Stochastic models in transportation and energy

Education

RESEARCH

TEACHING

GRANTS

Collaborators

Publications

awards

links

FULL CV

 

 

 

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.
  • 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 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.

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 decision-maker who is risk-averse. 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 so-called Quasi-Monte 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.

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TEACHING

  • Foundation of Operations Management (undergraduate course)

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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: "Improved Operations at Coyote Logistics: Solving the Network"
    Co-PI: Karen Smilowitz (Northwestern)
    Funding source: Coyote Logistics
    Date: April, 2008, through March, 2009

  • Project: "Yield Management Opportunities at Carry Transit"
    Co-PIs: Mark Daskin and Karen Smilowitz (Northwestern)
    Funding source: Superior Bulk Logistics
    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)
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

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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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