The field of Operations Research comprises analytical methods that can be used to aid the decision making process. This is typically accomplished by building mathematical models that represent the real system, then analyzing the models using appropriate tools - which often include using a specialized algorithm - and finally translating the solutions back into the real problem. As such, the discipline has both methodological and application components. The goal of the former is to devise new tools with solid mathematical foundation, which one can use to build new models and/or to devise new solution methods to existing models. In the application component the goal is to solve a novel practical problem, using the most suitable methodology available. Of course, oftentimes these two components intersect, for example when some application requires a new methodology to solve the problem, which in turn leads to the development of a general tool that can also be applied to other settings.
The Operations Group at Universidad Adolfo Ibañez consists of faculty from both the School of Business and the Faculty of Engineering and Sciences, thus providing an excellent avenue for collaboration across schools. All of the members of the group are very active in research. They publish regularly in peer-reviewed international journals, participate as principal investigators in sponsored research projects and present their work at the main international conferences in their areas of expertise. They work with students of all levels (undergraduate, masters, PhD) on research projects.
Methodology research conducted by the Operations Group includes work in the following areas:
Large-scale optimization: we develop decomposition methodologies for solving large-scale linear and/or integer programming such as cutting planes, lifting, and tilting. We also focus on the development of methodologies for decomposition of conical optimization problems and for "fractional programming". The emphasis is on computational methods, involving also applications of parallelism.
Optimization under uncertainty: we develop new models and theory for control of risk in stochastic optimization problems, including for example models with chance constraints or with risk measures. We also work on data-driven distributionally robust problems where distributions are not known but data are available. One component of the work is the development of efficient parallelizable algorithms for stochastic optimization problems.
Game theory: we use optimization and game theoretic tools to model traffic flows in congested networks such as in urban traffic and packet-switched networks. The models studied comprise both static equilibrium in networks as well as the adaptive dynamics of boundedly rational players in congestion games, considering also the effects of uncertainty in travel times.
Behavioral decision making: people tend to make decisions that systematically deviate from the optimal or rational solutions and the irrational choice can be influenced by the game design. In particular, we investigate how people perceive uncertain events under different game design.
Networks and combinatorial optimization: we design enumerative and dynamic programming methods for solving combinatorial optimization problems, including hybrid metaheuristics. Also studied are problems of reconstruction in networks and robust optimization problems.
The faculty in the Operations Group work in multiple areas of applications. Some of the projects are listed below:
Healthcare management: we use Operations Research tools to improve the efficiency of healthcare system and effectiveness of healthcare policy. Topics include appointment scheduling, operating room scheduling, cancer screening policy, and over-crowdedness in big hospitals in China due to unestablished healthcare assurance system, referral system, and trust issues between patients and physicians.
Natural resources: our work in this areas involves mostly the development of models and methods for large-scale strategic planning problems in mining production and forestry, including the incorporation of uncertainty in prices and in geological information (in the case of mine planning) and the modeling of spatial constraints.
Finance: we have several lines of work in this area. The first concerns the study of structured products such as Collateral Debt Obligations, where we propose models to correctly assess the risk faced by investors. The second line is on pension fund problems, including developing algorithms for life-cycle models and analyzing the use of passive investments to manage an individuals's portfolio. A third line is the use of applied optimization and machine learning techniques for finance applications such as asset management, FX strategies and family business equity management.
Transportation and logistics: Some of the work involves scheduling problems (for instance, job shop and/or project scheduling), assembly line balancing, supply chain management, transportation network design and optimization of itineraries such as in vehicle routing problems. We also work in air cargo problems, where the goal is to optimize the transportation cost subject to uncertainty in the capacities of the air plane, customer demand and show-up-rate.
Energy management: we use optimization and modelling tools to solve energy management and control problems. In particular, we use robust optimization and stochastic programming to deal with uncertainty in energy control in small grids and using renewable energy with high volatility.