We work on
the following areas:
Multioutput Cost Functions:
Transport networks can be analized through cost functions to
understand the relationship between scale, density and scope
economies. Work in this area has been able to reveal confussions
in estimates for such variables and problems with product
aggregation, allowing us to obtain key indicators as marginal
costs or the degree of scale economies rigorously.
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User's Behavior Theory and Modeling:
We are developing and testing a unified model for time
allocation decisions and trip choices. From this formulation,
analytical procedures to estimate the subjective value of travel
time are derived. The model includes a set of technological
constraints between good consumption and time assigned to
activities.
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Econometrics:
We are exploring Mixed Logit formulations with a discrete-continous
approach for transport demand forecasting.
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Transport:
Work in this area includes a) estimation of transit
optimal fares taking into account operators costs' and users'
costs; b) microscopic simulation of operations for buses and
pick-up services; and c) vehicle routing.
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Land Use and Location of Activities:
A equilibrium model for the land use market has been developed,
considering multiple agents with different preferences, able to
evaluate territorial public policies and urban interventions. The
work is currently focused on further development of the model,
including new elements and finding new solving algorithms.
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Optimization/Equilibrium Models:
Economic equilibrium is often described in terms of variational inequalities. In this area we extended the second welfare theorem to nonconvex economies with finite or infinitely many goods. This was done by proving a nonconvex version of the Hahn-Banach separation theorem, which was used to compute the subdifferential of a distance function and to establish the existence of singular multipliers in optimization. We also proved subdifferential stability for the distance function associated to prox-regular consumption and production sets. The existence of equilibrium for an extended Walrasian economic model of exchange was confirmed constructively using epi-convergence methods applied to a sequence of variational inequalities in which the agents' budget constraints are penalized. Another application is related to the urban land use equilibrium model. In a different area, we established a new foundation for truss optimization under multi-load mechanical equilibrium constraints, showing that optimal expected compliance under stochastic loading is equivalent to the dual of a special convex minimax problem which may be solved efficiently.
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Nonlinear Convex Programming:
We have introduced and analyzed new iterative minimization methods for (possibly nonsmooth) constrained optimization problems, in which discretizations of some underlying continuous dynamical systems are coupled with penalty or barrier schemes. Several approaches have been considered along this line of research. A coupling of relaxed extra-gradient proximal iterations with general classes of penalties. Steepest descent flows under a nonlinear scaling that takes into account the local curvature of the penalized objective function. Gradient flows with respect to Riemannian metrics induced by Legendre and Bregman barrier functions as continuous in time versions of variable metric proximal methods. These studies were completed by the consideration of Newton 's method on Riemannian manifolds, unifying different local convergence results such as Kantorovich's theorem, Smale's alpha-theory and Nesterov-Nemirovskii's self-concordance theory.
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Applied Combinatorics and Graph Theory:
In Graph Theory, we have been studying different classes of graphs, algorithmic aspects, computational complexity and applications of these results to real life problems with collaboration of groups of the University of Buenos Aires (Argentina) and the Federal University of Rio de Janeiro (Brazil). In Applied Combinatorics, work has been carried out in the study of the symmetries of the problems to be considered in order to develop efficient methods for the solution of integer problems.
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Forestry:
We have long been working in the application of Operations Research models to Forest Management problems, particularly developing operational models to support decisions in terms of scheduling trucks from the forest to plants or ports, machine location and short term harvesting. These systems have been implemented in Chile , Brazil , Colombia , South Africa , Uruguay and
Venezuela .
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Mining:
Members have worked with CODELCO, the largest copper firm worldwide, in planning long range mine extraction sequencing and investment in infrastructure for underground and open pit mines. Developments implemented in El Teniente caused gains in the mine worth about US$ 100 million.
Similar models were developed for CODELCO open pit mines in Northern
Chile. The challenge in this case was to integrate the operation of three large mines which share processing plants, and consider that one mine will go from open pit to underground. We also started work related to sophisticated approaches to long range planning, including spatial decision options and future uncertainty in copper prices; and in the analysis of rock instability through dynamic models for the mechanical response of the rock mass to the loads induced by the redistribution of stress in the area of subterranean excavation. These are open problems research-wise, which will require long range time frames.
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Public Services:
One important development has been a combinatorial auction procedure to support contract assignments to about 30 firms supplying meals to low income schools, with yearly savings of about US$ 40 million (15% of budgets). This work won the Developing Countries Prize for best work of the International Federation of Operational Research Societies (Edinburgh , 2002). We also worked in the project supporting the Treasury Department deciding on the best use of its resources to collect tax debts which now is in its final stages.
Members from our group participated in the development of a system for fraud detection based on data mining techniques for SUNAT, the Peruvian tax
collection authority, a pioneering experience in Latin America*. Other projects developed include location of facilities (jails and schools) and pricing telecommunication services (presently applied) for the Chilean government. These projects have involved specific use of statistics, information technology and operations research tools.
* For its business and technology accomplishments, SUNAT received an award in 2004 from the Peruvian IT community.
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Data mining:
We are developing data mining systems to better undestand
complex systems such as client behavior in the financial market,
public services and vehicle traffic. Efforts can be divided in
methological and applied research. As for methodologies, we have
developed advanced systems to select attributes, dynamic data
mining and support vector machines. Applied work focuses on
clients-keeping in banks and supermarkets, traffic analysis, and
alarm systems in the mining inudstry.
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Energy:
The research team includes economists and engineers who have
studied the strategic behavior of firms in the energy market, have
analized vertical and horizontal integration, and have developed
studies on contracts and their effect on regulated energy prices.
The area has interest in operations problems, such as stability of
power networks and optimization of hydrothermic dispatching, as
well as planning and pricing from generation to distribution.
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Industry Organization and Regulation:
We are studying economic regulation problems such as: franchising systems for infrastructure concessions, industry organization and regulation of specific industries, like ports and energy. In particular, we have explored collusion in port concessions, efficiency problems associated to power plants minimum size, competitive efficiency in social areas, and competition between congested privately-owned highways. The methodological tools we use are those of the modern theory in industrial organization.
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Marketing:
Research work is advancing in several areas:
Retail: We
are studying behavoir in the retail industry, for example, the
effect of introducing new brands in retail activities and micro-segmentation
of categories in stores.
Quality of
service and client fidelity: We are analyzing life cycle of bank
customers through Markov chains and stochastic modeling.
Data mining:
We are studying advanced methods to gather information, such as
neural networks, clustering, decission trees and support vector
machines.
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Facilities optimal location:
This research lines seeks to optimize location decisions for facilities and infrastructure in several contexts, developing better models and precedures to search for solutions in problems of important size and complexity. In logistics, a good location of warehouses, distribution centers and retail points, can reduce costs, allows offering a better service, and helps to increase the number of customers. As for emergency services, location of parkings for vehicles is crucial in terms of assuring a fast response. Models we have developed consider costs, demand estimation, system's availability and reliability, competitive environments, etc.
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Preferences models and valuation of intangible goods:
Through the estimation of different discrete choice models structures (logit, hierarchal logit, mixed logit), with linear and non linear utility functions, the objective is to investigate the influence these different specifications have on project evaluation functions (such as value of travel time or statistic value of life). It is also important to advance in experimental design and model estimation with stated or revealed preferences data, and to examine feasibility and consequences of mixing these two types of data.
As for techniques to determine willlingness to pay for environment improvement, the emphasis is on valuating local transport externalities such as accidents, air quality and noise. These external factor generated by transport have a negative impact on people's wellbeing and this loss can be estimated based on preferences surveys aimed at determining demand for given environmental attributes.
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